Kathy Dopp | 23 Apr 21:24 2015

United Kingdom: Does 'vote swapping' work? | BBC




Kathy Dopp
Town of Colonie, NY 12304
 "A Christian who does not protect creation . . . is a Christian who
does not care about the work of God." Pope Francis

Fundamentals of Verifiable Elections

View my working papers on my SSRN:
Election-Methods mailing list - see http://electorama.com/em for list info

C.Benham | 13 Apr 20:10 2015

"non-cyclic" pairwise loss?

The Electowiki  page on Heitzig's  River method includes:

River can be interpreted as a Minmax method, Minmax(non-cyclic pairwise loss) or MMNCPL. It is similar to Minmax(winning votes) except that River elects the candidate whose greatest non-cyclic pairwise loss to another candidate is least. As in Ranked Pairs, the greatest pairwise loss (GPL) of each candidate is considered in order from largest (among all candidates) to smallest and locked. If a candidate's GPL is cyclic, it is discarded, and the next-greatest pairwise loss of that candidate is added to the list. When the non-cyclic greatest pairwise losses of (N-1) candidates have been locked, the remaining candidate is the winner.


What is the clear and simple definition of a  "cyclic" pairwise loss?  

If all the candidates are in the Smith set, aren't  *all* the pairwise losses (at least in some sense)  "cyclic"?

Chris Benham
Election-Methods mailing list - see http://electorama.com/em for list info
steve bosworth | 8 Apr 10:20 2015

17) APR: Steve's 17th dialogue with Richard Fobes

(17) APR: Steve's 17th dialogue with Richard Fobes (Steve)

> Date: Sat, 4 Apr 2015 12:01:59 -0700
> 1. Re: (16) APR: Steve's short 16th dialogue with Richard Fobes
> (Steve) (Richard Fobes)

> From: Richard Fobes <ElectionMethods <at> VoteFair.org>
> To: "election-methods <at> lists.electorama.com"
> <election-methods <at> lists.electorama.com>

R:  Steve, in your latest message (copied below) you asked several questions for which you want a yes or no answer, but your introductory wording includes the word "not," which results in questions that are double negatives. Plus, some of your questions are worded as if they are a single question, yet actually they are multiple questions. …


S:  Sorry for these ambiguities.  However, now that I have read your book, I will try to answer all the questions that I had in mind in the way that I think you would have done if I my questions had been free of these ambiguities.  Please correct me if any of these answers do not reflect an understanding of your VoteFair popularity ranking method: 

 1a) VoteFair popularity ranking could elect California’s legislative assembly by all of its citizens in one day (i.e. one day for the primaries and one day for the general election).

1b) However, even theoretically it could not do this by giving each citizen the opportunity to rank as few or as many candidates in the whole state as she might wish.  It only gives each citizen in a given electoral district the opportunity to rank all the candidates seeking to be the one elected for that district. In doing so, VoteFair ranking has the advantage over all other single-winner systems in that it guarantees that the one elected will have been preferred by more voters than any of the other candidates for that district.
2) At the same time, unlike APR, VoteFair ranking cannot allow each elector to guarantee that her one vote will continue to count in the assembly through the elected candidate (i.e. rep) she ranked most highly.  APR allows this but no electoral system (including APR) could guarantee that her rep will always vote exactly as she might wish. I only claim that APR allows each citizen to guarantee that her one vote will be add to the weighted vote in the assembly of the rep she most trusts to vote as she wishes (e.g. the one congressperson among the 435 she believes is the most like to vote in the House as she wishes).  APR seems to have this representational advantage over the rep(s) elected by VoteFair or by any other method.
3) Also, unlike APR, VoteFair rankings cannot allow each of its reps to have a weighted vote in the assembly exactly equal to the number of electors throughout California who had similarly ranked him most highly.
4) Given a suitable US constitutional amendment, unlike APR, VoteFair ranking could not allow such a voting system to elect all 435 congresspersons in one day, i.e. each citizen in the country also being allowed to rank candidates in states other than the one in which they reside.

R: Here are my answers:

 VoteFair Ranking takes place during one day for the primary election, and another (separate) day for the general election.
> When you read my book, pay close attention to the election that Arnold
> Schwarzenegger won to become governor of California. That was a special
> election that did not have a primary. As a result, there were more than
> 100 candidates on the ballot competing in a single race for governor.
> This demonstrates the essential role of primary elections.
> One of the weaknesses of your APR method is that it does not (yet)
> accommodate primary elections. I recommend that you modify your method
> to include them.


S: Please recall our 10th dialogue in which you welcomed my simple description of how APR would work.  This description included an explain of how APR’s primary would allow each citizen to determine through which ‘association’ she will later rank as few or as many candidates in the whole state (or country) in the general election.  At the same time, I believe we agreed that the number of candidates would be limited to those who had either submitted enough signatures of support to the central electoral commission, or had submitted an appropriate, returnable money deposit.  Thus, there would appear to be no need for an additional primary to reduce the number of candidates for an APR general election.  Also, I see APR’s primary as a way of recruiting the most attractive candidates for the election of a state’s (or the country’s) legislative assembly.  At the same time, APR’s way of counting votes easily copes with the rankings of many candidates.

However, for the election of a governor (or major, or president), I entire agree with you that VoteFair popularity ranking is the best system.


R:  You again asked about wasted votes (although without using that term).  For VoteFair Ranking, the worst-case scenario can produce up to 49 percent wasted votes.
For comparison, your APR method can produce up to 90 percent wasted votes.

> Of course both methods can achieve zero percent wasted votes in the
> best-case scenarios.
> For VoteFair Ranking, the typical real-world range of wasted votes would
> be about between 30 percent and 15 percent. This is an estimate.
> For your APR method, the typical real-world range of wasted votes would
> be about between 30 percent and 10 percent. This too is an estimate.

S: I need you to explain the process by which you arrived at these percentages.  I accept that an APR citizen can choose not to guarantee that her vote will be added to the weighted vote of her most favoured rep, e.g. when none of the candidates ranked by a citizen are elected, she can tick the relevant box on the ballot so as to prevent her first choice but eliminated candidate to transfer her one vote to the rep most favoured by that eliminated candidate.  However, I know of no way for us to say that any particular percent of electors will do this.  My claim is only that each APR citizen has the opportunity to guarantee that her vote will continue to count for one in the assembly as described above.  What makes you think this is not the case?

R:  Regarding another question you have, if VoteFair Ranking were used to
> elect representatives in the state of California, a voter would only
> choose among candidates running in their district, yet a vote for a
> non-winning candidate still influences the results in two or three
> additional ways -- which you will read about in my book.


S: I understand this but this probable “influence” would seem not to be nearly as motivating to a citizen as APR’s offer to guarantee that her vote will mathematically count for one within the weighted vote of her most favoured rep.


What do you think?
> ………………………………
> > Steve


Election-Methods mailing list - see http://electorama.com/em for list info
Alexander Praetorius | 28 Mar 20:42 2015

Fwd: Question about "Voting System"

---------- Forwarded message ----------
From: Alexander Praetorius <citizen <at> serapath.de>
Date: Fri, Mar 27, 2015 at 1:18 PM
Subject: Re: [EM] Question about "Voting System"
To: Kristofer Munsterhjelm <km_elmet <at> t-online.de>
Cc: Alexander Praetorius <citizen <at> serapath.de>

Thank you for your suggestion.
I like the winsorized more than the clipped version.
I don't get your argument for the "median", everything you showed was related to "mean".

1. The method successfully prevents huge jumps, so a voter, switching from -8 to 100 or -8 to 1 million makes the same difference and only introduces a jump, if a person that was right next to the "winsorized cutoff point" (or how you call it) had an extreme vote, which is pretty rare because there are a lot of voters.

2. Every voter can change his vote at any given period, but a period might last just "1 minute", so people will react to such a problem pretty fast.

If the "innermost votes" are not very close to each other, the "median" always introduces jumps, while the "mean" makes transitions way more fluid.

I kind of like the idea of having a percentile like the "lower or upper 36% of votes", because voters switching their mind can change the A and B that define the interval.
A=-5, B=5

  • [x1, x2, x3, -5, -4, 0, 4, 5, x4, x5, x6], so someone switching his mind inside the interval, just changes the mean.
  • x1, x2, x3 can get into the interval by having a less extreme opinion than before.
  • x4, x5, x6 can do the same from the other side of the spectrum.
I'm not convinced that the "median" would be the better method. I like the median with the possibility for having A and B move and winsorizing extreme values a lot.
The only thing that I'd like to see is the 36% of votes thing set to something more dynamic, thus, if there were only "honest voters", it should count every vote (100%),
but if voters start to vote strategically, people (voters) should be able to set 0% to a bigger value, to cut off strategic votes.

The result would be, that strategic voters now have to ally up with like minded and ally up in voting strategically, to make the last vote that's still in the intervall a HIGH ONE, thus -5 way smaller or 5 way bigger (in above example).

I think it is hard to get a lot of allies to support an extreme policy.
So imagine the interval that counted above was ..., -4, 0, -4, ...., that means more than 40% of voters would need to have an extreme policy, without the 40% of voters that oppose their oppinion the most not doing something similar in the other extreme direction.

So I just wonder, what kind of method could be used to enable the population to set the  "winsorized cutoff point" dynamically :-)
Basically, it is about people's trust in their fellow voters and whether they believe they vote honest or not.
The more they distrust, the higher they would set the cutoff point, the more relaxed they are in believing their fellow voters to express their honest, but maybe extreme opinion, the more they would maybe allow for a low cutoff point.

Given: [x1, x2, x3, -5, -4, 0, 4, 5, x4, x5, x6], which has a mean of "0"

Now if voter that votes for "0" changes his mind and votes for "10", that would result in
 [x1, x2, x3, -5, -4, 4, 5, 10, x4, x5, x6], which has a mean of "15".
So it gives those people on the border of the interval a lot of power, because they decide the value of all the extreme votes outside the interval. So if someone there becomes an extreme voter, but is still inside the interval, he has a lot of power... but people might decrease trust and put him out of the interval.

If this continues to happen, even though the "cutoff point" is already high, people should start discussing the issues of extreme voters, which would never be a need with "clipping", because they can just ignore it then. It's even more extreme with median, where a big minority has no chance, e.g. [5, 4, 3, 3, 0, 2, 36, 38, 45, 46, 50] ... so the result is still "2", even though its obvious that something is not ok here and its not just extreme voters.

So the "winsorized" method with a method to adapt A and B based on trust (however that might work), would enable the majority to cut off EXTREMISTS by increasing the "cutoff point" (e.g. from 0% of votes to 36% of votes, but if they want to just ignore people, it doesnt work, because the person that is close to the interval, once convinced that extremists are NOT just mad or strategic, could adapt his vote to some thing very high or very low (depending on his opinion) and get all the cutoff people as votes with a similar value as him.

The majority can now decide to accept that and discuss the problem or increase the "cutoff point" further to get rid of another "maniac".


On Fri, Mar 27, 2015 at 11:28 AM, Kristofer Munsterhjelm <km_elmet <at> t-online.de> wrote:
On 03/09/2015 10:33 PM, Alexander Praetorius wrote:
I am not sure if i reall ask for whatever zou ean bz "continuous
election", but from what you write, i for sure might ask for it compared
to the other option you give me, which would be a "candidate election".

To express it again in my words. There are "a lot of voters" who can
each vote on a "number" in the interval of ]-oo,+oo[ and they can change
their vote in every "tick", where each "tick" might be a few nanoseconds
after the former tick.
The "result" of each "tick" is calculated from all the numbers voted on
in each "tick".
The "result" will be a number in the interval of [-B, A], where the
numbers B and A are calculated from the "overall picture of votes" in
each tick, maybe also taking into account former "ticks".

I'm searching for a method that calculates a mean, where extreme votes
w>A or w<-B are counted with the value of A or B respectively.
If a voter does NOT CHANGE his vote in the next "tick" it will be
counted with the value of the former "tick". (Think of a "tick" as a
"micro period of a few nanoseconds")

If a vote w>A is casted and a future "tick" changes the value of A, the
value with which this vote w>A will be counted will adapt to the new A.
Only if the new A will make w <= A, then w will NOT be affected by A,
because it is well within the current Interval of [-B,A]

That does seem like what I'm calling a continuous election. It could be discrete (if you want an integer result), but in that case, it would be easy to convert to it by rounding.

The setting you give, where extreme votes are disregarded or clipped, seems to be close to robust statistics: you want to find out some value or estimate (in your case, of the wishes of the voters) without having extreme ("outlier") votes affect the result too much. The statistical perspective makes no assumptions on what the voters may decide to do, as long as the votes are extreme. So methods taken from robust statistics should resist extreme-value strategy as long as not too many employ the strategy.

The two most common approaches to deal with extreme values are trimming and Winsorizing; and of these, trimming is most common. For both of these, your A and B limits come from the number that the lowest or highest x percentile voted, for some x. This lets one adjust sensitivity of the method against resilience to strategy (I'll get back to the implications of that). Both of them also reduce to methods equivalent to the median when you set x to the highest level possible.

So in both methods, you have an A and B. Say A is the lower of the two, i.e. the lower limit. Then if you use trimming, that will throw away every vote with a rating less than A or greater than B. That doesn't mean that these are not taken into account. If someone votes just below the current A, and then two others come along and votes a very low value, then because A is based on the percentile (x% from the bottom), it will shift and the first voter's vote will then be counted.

As an example, consider the votes [-10, -8, -5, 3, 6, 7, 10] and suppose that A and B are set to the value of the lower and upper 36% of the votes. This turns out to be the third from either end, so the trimmed mean throws away the two most extreme votes on either end, while the Winsorized method clips their values to A and B.

As it stands, the trimmed mean is the mean of [-5, 3, 6] = 1.33, and the Winsorized mean is the mean of [-5, -5, -5, 3, 6, 6, 6] = 0.86. Now suppose two voters introduce the extreme value of 1000 each. I've set the 36% value so that this still is equivalent to removing the two extremes on either end, even after adding two votes.

After the voters have done so, the full vote list is [-10, -8, -5, 3, 6, 7, 10, 1000, 1000]. The trimmed mean is the mean of [-5, -3, 6, 7, 10] = 3, and the Winsorized mean is the mean of [-5, -5, -5, 3, 6, 7, 10, 10, 10] = 3.44.

Note that in the trimmed case, the 1000-votes were never directly altered the mean. However, they had an indirect effect by shifting the window so that the votes with rating 10 were now included. If more people contributed, voting for, say, 5 and 6, then the rating of 10 might again be pushed back behind the curtain, as it were.


You've mentioned that one of the things you find problematic with median and trimmed/Winsorized methods is that they might lead to sudden changes. Consider an example like:

[-100 -100 -50 50 100 200].

The median might swing to -100 to 100 if either of these gain a majority, and this swing, you say, might be too extreme for the voters.

But there's an unavoidable tradeoff here. The method itself can't know if

[-100 -100 -50 50 100 200]

means that there are six honest voters and their real consensus is 16.7 (the total mean here), or if it means that there are two honest voters and four strategizing extreme voters, and the most extreme voter on the + side just happened to write down a larger number than his counterpart on the - side.

If it is the former, then the method should take all the votes into account. If it is the latter, then it should modify the extreme votes so the strategy does not pay off. And if it is the latter, then it should be as unaffected by those extreme votes as possible. In other words, it has to have a sudden change because it treats the example above as [-50 50] and any ordinary voting system using the mean will have a rather sudden change when you add, say a 100 to a list of (-50, 50).

Hence, the more the method ignores extreme values, the more it is prone to shift when additional ballots show that something that used to be considered extreme no longer should be. Winsorized methods are a little softer in that regard, but you can still contrive settings where the jump is rather dramatic, e.g.

[-10^9 -10^9 -1 0 0 1 10^9 10^9]

where the limit is set so that the one-billion votes are clipped to -1 and 1 respectively. Add enough 10^9 votes on the right side and the method will suddenly shift from 1 to something greater than a million.


Finally, I'd like to answer your Winsorizing question, and then argue in favor of the median:

This goes in the right direction.
But: What if current votes would be [-100, -99,
-10,-10,-10,-8,7,10,10,10,99,100] or in a more extreme version
[-10,-10,-10,-10,-10,-8,7,10,10,10,10,10] ?

    What could be the "mean" in those two examples?

How would that be affected, if the voter who chooses his vote to be
weight w=-8 to switch to 100?

Let's take the first one first. That is,
[-100, -99, -10,-10,-10,-8,7,10,10,10,99,100].

And let's set A and B to the third from each end, in this case 10 and -10.

Then the Winsorized mean is the mean of
[-10, -10, -10,-10,-10,-8,7,10,10,10,10, 10] = -0.0833 as above. Note that 99 and 100 were clipped to 10, and -99 and -100 were clipped to -10.

Now, suppose the -8 voter altered his vote to 100. Now the full thing is
[-100, -99, -10,-10,-10,7,10,10,10,99,100,100]. The votes at third from each end are -10 and 99 respectively, so the Winsorized mean is the mean of
[-10, -10, -10,-10,-10,7,10,10,10,99,99,99]

which is 23.67. If the -8-voter altered his vote to a million, the Winsorized mean would still be 23.67.

This might be what you desired, but suppose that the 99 vote was also strategic. Then you'd want to have a less sensitive method, e.g. one that sets A and B to the fourth from each end. If you did that, you'd get:

Winsorized mean first time around:
[-10, -10, -10,-10,-10,-8,7,10,10,10,10, 10] = -0.0833
Full thing after -8 becomes 100:
[-100, -99, -10,-10,-10,7,10,10,10,99,100,100], so A and B are -10 and 10 respectively, and the modified list is
[-10, -10, -10,-10,-10,7,10,10,10,10, 10]
which gives a Winsorized mean of 1.417.

Here you can see that the further towards the center you set the barriers, the more it takes to change the value. Yet, since these are all responsive to the people, it's obvious that with enough added votes, the result *will* change. That's true for the median as well.

And just for completion's sake, I'll do the other one as well.

Take the third from each end as A and B to give A = -10, B = 10, so the Winsorized mean is here the exact same thing as the ordinary mean, namely -0.0833.

Now suppose the -8 voter switches to 100:

Again A and B are -10 and 10 respectively, so the mean is the mean of
[-10,-10,-10,-10,-10,7,10,10,10,10,10,10] = 1.417. It would have been so even if the -8-voter switched to a million.

(Do note that as the number of votes increase, the A and B spots will change from being "third from each end". But here we're dealing with the same number of votes every time, so I've mentioned the cutoff in terms of list index rather than percentile for simplicity's sake.)


The median is an extension of majority rule in this way: suppose you're deciding on something like a tax rate. If you pick something that's greater than the median, at least a majority would prefer a lower rate. If you pick something that is less than the median, at least a majority wouldn't mind paying more.

So if you want majority rule, where one man has one vote, i.e. that all those who desire a lower rate than what you proposed pull equally hard, and all those who desire a higher rate than what you proposed pull equally hard in the other direction, then median is the way to go.

If you want to incorporate the strength of preference and depart from majority rule - e.g. if someone who desires a rate of 0% should pull harder than someone who desires a rate of 10% if your proposal is 20%, then the above is no longer applicable. But strategy means that you might not be able to trust the voters' expressions: they might pick a more extreme number just to pull more strongly. Thus you get into the strategy concern above: the more attention you pay to strength, the more vulnerable your method is to extreme positions. So there is a balance, and that is particularly true when you don't set any limits on the numbers that may be submitted as votes.

Everything I have written above is my personal experience/opinion on things, no matter what kinds of words i did use
(e.g. "always", "never", "impossible", "waste of time", ....).
Such extreme words only do indicate, that my experience/opinion on something is very strong and i currently cannot imagine that there are other possibilities until new arguments/insights/whatever open my eyes that there are alternative perspectives too :-)
Please do not feel discouraged to challenge my opinion if you have a different one.

Best Regards / Mit freundlichen Grüßen
Alexander Praetorius
Bornemannstrasse 17
D - 60599 Frankfurt am Main
[skype] alexander.praetorius

Everything I have written above is my personal experience/opinion on things, no matter what kinds of words i did use
(e.g. "always", "never", "impossible", "waste of time", ....).
Such extreme words only do indicate, that my experience/opinion on something is very strong and i currently cannot imagine that there are other possibilities until new arguments/insights/whatever open my eyes that there are alternative perspectives too :-)
Please do not feel discouraged to challenge my opinion if you have a different one.

Best Regards / Mit freundlichen Grüßen
Alexander Praetorius
Bornemannstrasse 17
D - 60599 Frankfurt am Main
[skype] alexander.praetorius
Election-Methods mailing list - see http://electorama.com/em for list info
Kristofer Munsterhjelm | 27 Mar 14:16 2015

Reduction for rated multiwinner methods

Some time ago, I mentioned a Bucklinesque weighted multiwinner method I 
devised based on a CS problem reduction. For that method, the problem I 
reduced from was the uncapacitated facility location problem:

Given a number of facilities and a number of customers as well as 
distances between each customer and facility, pick k facilities so that 
the sum of distances from each customer to his closest facility is 

(The classical facility location problem also permits an opening cost to 
be applied to each facility. That's not really important for the voting 
reduction unless you'd like to find the optimal number of seats, not 
just the allocation of candidates to seats.)

The voting reduction is simple: the customers are voters, the facilities 
are candidates, and the distance between a voter and a facility is some 
constant minus the rating of the candidate by the voter. Then minimizing 
the sum of distances from each customer to his closest facility is 
equivalent to maximizing the sum of ratings between voters and their 
most preferred candidates.

The actual uncapacitated facility location problem is NP-hard (and the 
decision problem is NP-complete) but there are reasonable polytime 
approximation schemes for them. So I chose one that didn't seem too 
incomprehensible while still having a reasonable approximation factor, 
and got the Bucklinesque method.


After doing all that, I thought I should write a post about what other 
reductions might be possible, but I kind of got distracted with other 
things. I think part of the reason I didn't write anything was from 
thinking that I would have to explain in detail.

But very simply, these are the reductions I have found so far. Too bad 
that the polytime approximation schemes I've seen so far are extremely 
complex. The polytime approximation schemes for capacitated (unweighted) 
systems are particularly hairy. Still, it might give others ideas how to 
devise polytime multiwinner methods.

For weighted multiwinner methods that generalize Range: uncapacitated 
facility location or k-median[1].

For unweighted multiwinner methods (STV-likes) that generalize Range: 
uniform capacitated facility location or k-median[2].

For weighted multiwinner methods that generalize MJ: k-center or 
k-supplier with outliers[3].

For unweighted multiwinner methods that generalize MJ: uniform 
capacitated k-center or k-supplier with outliers[4].


Sometimes the term "k-median" is used for a problem where all voters are 
candidates and sometimes not. "k-center" is usually used to denote a 
problem where all voters are candidates, and "k-supplier" the equivalent 
when not all voters are candidates or all candidates are voters.

General capacitated problems are like their uncapacitated counterparts, 
except that no facility may have more than a certain number of 
customers. I think this can be used to make quota-obeying multiwinner 
methods: consider what happens if you set each constraint so that the 
facility can't have more than a Droop quota's worth of voters. Then the 
pigeonhole principle should keep facilities from having too few voters too.

k-supplier seeks to minimize the maximum distance instead of the sum of 
distances - or, in voter terms, to maximize how satisfied the least 
satisfied voter is. By itself, this is very susceptible to extreme 
votes, so the MJ reduction is to permit the method to disregard a 
fraction of the voters as outliers. Let that be just short of a Droop 
quota and you get median in the single-winner case.

Uncapacitated k-supplier has an interestingly simple polytime 
approximation algorithm that is reminiscent of the "pick the winner with 
greatest approvals, then the winner with greatest approvals of those 
that didn't approve of the first winner" approach. See [3], "Robust 
clustering for arbitrary metrics". It seems rather tricky to massage the 
algorithm into reducing properly to MJ, though: its approximations don't 
always yield median winners in the single-winner case unless one 
optimizes for a certain parameter, and I don't see how to do so in the 
general case.


Party list methods can either be based on soft capacitated methods 
(which directly gives the number of seats for each party) or by rounding 
the results from uncapacitated methods (like applying Webster to the 
result of the Bucklinesque algorithm). I would expect the former to be 
slightly better all other things equal, since it can move around votes 
to contribute the most to getting a party a seat. That is, the weighted 
vote version sees in principle no difference from raising a candidate's 
weight from 0.1 to 0.2 and raising it from 0.45 to 0.55, although in 
some situations, the latter may give an extra seat after the rounding 
where the former would not. However, the polytime approximations usually 
have worse ratios for soft capacitated than for uncapacitated problems, 
so the theoretical improvement might be lost.

The reductions could also be used to make integer programs for the 
voting methods. These may take a long time to solve, but IP solvers are 
pretty good nowadays. The IP equivalent of uncapacitated k-median / FLP 
is Monroe's method, so that approach doesn't lead to anything new there, 
but it could be used to construct the MJ-like methods. The main problem 
with this idea is that it would seem fairly incomprehensible to the 
voters: you input ballot data and run a solver and it opaquely 
calculates an assignment.


[1] e.g. http://web.stanford.edu/~yyye/myz-final.pdf or 

[2] e.g. http://www.or.uni-bonn.de/~vygen/files/tokyo.pdf

[3] e.g. https://www.cs.princeton.edu/~moses/papers/faclocn-outliers.ps

[4] e.g. http://students.mimuw.edu.pl/~kociumaka/files/stacs2014_draft
Election-Methods mailing list - see http://electorama.com/em for list info

steve bosworth | 26 Mar 18:05 2015

(16) APR: Steve's short 16th dialogue with Richard Fobes (Steve)

(16) APR: Steve's short 16th dialogue with Richard Fobes (Steve)


> From: election-methods-request <at> lists.electorama.com
From: ElectionMethods <at> VoteFair.org

> Subject: Election-Methods Digest, Vol 129, Issue 12
> To: election-methods <at> lists.electorama.com
> Date: Mon, 23 Mar 2015 09:14:18 -0700

To Richard and others,


I have just now downloaded your “Ending the Hidden ...” book.  Consequently, I think it would be more efficient if I plan to reply to the most recent additions you have made to our 15th dialogue only after reading this book. 


Still, please help me focus my careful study of your book by saying if you believe it should make it clear to me why you agree or disagree with each one of my following current understandings of your FairVote counting system.  You may want simply to say “yes”when you see one of the following understandings is correct, and “no” when you do not.  It would not even be theoretically possible for FairVoting:

1)      to elect California’s legislative assembly by all of its citizens in one day, i.e. with each citizen having the opportunity to rank as few or as many candidates in the whole state as she might wish (yes/no);

2)      to allow each elector to guarantee that her one vote will continue to count in the assembly through the elected candidate (i.e. rep) she ranked most highly (yes/no);

3)      to allow each of these reps to have a weighted vote exactly equal to the number of electors throughout California who had similarly ranked him most highly (yes/no); and,

4)       given a suitable US constitutional amendment, also to allow such a voting system to elect all 435 congresspersons, i.e. each citizen also being allowed to rank candidates in states other than the one in which she resides (yes/no).


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Jameson Quinn | 23 Mar 17:13 2015

20 theses on Condorcet, FBC, and SODA

So imagine I nailed this to the Electorama cathedral door:

1. Any good voting system is somewhere on the continuum between Condorcet and FBC criteria.

I consider this pretty much axiomatic. Thus, IRV and Plurality are not "good" in this sense, but pretty much any Condorcet or evaluative system, or any hybrid thereof, is.

2. The Condorcet criterion is worthwhile because it is saying that if all voters are honest, they get the same result as if all voters are strategic, insofar as that's possible.

In other words: the main way a sane voting system can have a strong Nash equilibrium (so that "the result if all voters are strategic" is well-defined) is if the Nash outcome is the Condorcet winner.

3. Thus, the CC reduces the cognitive burden on voters who are "risk averse" and/or who "trust democracy", that is, on those who find the CW to have a higher utility than the expected result of strategy (which is the probability-weighted average of the winners under strategy).

If candidates are ABC on a 1D spectrum, and B is the CW, then A voters might strategize by burying B. This would pay off if A wins, and backfire if C wins. So if their utility for B is "above average", that is, closer to their utility for A than to their utility for C, they're unlikely to want to risk it. This is in a sense "trusting democracy"; they'd rather compromise than roll the dice. In that case, the CC is telling them they don't have to bother considering the strategic possibilities.

4. The FBC directly reduces the cognitive burden on voters.

That's what it's about.

5. In a Condorcet system, burial is a strategy for creating dishonest Condorcet cycles, while betrayal is a strategy for breaking (honest or dishonest) Condorcet cycles.

6. Honest Condorcet cycles are unlikely in practice. 

Not impossible, but <<10% of the time marginally, and <<50% of the time even if polls suggest they might happen.

7. Successful burial strategy is unlikely in practice. 

Not impossible, but <<10% of the time, and <<50% of the time even if conditions are favorable.

8. Betrayal strategy has some cost.

It is clearly less expressive, and in many cases it will have some risk of backfiring.

9. Therefore, betrayal will very very rarely be strategic in practice in a Condorcet system. 

Low expected payoff, non-zero expected cost.

10. Therefore, if you care about FBC, you shouldn't be to harsh on Condorcet systems.

11. However, burial is a real issue in Condorcet systems.

12. On the other hand, FBC systems have a "corresponding" issue with the chicken dilemma.

13. I think that chicken dilemma scenarios with an FBC system are more likely than burial ones with Condorcet. 

Though CD could, in theory, be an issue under a Condorcet system, I don't think it's likely in practice. It would have to involve either massive truncation by all three factions, or burial; and as far as I can see, the burial scenarios just don't work with any of the commonly-advocated Condorcet cycle-breaking rules.

14. SODA is, among other things, an attempt to "square the circle" of FBC and Condorcet.

Remember, SODA splits the process into three stages (predeclaration, voting, and allocation), with the candidates acting in stages 1 and 3 and the voters acting in stage 2.

15. SODA passes Condorcet if you assume that candidates are honest in phase 1 and strategic in phase 3.

16. SODA does not pass FBC, even under the assumptions above.

It's easy to make a standard 3-candidate cycle and see that the least-satisfied voters have an incentive to betray.

17. However, SODA is robust to cycles created by burial in stage 1.

In stage 3, the honest CW can just "call the bluff" of the burying candidate.

18. You can patch SODA to make FBC failures even more unlikely, under an honest Condorcet cycle.

The patch involves letting weak candidates drop out after the ballots are counted.

19. Even with the patch, SODA doesn't meet FBC. But failures would be utterly implausible.

I am quite confident of this point, having played with scenarios a lot. Still, I'd haven't figured out a rigorous way of putting this, and I'd really like to.

20. SODA "solves" the chicken dilemma, in that laziness by the non-CD faction defuses the dilemma between the two CD factions, leading to a strong non-CD Nash equilibrium.


I realize that some of the "theses" above are not obvious, and that I'm skimping a bit on the discussions/demonstrations/arguments. Believe me when I say that I've done my homework on this. I'd be happy to expand on any of it if asked.

I still believe that Approval, not SODA, is the Schelling point for practical reform. But if I were the Voting Czar, I'd implement SODA (and, correspondingly, PAL for multi-winner).

Also, note that the above theses are NOT focused on the main arguments in favor of SODA, but rather the tricky points which took me a lot of head-scratching to work out.

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steve bosworth | 20 Mar 10:10 2015

APR (19): Steve's 19th dialogue with Toby (Steve)


APR (19): Steve's 19th dialogue with Toby (Steve)


> From: election-methods-request <at> lists.electorama.com
> Subject: Election-Methods Digest, Vol 129, Issue 9
> To: election-methods <at> lists.electorama.com
> Date: Sun, 15 Mar 2015 12:01:20 -0700
 Re: APR (18): Steve's 18th dialogue with Toby (Steve)
> (Toby Pereira)
> Steve (and everyone)

To Toby and others:


My most recents responses are tagged with *S:


*S:  Thank you for recalling your 4/12/14 post to me. I see now that I did not sufficiently appreciate the degree of importance you attached to the issue raise by your response to my claim quoted starting with the next paragraph. Therefore, I propose to concentrate on this issue in this dialogue because I think it may be the at the bottom of our most important current disagreement, namely, the question of whether the “good legislation” which we both want would be more likely to emerge from a House of Commons elected by APR or by score voting.  My argument that APR would seem to be more efficient in this regard is summed up in the 4th “Additionally” paragraph below as follows:  An APR House, as “composed of such able, different, well informed, clashing, and focused reps would seem to provide an optimal debating and negotiating chamber for the production of creative, evidence based solutions to common problems.”  Let’s try to resolve our differences over this issue before turning later to any other important differences.

S: APR, more than other systems, would seem to assist the development of a much closer identity between each elector and his representative, i.e. a more intense personal, ideological and mutual bond. This would seem to contrast, on average, with the more defuse and vague relations between the agendas of each elector and the representatives elected by other systems (i.e. including score voting).

*T: I'm not sure this bond is such a good thing.   I think politicians should want to appeal to as many people as possible, by using good arguments …

*S: Yes.

*T: …. rather than just appealing to the people that have voted for them by appeasing them.  

*S:  For the reasons I will explain below, I believe that an MP elected by APR would be less likely to be able to be successful by simply “appeasing” electors (i.e. by telling them what they want to hear but ignoring them in practice).  No, the APR “bond” I have in mind between an MP and his electors is less likely to be servile because it would be entirely voluntary, i.e. given the many other seemingly similar candidates to which they could give their vote (ranking) instead.  Their bond is more likely to be based on the similarity between his and their ideological positions.  If so, they would be more likely to hold him to account if they later observed that his behaviour conflicts with their claimed common ideology.


*T: …This is another reason to prefer a system that looks at a voter's ratings of all candidates rather than them having just one MP that they've helped elect.


*S:  No, because APR allows each citizen to guarantee that the focus of his whole vote will be on the MP whose scale of values is closest to his.  He will expect that MP to speak, work, and vote to promote their common agenda.  This will make it more likely that each MP will be motivated to put the best possible case for this agenda.  This should help to raise the level of the debate in the House and prompt more rational decisions to be made.  This motivation and these expectations should also help his MP to defend this agenda against threats, and to work to form the necessary compromises with somewhat opposing fellow MPs in order to achieve the highest possible measure of these objectives, e.g. by helping to form and to become a part of a working majority coalition in the Commons.  My rationale for expecting this productive activity is more fully explained below by something I wrote when also proposing that APR be used to elect the US House of Representatives:


APR: Finding Common Ground and Forming a Working Majority Coalition

With regard to finding common ground and forming a working majority in the assembly with ideologically different congresspersons, paradoxically, the advantage that each APR member of the House is likely to have is that she knows that she has been elected by citizens who expect and trust her to work and vote to promote their common scale of values. As elaborated below, this ideological bond between each citizen and his rep would seem to provide the human resources that would enable enough of the congresspersons to engage in the kind of productive debates and negotiations in the House to form a majority coalition to help solve the real problems facing the country.

Of course, in the last instance, this advantage would be enhanced during APR’s general election when each citizen guarantees that his vote will be added to the ‘weighted vote’ in the Commons of his most favoured representative (or the one most favoured by his first choice but eliminated candidate).  However, a foundation for the growth of this advantage would have been provided earlier by the way APR recruits its candidates.

Firstly, APR’s primary election discovers the voluntary organizations in the country that are most trusted by its citizens. It then politically energizes these organizations by recognizing them as the official electoral ‘associations’ through which all citizens will later elect their own congressperson.  This recognition, in turn, should stimulate more attractive candidates to seek to represent both one of these association and the citizens with whom they have an ideological bond.  In contrast to other electoral systems (including score voting), APR’s later election of the most favoured of these better candidates would seem also to combine to raise the average quality of representation in the assembly even further both for citizens and these associations.


1)      The growth of these closer bonds between citizens and their representatives would seem to be assisted by another element of the “bottom-up” primary election itself.  It asks citizens to start to familiarize themselves with the existing members, officials, and other potential candidates of their preferred organizations months before each voter has to finalize his ranking of candidates during the general election.  If so, the average breadth and depth of knowledge so acquired by voters to rank individual candidates would also seem to be more than is generally acquired by citizens using other electoral systems.

2)      The average closer bond between each citizen using APR and his rep would also seem to grow partly as a result of the time between APR’s two elections.  These months would allow each association, its candidates and its registered voters to coordinate their thinking and planning about how best to run their common campaign in the coming general election.

3)      Because an APR congressperson would be more clearly expected to work and vote to promote the scale of values she shares with her largely homogeneous electorate, she would seem to be both more able and likely to negotiate solutions to common problems together with fellow but ideologically different congresspersons.  This is because each APR rep would probably enjoy more trust from her electorate.  Consequently, each member’s explanation of why she and her electorate should support a given compromise solution to a common problem is more likely to be accepted by this electorate.  While no one may see the compromise as being perfect, each congressperson and her electorate is more likely to accept that it at least provides net benefits for each ideologically different sponsor and his electorate.  A trusting voter is more likely to believe his own congressperson’s claim that a given compromise is necessary.

4)      This closer bond between each rep and her electorate would also seem to make each congressperson’s work in the assembly more focused and known to be backed by his association and his electors. This greater clarity and focus would seem to help each APR to present the strongest possible case for his legislative proposals to the other members of the House.  Consequently, an assembly composed of such able, different, well informed, clashing, and focused reps would seem to provide an optimal debating and negotiating chamber for the production of creative, evidence based solutions to common problems. Consequently, the wisdom of any decisions resulting from this deliberative process is also likely to be aided by the simple fact that it would take place in an assembly whose composition most accurately reflects the real variety and intensity of the concerns of all citizens.

5)      The extra ability with which APR reps would seem to be able to negotiate compromises, would also seem to make it more likely that APR congresspersons would respond to the imperative to form a working majority in the assembly. Without such a majority coalition, any wise legislative solutions to problems that such rational deliberations might have discovered could not be passed into law.  Each APR rep is more likely to see that if she is not part of the majority that will shape the assembly’s binding decisions, her own agenda, and that of her electorate, will not be advanced.

6)      In a parliamentary system, the formation of such a coalition also has the advantage that the assembly can ensure that the government (the executive organ of the state) will be led by a chief executive (prime minister) who can be most trusted to apply the laws as expected by the assembly.

In summary, it is because APR is more likely to produce, on average, a closer ideological fit between each citizen and his congressperson that APR is more likely to help solve the real problems facing the country.  They are more likely to do this because of the greater expectation on the part of their different electorates that progress must actually be made with respect to the goals of each of the ideological different electorates who elected them. To do this, compromises must be made and a working majority coalition must be formed.  The likelihood of this happening contrasts with the gridlock that is frequently produced by the more defuse, vague, and often conflicting agendas held by the congresspersons and their electors using existing systems.

*S:  The same virtues of each congressperson being elected by an ideologically homogeneous electorate are also convincingly supported by Sol Erdman’s evidence based proposal that Congress be elected by Personal Accountability Representation (PAR, i.e. APR with a “primary” and the associations it discovers) [see: solerdman <at> igc.org; http://www.solerdman.org/;http://www.solerdman.org/content/about-cure.html; https://www.youtube.com/watch?v=XwOlfXFcWk8].


He believes that a higher quality of representation would result from an electoral system that would allow representatives to be elected by relatively homogeneous ideological groupings of citizens. He contrasts this with that quality of representation typically found among US congresspersons as currently elected. He sees the latter as having an incentive to ignore possible solutions to society’s problems. This is largely because of the many conflicting scales of values held by the voters living in each congressperson’s existing electoral district. Consequently, any solution each candidate or rep might propose is likely to be strenuously opposed by a key section of each congressperson’s electorate. Therefore, to be re-elected, it is saver, instead, for existing congresspersons (or candidates) simply to paint the other party’s candidate’s ideas as even more dangerous. This is a recipe for inaction and “gridlock”. As a result, Sol Erdman convincingly argues that the more focused and trusted reps who are more likely to be elected by a system like APR’s would more successfully negotiate with their opponents to produce solutions to the real problems that would be agreed by a working majority in an APR assembly.


What do you think?



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steve bosworth | 17 Mar 15:19 2015

(15) APR: Steve's 15th dialogue with Richard Fobes (Steve)

(15) APR: Steve's 15th dialogue with Richard Fobes (Steve)

> Date: Sat, 14 Mar 2015 11:56:29 -0700
> From: ElectionMethods <at> VoteFair.org
> To: election-methods <at> lists.electorama.com
> CC: stevebosworth <at> hotmail.com
> Subject: Re: (14) APR: Steve's 14th dialogue with Richard Fobes (Steve)

To Richard and others:

R:  Steve, your questions seem to be based on comparing your APR method with
> voting methods you already know about, yet you don't seem to be familiar
> with the diverse possibilities for "proportional" methods.


S:  If you (or any other participants in this forum) know of any proportional methods which rival the advantages of APR, please explain how they are superior.  At the same time, my draft article which more fully explains APR does compare APR with earlier versions of STV (e.g. Hare, Meek) as its use in Ireland, Australia, Scotland, and the UK for EU elections; party-list (with and without preference candidate options, e.g. also see my earlier EM dialogues with Juho); Germany’s mixed system; and France’s double round system.  If I have not sent this article to you, I would be very happy to do so.


You may also be interested in my many EM dialogues with Toby about approval and score voting.

R: Of course the "proportional" method I recommend is VoteFair Ranking,
> which I've described in my book titled "Ending the Hidden Unfairness in
> U.S. Elections."

So, at this point I recommend that you read my book about VoteFair
> Ranking -- "Ending The Hidden Unfairness In U.S. Elections." It
> includes examples and lots of illustrations. I priced it as low as
> current conditions allow (three U.S. dollars) and a significant portion
> of that amount pays for the download fee. (I tried to offer the book
> for free, but that effort was not successful.)


S:  As I understand VoteFair Ranking from your various web pages, of course I see how it would be a great improvement on the single-winner elections currently used in the US for electing congresspersons.  However, I do not yet see how it could be practically used for a multi-winner system to elect all 435 at the same time.  Also, unlike APR, it seems that it could not guarantee that each citizen’s vote will be added to the weighted vote in the House of the one congressperson in the whole country she favours most (or is most favoured by her 1st choice but eliminated candidate).  This is what APR’s version of STV would seem to do practically and most efficiently.


Have I misunderstood VoteFair Ranking in this regard?  Could it be used to elect 435 winners countrywide?  Would there be no wasted votes?


In any case, I would be happy to download your book.  Please send me the details of how I can do this.

R:  There are other "proportional" methods. I'm using quotation marks
> around the word because I'm using it here in a broad sense, rather than
> in any of its more specific meanings.

S:  APR is “proportional” in the exact sense that it gives weighted votes to each rep exactly equal to the number of citizens who have ranked (voted for) him or her, i.e. the percentage of the citizens who favour the scale of values held by a given rep is exactly equal to the percentage (“proportion”) of all the weighted votes in the House.  Similarly, each political party or ‘association’ would be represented proportionately.  Consequently, no citizen’s vote need be wasted in that it will always help elect her most favoured congressperson. 

R: … Your APR method is competing with these and other proportional voting
> methods. Your APR method is not just competing with single-winner
> methods such as approval voting and score voting. I thought I had
> previously made this clear, but your recent questions indicate that you
> are not aware of other "proportional" methods …


S: Please, which of my questions mistakenly “indicated” this?


R: … beyond the one by Sol Erdman (which I was not aware of).


S: By now, you may already be aware that Sol Erdman also believes that a higher quality of representation would result from an electoral system that would allow representatives to be elected by relatively homogeneous ideological groupings of citizens.  He contrasts this with that quality of representation typically found among US congresspersons as currently elected.  He sees the latter as having an incentive to ignore possible solutions to society’s problems. This is largely because of the many conflicting scales of values held by the voters living in each congressperson’s existing electoral district.  Consequently, any solution each candidate or rep might propose is likely to be strenuously opposed by a key section of each congressperson’s electorate.  Therefore, to be re-elected, it is saver, instead, for existing congresspersons (or candidates) simply to paint the other party’s candidate’s ideas as even more dangerous.  This is a recipe for inaction and “gridlock”.   As a result, Sol Erdman convincingly argues that the more focused and trusted reps who are more likely to be elected by a system like APR’s would more successfully negotiate with their opponents to produce solutions to the real problems that would be agreed by a working majority in an APR assembly [see: solerdman <at> igc.org;  http://www.solerdman.org/; http://www.solerdman.org/content/about-cure.html; https://www.youtube.com/watch?v=XwOlfXFcWk8].

R:  You ask the question "what would be lost by trying [APR]?" The answer
> is: reduced suffering.
> Lots of people are suffering unnecessarily because of the world's
> current use of voting methods that are so primitive that the results are
> easily corrupted through unfair tactics, such as financially supporting
> vote-splitting candidates.
> The longer it takes to implement effective reforms, the more that
> suffering will continue.

S:  We totally agree about this “suffering”, but perhaps you are not yet convinced that APR has the potential to reduce this suffering more than any other known electoral system.

R: … The biggest campaign contributors would, if necessary, happily "try"
> your method or any other method that they thought might be vulnerable to
> corruption. This is why I pointed out which tactics would be effective
> against your APR method.


S:  Yes, they would “try”, but you have not yet explained to me why APR would be more vulnerable to such corruption than the system you favour most.  Please explain.  Would you like me repeat the arguments that suggest that APR would be less vulnerable?
> ……………………
> (As an historic perspective, European nations adopted "closed-list"
> forms of PR (proportional representation) rather than the fairer
> "open-list" forms because they knew that election results would be
> easier to control.)

S:  Yes.

R:  As an example of "trying" an election reform, here in the United States
> a voting method called "top two runoff" is being tried by a few states.
> Predictably it is failing in the ways that election-method experts
> predicted. (It fails because it continues to use single-mark ballots
> instead of adopting better ballots and better counting methods.) The
> people in power are willing to allow reformers to "try" these reforms,
> but they oppose reforms that would actually be effective. The result of
> ineffective "trying" is a long delay before real election reforms occur.

S:  Yes.

R:  Your APR method uses a better ballot, but it uses a counting method that
> is based on the same flaw as the "top two runoff" method, namely it
> assumes that the candidate with the fewest first-choice votes is the
> least popular. This is the same mistake that is made by the counting
> method used in instant-runoff voting (IRV).


S:  Yes, you are correct if you are saying that APR might not always elect the 435 reps

1)      who together have received the most preference rankings of any degree, or

2)      each of the 435 candidates who received a larger number and highest possible average ranking from all the many millions of voters in the country, as contrasted to those received by all the other candidates.

However, even if it were practically possible to count the millions of rankings to discover (1), i.e.  “the 435 who had received the most preference rankings of any degree”; this would seem to be less satisfying to citizens than APR’s discovery of the one rep for each citizen who had received that citizen’s highest ranking.  It is by that easily identified and favoured rep that that citizen is most likely to feel best represented.


If, on the other hand, a practical count could elect (2), theoretically, that would be better than APR, i.e. except that the counting process required would be much more complicated to carryout, let alone be understood by most citizens. 


However, given the above numbers of reps, voters, and rankings, I assume this latter complicated count could not be made with current resources and given the time it would take to compete.  The very complicated and time consuming counting method I have in mind her is the one provided by Tideman and Richardson: Comparison of Pairs of Outcome (CPO), a very sophisticated method for implementing STV.


What do you think?


R:  If you want to "try" your method, I suggest that the next step is for
> you to get help implementing it in software. That (or doing it
> ourselves) is what some of us have done to "try" our recommended voting
> methods.
> When I wrote VoteFair Ranking software I discovered the need to refine
> details that were not evident based on having only described counting
> "rules."
> Until you have "tried" your voting method as software that is used in
> real (non-governmental) situations, the credibility for your method is
> limited.


S: You may be right, but given the simplicity of APR’s counting procedure, have you already seen any particular difficulty in using it?, or even “implementing it by using software”?

R:  Shifting to another topic in our discussion, you say that my
> understanding of the situation in Cyprus (based on what I read in
> Wikipedia) is outdated, but you did not state why you think your APR
> method would work better than any other method (which must include
> proportional methods).


S: If you would like me to, I would be happy to email to you a copy of a short piece that I have written about how APR might be used in a future Cyprus.
> ………………………………………..
> Richard Fobes


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steve bosworth | 9 Mar 10:38 2015

(14) APR: Steve's 14th dialogue with Richard Fobes (Steve)

(14) APR: Steve's 14th dialogue with Richard Fobes (Steve)


To Richard and others,


Again, thank you for your feedback,


Initially, of course, I am most interested in receiving your views on my responses to your most resent replies.


However, if you can find the time, I would also like to receive your responses to the remaining points I made in dialogue 13.


Thank you,






> Date: Fri, 27 Feb 2015 11:26:34 -0800
> From: ElectionMethods <at> VoteFair.org
> To: election-methods <at> lists.electorama.com
> CC: stevebosworth <at> hotmail.com
> Subject: Re: (13) APR: Steve's 13th dialogue with Richard Fobes



R: Regarding the island of Cyprus, from what I learned by reading about it
> in Wikipedia, the dominant conflict is between residents who want the
> island to be administered by Greece and residents who want the island to
> be administered by Turkey.

S: What you report is not really relevant to Cyprus after 1974. This description was more true of the 1950s.  In 1963 to 1974 the Greek Cypriots, aided by Greece, destroyed the 1960 partnership federation between the 2 communities by trying to ethnically cleans 20% of the Cyprus population, i.e. the Turkish Cypriots.  By 1974 the Turkish Cypriots had been forced to relocate to about 3% of the island, having owned about 30% in 1960.  In 1974, a fascist coup among the Greek Cypriots, with the support of the Military Junta in Greece, violently tried to complete the ethnic cleansing.  That is when Turkey finally acted upon its 1960 treaty obligation to protect the TCs within the 1960 partnership federation.  It did this by making the North territorially safe for the TCs.  In this context, the TCs established their independent Turkish Republic of Northern Cyprus in 1983.  Unfortunately, ever since, the rest of the world has largely ignored the injustices inflicted upon the TCs, as well as the 1960 treaty obligation that the UK, Greece, and Turkey had, separately or jointly, to guarantee the 1960 partnership Republic, e.g. no state other than Turkey recognizes the TRNC.


R: This kind of "us versus them" conflict is much simpler than the
> conflicts among the residents of California.
> ……………………..
> The situation in California is much more complex. Here are some sample
> issues that dominate the politics of California:
> * Water. Who gets it? Farmers? Ranchers? Cities? Which cities?
> Rural areas? Etc.
> *Money. Who gets it? Business owners? Hard-working employees? Which
> businesses get more? Does the money go to rural areas or cities? Which
> cities benefit more? Etc.
> *Religion. This conflict has multiple sub-conflicts including abortion,
> animal rights, marijuana use, lottery/gambling, gay-and lesbian rights, etc.
> As a specific example, let's suppose that a voter is a lesbian,
> animal-rights activist who lives in the region within California called
> "the State of Jefferson, which is the less-populated region well north
> of San Francisco and Sacramento, and by some reckoning even north of
> Redding. Her interests would conflict with a neighbor who is a farmer
> or rancher who sells to agribusiness customers. Yet she would not vote
> for a politician from an animal-rights and gay/lesbian-rights group
> based in Los Angeles – because that conflicts with the issue of
> far-northern Californians paying taxes and yet getting fewer
> state-funded services, and because the group in Los Angeles would favor
> sending water from Northern California to Southern California, and
> because Los Angeles has lots of corruption that she would not want to
> help support. In a similar way she would not be well represented by
> such an organization in another large city (within California).

S:  Yes, some lesbians in ”Jefferson” might be as you imagine, but others might want to join a lesbian friendly association that is also appreciative of the need to send water to LA, etc.  The use of APR would test the extent to which this is true, e.g. test the extent to which some citizens’ values are not geographically defined.

R:  You would probably say that she and similar voters in her region should
> create an "association," but a political group of gay/lesbian-rights and
> animal-rights folks in far-northern California would not be able to
> raise even $15,000 …


S: Perhaps and perhaps not.  Perhaps there are enough such like minded people in the whole of California to establish a relevant association.  APR would discover whether or not.


R: …  to get listed on your APR ballot. Plus such voters would be harassed locally if they became vocal as a group.

S: APR does not require anyone to be locally “vocal”.

R:   Are you beginning to understand why your APR method would not work well in California? There are too many issues dividing the state into too many combinations of political interests.

> The complexity of political issues throughout the United States is even
> more dramatic.

S:  Why are you so sure that APR would not provide an efficient process by which more of these “issues” could be proportionately represented and resolved?  What would be lost by trying?
R:   You might assume that similar-minded voters would band together to
> create what you call associations, but similar-minded voters in one part
> of the nation have only some limited overlapping similarities with
> voters in another part of the nation.


S:  Yes, but there also may be enough other “overlapping similarities” countrywide so that some important interests would be proportionately represented in and APR Congress that are currently ignored.
R:   Of course your APR method initially would increase the voice that each
> person has in terms of feeling represented by their favourite
> association. However, as soon as the biggest campaign contributors
> learn the new political landscape, those contributions would be
> channelled to the associations that get the most votes in U.S. Congress.


R: The point is that your method is vulnerable to corruption.

S:  You seem to be offering a counsel of despair.  Why do you not accept my earlier suggestions that the primary and associational element of APR would seem both to make it less “vulnerable to corruption”, and to provide an extra degree of electoral independents for citizens from the power of big money, celebrity, and the mass media?
R:  For reasons I've already explained, the results would be similar to what
> we have now, …


S: Given my above suggestion and the fact that APR would enable citizens to help elect much more attractive candidates (from their point of view) than are available to them under the existing system, I do not see how we could be at all confident that “the results would be similar to what we have now”.  Do you not think that most citizens would prefer to be able to guarantee that their vote will be added to the weighted vote of the rep in the whole assembly they most trust?  All the other so-called “fair voting methods” I have studied cannot guarantee this benefit, e.g. approval voting, score voting.  Do you know of one that does?

Endnote 6 of my article, in effect, also endorses "liquid democracy".  However, it argues that it should have only an advisory function regarding the finalization of legislation by the APR elected legislative assembly.  This alone guarantees that each member of the majority that has made a given law will be known, and thus able to be held to account.


Also, are you familiar with the evidence that Sol Erdman sees as supporting the argument that if each rep is elected by like minded citizens, these reps will be more easily held to account by them, as well be able to negotiate workable compromises with their opponents?  His Personal Accountability Representation (PAR) is like APR in this respect.

> …………………………….
R:  Again I'll say that your APR method might be suitable for use in some
> situations. It gives voters the ability to bypass knowingly corrupt
> organizations, which is a useful advantage.
> ………………………………….

> Richard Fobes
> On 2/24/2015 8:21 AM, steve bosworth wrote:
> > Subject: (13) APR: Steve's 13th dialogue with Richard Fobes
> >
> > To Richard and all others,
> >
> >> Date: Fri, 20 Feb 2015 11:13:36 -0800
> >> From: ElectionMethods <at> VoteFair.org
> >> To: election-methods <at> lists.electorama.com
> >> CC: stevebosworth <at> hotmail.com
> >> Subject: Re: (12) APR: Steve's 12th dialogue with Richard Fobes
> >>
> > R: Which nation do you live in?
> >
> > S:I was born and raised in Michigan, got my B.A. from the U. of Mich.,
> > taught Ghanain high school students for 2 years while in the U.S. Peace
> > Corps, received my Ph.D. from the U. of London (L.S.E.), taught
> > political philosophy for many years at the University of Portsmouth (
> > UK), and have taught comparative politics and political ideologies in 2
> > universities in the Turkish Republic of Northern Cyprus for many years.
> >>
> > R: Perhaps the answer to this question will help me understand why you do
> >> not understand the concept of each nation wanting to follow laws that
> >> are different from the laws in neighboring nations.
> >
> > S:Perhaps both of us would define a “nation” as a group of people who
> > want to live together and to have some degree of sovereignty because of
> > their shared values. If so, let me assure you that I do understand that
> > different nations want to follow somewhat different laws, e.g. Ireland,
> > Scotland, Wales, England, France, Germany, Turkey, Greece, Turkish
> > Cypriots, Greek Cypriots, etc.
> >
> > However, I do not yet understand why you do not see that APR would allow
> > these different desires to be most accurately expressed in the laws that
> > could be adopted by each nation.  In fact, I have just recently written a
> > suggestion of how APR might assist the 2 ethnic communities in Cyprus to
> > establish a better federation than the 1960 partnership one that the
> > Greek Cypriots destroyed in 1963-4, i.e. a new federation in which APR
> > would enable different laws to be adopted in the north and in the south
> > of the island, as well as the set of the joint adoption federal laws
> > that would apply to all the people living on the island.
> >
> > Similarly, I see that APR could make the decisions made both by the EU
> > (a confederation) and by the US (a federation) more democratic. It would
> > maximally help their central authorities and their respective member
> > “states” to make their different laws more proportionately to reflect
> > the actual range of values held by their different populations.
> >>
> > R: Rhode Island is small enough to be politically homogeneous (about the
> >> same throughout the state). In contrast, people in geographically
> >> different parts of California want to follow laws that are different
> >> from the laws in other parts of that state/nation.
> >
> > S: Again, please try to explain why you seem to think APR would not
> > efficiently allow both “homogeneity” and diversity to be reflected
> > exactly in the legislation of any province, “state”, nation, unitary
> > state, confederation, or federal state to the extent either or both
> > happened to exist within its population.
> >
> >
> > R:  Please pop the bubble on your fantasy of thinking that your APR method
> >> might be suitable for use in the European Union or the United States --
> >> which are both federations in which there is only a limited degree of
> >> cooperation among their separate nations/states.
> >
> > S: Is this “fantasy” as you see it, only my seeming expectation that APR
> > might be adopted by any “state” or federation in the near future, or,
> > rather, my thought that APR would be rationally the most democratic
> > electoral system if it were ever put into practice?  I see the first
> > suggestion for me as being probably correct because it certainly is
> > possible that human inertia might be so powerful, apathy so great,
> > traditionalism so strong, or the selfishness and skill of the current
> > power elite so great that APR will never be accepted.  However, I do not
> > yet see why the 2nd suggestion should be dismissed as mere
> > fantasy.  Please explain.
> >
> > S:  Of course, if you can find the time after responding to the above, I
> > would also very much look forward to receiving your thoughts about the
> > remaining questions I posed in the course of our 12th dialogue.
> >>
> >> Richard Fobes


Election-Methods mailing list - see http://electorama.com/em for list info
steve bosworth | 5 Mar 15:29 2015

APR (18): Steve's 18th dialogue with Toby (Steve)

APR (18): Steve's 18th dialogue with Toby (Steve)

Date: Wed, 25 Feb 2015 22:27:24 +0000
From: tdp201b <at> yahoo.co.uk
To: stevebosworth <at> hotmail.com; election-methods <at> lists.electorama.com
Subject: Re: APR (17): Steve's 17th dialogue with Toby (Steve)

To Toby and everyone:


Thank you for being willing further to explain your current understandings. I think they have allowed our dialogue to make progress, i.e. to avoid “circles”.  After combining some of your recent words with your earlier sentences, I think I may have finally grasped what you mean by “full proportionality”, i.e. what you want an electoral system to offer.  Consequently, the core of my responses today are in my first posts (located between the two +++++++++++ lines below).


Perhaps you will discover that you only need to respond to this post because you may see the remaining posts below the second ++++++++++line as only repeating or elaborating upon the elements in this post.


I’ve also tagged our previous posts with XT: and XS:, and our newest posts with T: and S:


I look forward to your thoughts.






1S: When re-reading your various sentences listed below, perhaps now I understand what you see as “full proportionality”.  Correct me if I am mistaken, your ideal electoral system would provide each citizen with exactly equal voting power in the Commons, i.e. the total voting power that each citizen would have through the votes of the MPs who represent her would be equal to the total voting power of each other citizen.  For you, this calculation for each citizen would include all the votes or parts of votes in the Commons of the MP or MPs who have a similar scale of values to her own.  You like score voting because the scores given to any number of candidates by each citizen determine the degree to which she sees the scale of vales of each of the candidates she has scored as according with her own. Consequently, a voting citizen’s total voting power in the Commons is calculated by adding together the contribution her scores have made to every MP she has helped to elect.  Each such contribution marks the extent to which each citizen believes that she will be represented by each MP she has help to elect.  At the same time, however, you already accept that score voting cannot completely offer this “full“ proportionality. In fact, I will argue later that this full proportionality is neither possible nor desirable.


However, the above calculations would at least offer a measurement of the extent to which the total voting power of each voting citizen in the Commons approximates or deviates from the mean.  You believe that the result of an election is better to the extent that the deviations it produces from the mean are as small as possible.  You also accept that some citizens’ scores may fail to help elect any MP and so they would have no voting power in the Commons.  This failure might even continue as a result of this citizen’s top scored but eliminated candidate being delegated by her to passing on another copy of his pre-declared scores to other candidates on her behalf.  This contrasts with APR’s guarantee that each voting citizen’s vote will be added to the weighted vote in the Commons of her most trusted MP.


Your criticism of APR is twofold:

1)     With APR, only one of the rankings of candidates by each citizen can count when electing the official MP for each citizen, i.e. all her other rankings have no effect upon which other candidates will be eliminated or elected, i.e. APR has no electoral use for these other rankings.  This is in contrast to the possibility of many of the scores given by a score voter to many candidates can sometime help to elect more than one MP who will represent her.

2)     In addition to APR’s guaranteeing that one favoured official MP will be elected for each citizen (say, Citizen Smith), APR allows other citizens to elect a number of other MPs, each MP officially to represent each of them.  When, by chance, a number of these other MPs share the scale of values held by Citizen Smith, she will effectively but unofficially represented also by the combined weighted vote of this number of MPs.  She will be represented by many more weighted votes in the Commons than some other citizens.  You object to this chance inequality because it reduces the  so-called “full proportionality” that you want.. (Please see paragraphs 20, 21, 22, 39, 40, 41, 69-72, 81 and 82 below.)


However, the truth is that every one-person-one-vote electoral system must and should allow for this kind of inequality to be recognized.    It is the purpose of elections to discover and give more political power to larger groups of like minded citizens.  Each person’s power is appropriately increased the more she can cooperate with others.  Each weighed vote within a majority coalition has more power than each weighted vote held by MPs not a member of this coalition can actually make laws and elect the state’s chief executive in a parliamentary system.  When necessary, the majority rules the minority. This is democracy.  What do you think?




2XT: … Full proportionality is achieved if every voter has representation of c/v. …


3T:  We're going round in circles here. As has been made clear, APR does not guarantee full proportionality in any meaningful sense. …


4S:  Please explain what you mean here by “full proportionality in a meaningful sense”.  Above and previously I have understood that it is secured for you only when each citizen’s voting power in the Commons is the same.  I still do not understand that even though APR satisfies this test completely, it still does not satisfy you.  Perhaps this is why we may have gone “around in circles”.  Please explain.


5T: … APR only guarantees that each voter will be assigned a candidate.


6S:  Every APR voter is not “assigned to” an MP but directly or indirectly chooses her most trusted MP.  Even if this MP was her lowest preference candidate, he still is the best MP for her because all her higher preference candidates were eliminated.  They were eliminated because not enough other citizens ranked them.  He is her “best possible” MP, given the unavoidable constraints provided by the current distribution of preferences held by the voting population.  It is this “practical best MP” that APR offers to each citizen.  Unlike APR, score voting cannot guarantee this benefit.


No electoral system (including APR or score voting) could or should guarantee that each citizen’s top ranked (or top scored) candidate will be elected.




6XS: >Please explain the extra benefits you see in score voting which makes you prefer it to APR, i.e. even when APR:


>1) avoids violating the principle of one-person-one-vote,

7T: Addressed above. The score voting system does not violate one person one vote any more than APR. Under both systems, some voters will be better represented than others, but this disparity is more likely to happen under APR because of the fact that it allows chance extra representation that isn't measured.


8S: Rather than saying it “isn’t measured”, I think it would be better to say that an APR voter’s rankings below the one that is added to the weighted vote of her favoured official MP do not affect the election or elimination of any other candidate.  However, it would be possible for researches, after the election, to analyse all the rankings given by any citizen in order to calculate the extent to which she is also represented unofficially by other MPs, i.e. candidates that were also given one of these lower rankings by this citizen.  In this way, her “chance extra representation could be measured”.  In this way, these other ranking would not be ignored, even though they would still not affect which candidates are elected.  What do you think?

9XS: >2) uses voting and counting methods which are much simpler for ordinary people to understand, and

10T:  Ranking is not simpler than scoring, …


11S:  Correct.


12T: … even if the actual counting process is still a bit simpler under APR.


13S:  Please also see post 49S:

14XS:  >3) enables each citizen to guarantee that their one vote will be added to the weighted vote of her most favoured MP (or the MP most favoured by the eliminate candidate she most favoured).

15T:  It might be their 300th favourite candidate. This might be unlikely, but the same applies for someone's vote not counting in score voting as long as they score enough candidates, or delegate to their favourite candidate.


16S:  Please also see post 20S:




17T:  I want to summarise the key points here: First of all, we seem to be going round in circles somewhat. Some of the points I have made several times and go on being missed by you. I think this conversation is beginning to reach the point where it may have run its course. But to clarify two things:

1. You seem to think that APR is perfectly proportional because every voter has added an equal amount of power into the Commons. However, some voters are able to add weight to more preferred candidates than others. …


18S:  Correct me if I am mistaken:  you mean that while each APR voter only can add 1 vote to her official MP’s weighted vote, she may only have the option of giving this 1 vote to her least favoured but still favoured candidate.  I agree that this remains a possibility for citizens using APR.  An APR voter can only add her vote to a candidate who has also been ranked by enough other citizens so he can be elected, i.e. in the end she is only “able to add weight to” a candidate who is also “preferred” by “more” citizens (i.e. enough to elect him).


On the other hand, your words might suggest that an APR voter is able to add her vote to the weighed vote of more than one MP?  This is not the case.


19T: … Some voters would not get any of their top few elected and would only be adding weight to candidates they don't really like. …


20S:  No, an APR voter rationally would only rank candidates she likes.  If none of these candidates is elected, her top choice but failed candidate would automatically give her one vote to the weighted vote of the MP highest on his pre-declared preference list.  If she did not like the candidates on his list, she could tick the relevant box on her ballot to cancels this way of passing on her vote to an MP.  Still, if she did not like his list, why would she have ranked him first?  Alternatively, any APR voter could instead adopt the following strategy probably to guarantee that her vote will continue to support her scale of values in the Commons:  she could rank one or more very popular candidates last (ones that are safely predicted to be elected), e.g. the leader of the party she most favours.


Also, you may recall that APR’s primary enables each voter to help guarantee that there will be attractive candidate available for her to rank in the later general election, i.e. by ranking the applicant voluntary organizations with which she identifies so she can channel her vote in the general election through one of the candidates seeking to represent the “association” which she sees as promoting the scale of values closest to her own.


In contrast to score voting, not only would APR guarantee that each citizen’s vote can count for one in the Commons, this primary and associational feature of APR seems to make it almost certain that each voter will also be represented by an official MP she likes.


21T: … This is no better than some votes not affecting the result, which might [also] happen in score voting. But you simply define it to be fully proportional and think that that somehow settles the matter. But [APR] voters do not have equality despite your claims.

2. APR ignores representation from MPs that aren't a voter's official representative, unlike the score system I have described. Because of this, the actual representation that voters receive under APR has a much higher chance element than in the score voting system. This is objectively true


22S: The “chance element” here in both APR and score voting is determined by the number of other citizens (unknown in advance) who happen to rank or score the candidates in a similar way when compared to the rankings or scorings of any one citizen we might choose to study.  The difference is that APR’s counting of these rankings guarantees that each citizens will continue officially to count only for one in the Commons, while a score voter can only be assured that the scores she has given to candidates will help to elect only those candidates (i.e. perhaps none or many) who have also received enough scores by chance from enough other citizens. 


This means that she might not help any candidate to be elected and thus her vote will not continue to count at all in the Commons.  At the same time, if her scores for candidates do help to elect one or more MPs, her continued total official voting power in the Commons will be more or less than equivalent to one vote. It is in this respect that score voting violate the principle of one-person-one-vote.


Admittedly, unlike the counting of scores, the counting of the rankings that an APR citizen has recorded on her ballot do nothing to help that citizen to be ideologically represented in the Commons by any MPs in addition to her own official one.  Any such extra but unofficial representation would only result by chance, i.e. by enough other citizens happening to rank ideologically similar candidates to make them their own official MPs (and her unofficial reps).



In contrast to APR, score voting enables a citizen to try to help all the candidates she likes to be elected.  However, her success or failure in this regard is left entirely to chance, i.e. it depends on enough other citizens scoring the candidates in a similar way.  However, APR still has the advantage over score voting in guaranteeing that each citizen will have a continued voting power of one within the weighted vote of her official MP.  Score voting can only grant each citizen either no voting power at all or unequal official voting power in the Commons.  Do you agree with this conclusion?



23XS:  >You say that score voting uses more information but what extra benefit does this use provide?

24T:  It offers proportionality on a more sophisticated level, given that it takes into account the representation each voter gets from all elected candidates. …


25S:  Please explain what additional benefit is supplied by this “sophistication”.  If there is no additional benefit, “more sophistication” only means needless complication.


26T:  To be clear, where you said "APR has the advantage that it would guarantee any such multiple representation proportionately." …


27S:  More exactly, I would only claim that APR guarantees

1)     to elect all those favoured candidates who are ranked by sufficient numbers of citizens, and

2)     that to the extent that the number of a group of citizens share the same scale of values and is large enough to elect many MPs, all the weighted votes of all these MPs will unofficially represent all these citizens (i.e. except each of these citizens will have only one of these MPs as her official representative).


28T:   this was false but applies more accurately to the score system I have described.


29S: Again, I need you to explain the reasoning process by which you arrived at this conclusion.





30T: First of all, you weren't clear about some of my explanations. For example, the score conversion of the approval method. Basically because the system works using approval votes, the scores are converted into approvals. Let's say the max score is 10. Each voter is effectively turned into 10 mini-voters. All 10 approved candidates are given a score of 10, 9 of them will approve candidates and giving a score of 9 [each] and so on. So if a voter gives a score of 6 out of 10 to a candidate, then 60% of the mini-voters will approve the candidate and 40% won't.


31S:  Yes.



32T: APR makes no such guarantees that multiple representation will be proportional. In fact, I demonstrated [illustrated] it with my example in the last e-mail. I will present it again. Scores out of 10:

Voter 1: A=10, B=10, C=10
Voter 2: A=10, B=10, C=0

The score system would elect A and B. We can easily see that this is the best result.


33S: Yes, in this case, score voting gives each of these two voters equal voting power in the Commons from 2 MPs who have received their highest scores.  However, score voting cannot guarantee such equal representation to each and every citizen.

34T:  Under APR, [from the above scores] the same two voters might rank the candidates as follows]:

Voter 1: C>A>B [or C>B>A, or B>A>C, or B>C>A, or A>C>B, or A>B>C]

Voter 2: A>B

A and C are elected, giving voter 1 better representation because he has extra unofficial representation from A. To be clear, it is objectively incorrect to claim that APR gives more proportional "multiple" representation. …


35S:  Yes, in this example, voter 1 has one official rep and one unofficial rep.  This sometime happens in any electoral system and there is nothing wrong with this.  Also, please see post 1S:


36S:  In this case, you again seem to have a definition of “proportional” other than the one you seemed to have in mind on some other occasions. On those occasions, perfect proportionality seemed in practice to be present only when there is no difference between each person’s actual total voting power and the per capita mean voting power in an election. For your above use, please define what you mean by “proportional”.  Please also see post 1S:


37 T: … APR has no way of counting and checking multiple representation and has no mechanism to ensure that it is in any way proportional. The amount of representation voters get in APR is more down to chance than it is in the score voting system.


38S:  I need you to spell out your reasons for coming to your conclusion in the last above sentence. Please also see post 1S:


39S:  2) Also, in contrast to APR, scale voting would encourage groups of like minded voters to coordinate their individual scores of the candidates they favour so as to make it more probable that all these favoured candidates will be elected. Admittedly, score voting does not guarantee such results but to the extent that this strategy is successful, the total voting power of each of these citizens would be greater than that of individual voting citizens who are similarly members of smaller groups, or who are not members of any such like minded group. Perhaps these latter voters would know fewer candidates that they would want to score and thus each of these citizen’s total share in the voting power in the Commons would be smaller than that held by the individuals in the larger groups, i.e. score voting would allow such strategic groups to gain more power per person than other individuals would have with regard to all their official MPs. In this regard, unlike APR, score voting would allow violations of the principle of one-person-one-official-vote. It could do this by allowing some voters to produce greater deviations of their voting power from the mean (i.e. each member of a big group having a voting power greater than the mean, and thus leave other citizens, per person, to share even less voting power than the mean. This seems contrary to what you say you want.

Please explain if you think I am mistaken about this.

40T:  If you are saying what I think you are, then you are mistaken. If a group of like-minded voters get together in this way, then they will still only be able to elect the number of candidates that matches their proportion of the electorate. …


41S:  Not necessarily.  Please compare the following two cases:


1)     Each member of a group constituting 40% of the electorate gives a 10 to candidate K, but K is elected by having received only half of these 10s.

2)     Each member of a different group constituting 20% of the electorate give a 10 to candidate Q and these scores alone elect Q.

As a result, the 40% of the electorate in 1) has only the same voting power in the Commons as the 20% in 2) have.  Alternatively expressed, each voter in 1) has half the voting power in the Commons when compared with the voting power of each citizen in 2).  This shows that score voting cannot guarantee that “the number of candidates [elected] … matches their proportion of the electorate”.




42XS: Still, if I do understand you correctly, you have not yet attempted exactly to define and explain the extra benefit you see as provided by score voting as contrasted with APR, i.e. the benefit you see as making it worth

>1) denying equality to each citizen, …

43T: I wouldn't be denying equality. Of course, APR allows for inequality with "non-official" representation to a far greater extent than my score system. …


44S:  Again, I need you to explain the reasoning process by which you have come to this view.


45T: … I hope you understand this now. Also, some voters have their favourite candidate elected and some don't. This is another inequality of APR.


46S:  This possibility exists in all electoral systems as far as I know.  Do you disagree?

47XS: …2) using much more complicated mathematics that few citizens would understand, and

48T: It is more complicated. But there's a couple of points to make regarding this. Firstly, it's unclear exactly how one would decide how complicated is too complicated. …


49S: Any additional complication is too much unless it gives voters an important additional benefit.  As yet, I have not understood how score voting gives any extra benefit.  Please try to explain more. 


At the same time, APR only requires people to understand how to add whole numbers.  Score voting also requires people to understand subtraction, decimals, and why some numbers need to be squared, i.e. all this, in addition to understanding why their vote will probably not count equally when compared to the voting power of each other citizen.


50T:  APR is also fairly complicated. Secondly, I've said before that this score method is only a working model anyway. Thirdly, I only introduced it into this discussion to show up flaws in APR. The point is that those flaws still exist even if you want to separately argue for keeping APR on the grounds of greater simplicity or other flaws in the score system.


51S:  Please list the “flaws” you still believe infect APR.

52XS:  >3) denying to each citizen the capacity to guarantee that her vote will count fully within the weighted vote of the MP she most trusts (or the MP most trusted by her most favoured but eliminated candidate)?

53T: I am guaranteeing that someone's vote [scores] will count towards finding the most proportional result given that everyone's votes are counted equally. …


54S:  Please explain the reasoning process by which you arrived at this conclusion.  Firstly, your “someone’s” still means that some (not all) citizens’ votes will help some candidates to be elected, and those that do, will be unequal in the amount of voting power each gives to those elected.  If so, “everyone's votes are counted equally” could only mean that all votes are counted according to the same rules.  Is this correct?



55T: …Under APR, someone's favourite candidate might not be elected (as you acknowledge) but even if this is the case the MP most trusted by their most favoured but eliminated candidate might be way down their list, so not really a suitable representative for the voter. ………


56S:  Also, please see post 20S:




57XS: So you accept that with score voting some citizens’ votes will be entirely wasted (i.e. not help to elect any candidate), and those that do help will usually count somewhat unequally. If so, is this not a needless violation of the principle of “one-person-one-vote”?

58T:  It's possible that some votes will be wasted in this sense. If a voter gives positive scores to some candidates, it's possible that none of these will be elected. …


59S: Correct.


60T: … But obviously someone could give a score to all candidates, in which case their vote would count. …


61S:  Yes, but surely a score voter would only score the candidates she likes.  If she scored all of them in the same way it would be the same as not voting at all.


62XS:  In any case, above you seem already to “accept that with score voting, some citizens’ votes will be entirely wasted (i.e. not help to elect any candidate), and those that do help will usually count somewhat unequally. If so, in contrast to APR, you accept that score voting violates the principle of “one-person-one-vote”?”

63T:  Addressed above.


64S:  Yes but also please see post 1S:


65*XT: … On weighted votes generally, I think we have largely made our points about that and I don't really want to bring out all my arguments again because I think we'd end up going round in circles, but it's all there in the archives. But if you want to bring up something specific I have said, feel free to do so.


66S:  Please list any remaining objections you might have regarding weighted votes.  This would help me search the archives.

67T:  Just to add to this, it was you who steered the argument away from this. We last really discussed the weighted vote issue back in about December, and you didn't respond to my last points on it.


68S:  I do not recall steering this argument away but perhaps your above list will help me find this December exchange.


69XT: But I will make some points about APR's ranking v score now. When I've mentioned the measure of disproportionality in the score result, a few times you've pointed out that indeed any result would (realistically) have disproportionality, whereas you have argued that APR does not have this disproportionality. But this is not a reasonable comparison because they are not being compared by the same measure. …


70XS: Let’s again compare them by the same measure then. As I understand it, you want to measure the results of score voting by calculating the average per capita deviation from the mean of the voting power of all individual voters. As a result, you discovered that it is likely that some voters would have no voting power, while the rest would have varying degrees of voting power. You think the best result would be when this average deviation is as small as possible. By contrast, when we apply the same test to APR, we find both that there would be no such deviations and each citizen could guarantee that her vote will have exactly a power of 1 within the total number of citizens voting. Therefore, while score voting would probably provide unequal voting power for citizens, APR provides this equality. How do you justify this inequality?

71T:  No, because APR's proportionality is based on the fact that everyone has equal "official" representation. It says nothing of their true level of representation - i.e. how represented they feel by their official representative or indeed by anyone else. APR is likely to have more inequality than score, because it uses less of the information and leaves more to chance.


72S:  Given the above, perhaps it is your desire that each citizen have an equal number of votes of MPs in the Commons that agree with each citizen’s own scale of value.  Perhaps this is your idea of “full proportionality”.  If so, this would prevent larger groups of citizens from having more voting power than smaller groups in the Commons. I do not think this what you want? Also, please see post 1S:

76XT: … APR's measure is purely on wasted votes. As long as every voter is able to be assigned a candidate …


77S:  Also, please see post 1S:


78T: … that they have ranked (somewhere on their list), then no votes are wasted and APR has achieved perfect proportionality. All very well and good. Except that in the case where all voters give a full ranking of all candidates, every single result would end up as fully proportional under APR's measure. …


79XS: Not exactly. I think we already agreed that both systems should allow each voter


>1) to rank or score as many or as few of the candidates in the country as they might wish, and


>2) allow her to require her top ranked (or top scored) but eliminated candidate to pass on her APR vote to the rep most favoured in that candidate’s pre-declared ranked list of other candidates ( or to pass on one score vote worth of this eliminated candidate’s pre-declared scores to other candidates).


>This means that without needing to “give a full ranking of all candidates”, an APR voter could guarantee that her whole vote would at least be added to the weighted vote of an indirectly favoured MP.  However, it does not guarantee that any scores that are similarly passed on will help electing any MP.




80XS: Now you seem to be meaning something different by “perfectly proportional”. Previously you meant, each voter having a voting power in the commons that does not at all deviate from the mean. Now “perfect” seems to require that each citizen be represented by her top ranked candidate? In this sense, I grant that APR does not guarantee this. It only allows a citizen to guarantee that her vote will be added to the weighted vote of the MP (not candidate) she most trusts (or to the MP most trusted either by her top ranked but eliminated candidate, or trusted by the MP she has help to elect but who received more than 10% of the weighted votes in the Commons).

81T:  I'm using your meaning, not mine. It seems that you think as long as each voter has the same amount of official representation, then the result is fully proportional regardless of how represented they feel by their MP or how much extra representation they get from MPs other than their own.


82S: Yes, as proportional as it should be:  each citizen guaranteed to have one official MP that she favours, and perhaps other unofficial but liked MPs in proportion to the numbers of her fellow citizens that share her scale of values…  Also, please see post 1S:


83XT: … If, in a score voting election, voter 1's 10/10 candidate is elected and voter 2 just gets their 8/10 candidate elected, then the mechanism would measure some disproportionality. However, if this happened in APR it might be that voter 1 would have their top rank elected and voter 2 their second rank. One might still see some disproportionality in this, but APR ignores this. ..


84S: Yes. Also, please see post 1S:



85XS: Rather than calling this “disproportionality”, I think it would be more apt to say that such a result is not “perfect” in the above new sense, i.e. because “voter 2” is not as pleased with his MP as is “voter 1”. However, this is not the fault of APR but a correct result of the fact that more fellow citizen ranked voter 1’s top ranked candidate than voter 2’s top ranked candidate. At the same time, APR guaranteed that each voter’s vote was added to the weighted vote of the MP (not necessarily the candidate) that each most trusts.

86T:  Call it what you want but it's still deviation from the ideal result. …


87S: I assume that neither of us are primarily focussed on a concept of the “ideal” or the “perfect” when it is impossible in practice.  Again, no system could or should guarantee that each citizen will have their top choice candidate as their MP.


88T: … In an "ideal world" using APR logic, there would be no 10% limit for each MP's weighting and no limit on the number of MPs elected. …


89S:  You might suggest a limit other than 10% but I think we might also agree that a limit should be applied to remove the possibility that any one MP could be in a position to dictate to the Commons.


90T: … A perfect result would be for every voter to add the same amount as each other to their deviation, and APR would deviate.


91S:  In the context, I do not understand the above.  Why have you used the word “deviation” in relation to APR.  Please explain.






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