steve bosworth | 20 Jul 23:31 2016
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Re: (5) MJ better than IRV & MAM

Hi Kristofer,

Thank you for enabling me more fully to understand exactly how MAM is counted.  For example, the link you sent me for Steve Seppley’s MAM counting tool has been very useful.  With this tool, I have easily tested many other examples in an attempt to find a profile for which MAM elects a single-winner with a lower intensity of support from voters than the winner that would be elected by IRV.  I did not find any such an example.  For every example I tried, IRV and MAM elected the same winner.  However, since IRV (unlike MAM) does not consider all the voters’ preferences until the majority winner is discovered, I assume there must be examples of the two methods electing different winners with different intensities of support.  Still, I currently have no clear basis for continuing to suggest that IRV is more efficient at electing winners who have the highest available intensity of support from voters.

Do we agree that MAM has no disadvantage with respect to IRV except that MAM’s method of counting would be much more difficult for ordinary voters to understand?  Also, do you agree that MJ (like MAM) has the advantage over IRV in electing a single-winner only after counting all the votes of each voter (i.e. the ‘grades’ that every voter has given to all of the candidates)?  In addition, I see MJ’s method of counting these grades as being easier for ordinary citizens to understand than MAM’s method.  Consequently, do you also prefer MJ to MAM?  I also see MJ as more likely to prompt voters not to ‘rank’ the candidates but instead to ‘grade’ all of them honestly, i.e. to encourage more voters to grade or REJECT each candidate in the light of each of their own visions of what an EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, or POOR candidate looks like.  Electing the candidate with the highest ‘majority-grade’ also seems to give the least incentive to citizens to vote strategically. 

In this connection, below your say with regard to MJ that ‘it seems more that voters value expressing their true preference, and as long as the benefit to strategy is less than what they gain by expressing their preference, honesty wins.’ 

Of course, you say this only after listing a number objections that can be raised against MJ.  Nevertheless, do you currently believe with me that these objections are less weighty than those that can also be raised against the practical use of any other single-winner method?

Finally, your questions and arguments have also driven me to accept that each these three methods respect the principle of "one citizen one vote".

From: Kristofer Munsterhjelm <km_elmet <at> t-online.de>
Sent: Saturday, July 16, 2016 3:43 PM
To: steve bosworth
Subject: Re: (5) MJ better than
 IRV & MAM

 On 07/14/2016 06:11 PM, steve bosworth wrote:
[….}
K:  Here's my detailed count (see attachment). See also
http://mam.hostei.com/default.php which explains the procedure for any
given ballot set.

-km

From: Kristofer Munsterhjelm <km_elmet <at> t-online.de>
Sent: Wednesday, June 29, 2016 11:19 AM
To: Kevin Venzke; steve bosworth; EM list
Subject: Re: [EM] The easiest method to 'tolerate'

 

On 06/29/2016 01:03 AM, Kevin Venzke wrote:
> Hi Steve,
>
> Majority Judgment is a variety of "median rating" methods which I see as
> pretty similar. Woodall made one himself called Quota-Limited
> Trickle-Down and in fact if you google "woodall qltd" you can find a
> .pdf with a chart of some of the properties. The most noteworthy here
> are the failures of Later-no-harm and Mono-add-top. (Both are failures
> that IRV does not share.) For Later-no-harm: Suppose that candidate A is
> elected. It's possible that there is a bloc of voters who rated B above
> A, but A above zero, and that if these voters had lowered their A rating
> to zero, then candidate B would win instead, which is an outcome this
> bloc of voters would have preferred. They could criticize that the
> method should be smart enough to not use their A ratings to elect A when
> it would have been possible for them to elect B. If not a fairness
> issue, it's at least an issue of the method requiring voters to keep
> certain strategy in mind.

I'll also note that MJ fails:

- Participation: Failure means that a voter might make the outcome worse
from his point of view by going to the polls. (Participation is
notoriously hard to pass)

- All-equal ballots irrelevance: you can have a voter show up and give
every candidate the same rank, yet that changes the outcome. You'd
expect that to pull every candidate equally in the direction of the
grade that voter gave to every candidate, but that's not true.

See also, from a Range perspective:
http://rangevoting.org/MedianVrange.html

RangeVoting.org - Balinski & Laraki's "majority judgment ...

rangevoting.org

On Balinski & Laraki's "majority judgment" median-based range-like voting scheme And comparison versus ordinary [i.e. average-based] range voting




> The Mono-add-top issue works like this: Suppose that C is elected. It's
> possible under median ratings methods that when some ballots rating a
> different candidate "D" first (i.e. D is the first preference) are
> removed from consideration, then a candidate D becomes the new winner.
> In other words, when C wins, the D-first voters can criticize that they
> were penalized for showing up to vote.
>
> I should note that while IRV does not have these issues, probably *most*
> of our proposed methods do, so they aren't necessarily deal-breakers.

Incidentally, Minmax (margins) passes Condorcet and mono-add-top. It's
not one of the methods I'd call advanced, though.

> While median rating is more resistant to manipulation than Range, I
> still view the manipulation potential as bad. For example, if you
> "defensively" rate A as zero, in the Later-no-harm example above, out of
> a quite reasonable fear that you need to do this to help B win instead
> of A, this is the type of thing meant by manipulation. It is less likely
> to have an effect than in Range, but you will still have the incentive
> to do it.

There are two ways to consider strategic incentive. Suppose you have a
method whose benefit (additional utility) to a particular voter X is
something like:

http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29+from+0+to+0.5

where the x axis is the size of the strategizing coalition X is part of,
when everybody not in the coalition votes honestly.

It's clear that no matter the size of X's group, X has an incentive to
strategize. A rational voter will clearly always strategize.

Now suppose the utility given to X is more like:

http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29+*+%28-SquareWave[1.2*sqrt%28x%29]+%2B+1%29%2F2+from+0+to+0.5

i.e. there's a hard threshold before which strategy has absolutely no
effect, positive or negative.

A rational voter would still always strategize because there's no actual
harm to doing so, and if enough voters aligned with his candidate think
the way he does, he'll benefit. So it's a chance of getting something
better with no risk, and a rational voter would take that.

However, it seems unintuitive to me that a real voter would do so.
Inst
ead, it seems more that voters value expressing their true
preference, and as long as the benefit to strategy is less than what
they gain by expressing their preference, honesty wins.

> Your definition for "one citizen one vote" is difficult for me because
> it seems focused on how the winner is found. For example you say
> preferences should be counted equally "as long as possible, until"
> something happens, which seems to assume that an election method
> algorithm is something that unfolds over time. Normally I view an
> election method as defined by its results, and there need not be a
> single set of steps which finds the result. I wonder what would be an
> example of a method that violates "one citizen one vote," and if there
> m
ight be another way of describing what is problematic about it.

S:  I now accept that these three methods respect the principle of "one citizen one vote".

[….]

 


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Frank Martinez | 19 Jul 16:55 2016
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Condorcet Question

Is the Condorcet Candidate, by definition, the Candidate winning 1-on-1 against All Opponents or the Candidate winning against the most?
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Kristofer Munsterhjelm | 13 Jul 13:07 2016
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Re: Fw: MJ better than IRV & MAM

On 07/13/2016 07:47 AM, steve bosworth wrote:

> K:  As for the MAM example, it seems that F wins in MAM as well.
> 
> S:  Yes, F does win with MAM. I clearly made a mistake when counting. 
> However, I believe the following new profile does illustrate the point I
> was trying to make (see below).  This is that MAM (or any Condorcet
> method) is less efficient than IRV in discovering the winner with the
> highest available average intensity of majority support.  This is
> because MAM does not count the different intensities of preference as
> illustrated by the following calculations:  If each of the ordinal
> preferences within this profile receive a score out of 10, 10 being
> given to each 1^st choice, F receives an average intensity of support of
> 9.1 from the majority of 70 that elects her, or 8.47 from all 100 voters.
> 
> This contrasts with N who is elected both by MAM and Majority Judgment
> (MJ).  N’s average intensity of support from all 100voters is 7.51. 
> More exactly MJ elects N because she has received the highest
> ‘majority-grade’ of GOOD (i.e. perhaps this corresponds to a score of 8).

[snip]

> *PROFILE: A BETER EXAMPLE:*
> 100 CITIZENS RANK CANDIDATES EFGKMNP AS FOLLOWS:

I've restated that example into the standard ranked ballot format:

49: F>P>K>N
30: M>E>N>F
21: G>K>N>F

And Eric Gorr's MAM implementation http://www.ericgorr.net/condorcet/

says that F wins under MAM ("Ranked Pairs (Deterministic #1-Winning
Votes)") as well[1].

According to LeGrand's voting calculator,
http://www.cs.wustl.edu/~legrand/rbvote/calc.html

the only methods (among those implemented there) that make N win are
Copeland (with random tiebreak), Raynaud (ditto), and Small. Note that
LeGrand's calculator uses margins, so the defeats matrix will look
different.

I haven't checked your majority figures yet as I'm not feeling all that
well today. I haven't checked your MJ result either; but a very quick
and dirty Bucklin count seems to support that N would win under MJ.

I would also like to again mention that one can construct examples where
IRV does worse by your intensity calculations. I gave one such example
in a previous post, and here's another from
http://rangevoting.org/CoreSuppPocket.html:

35:A>C>D>B
17:B>C>D>A
32:C>D>B>A
16:D>B>C>A

IRV elects B. MAM elects C. Say first preferences are 10 points, second
is 9, third is 8, and fourth is 7, then

B has an intensity of

(35 * 7 + 17 * 10 + 32 * 8 + 16 * 9) / 100 = 8.15

while C has an intensity of

(35 * 9 + 17 * 9 + 32 * 10 + 16 * 8) / 100 = 9.16.

Come to think of it, any center squeeze example would do. Here's LCR:

48: L>C>R
32: R>C>L
20: C>R>L

IRV elects R while every Condorcet method (and Bucklin/MJ) elects C.

C's intensity is: (9 * 48 + 9 * 32 + 10 * 20)/100 = 9.2
R's intensity is: (8 * 48 + 10 * 32 + 9 * 20)/100 = 8.84.

-

[1] It's not strictly speaking MAM because MAM handles ties among
majorities differently, but I don't think breaking ties differently
would make N win.
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⸘Ŭalabio‽ | 28 Jun 21:13 2016

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--

-- 

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Skype:
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An IntactWiki:
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Kristofer Munsterhjelm | 28 Jun 14:14 2016
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A more Condorcetian Hare-based proportional method

(This is a sketch of the method that I mentioned in my post to Robert,
that I haven't been able to make into an actual method because of a
particular snag.)

Suppose that X and Y are two lists of pairwise comparisons (e.g. X might
be "A>B B>C" and Y might be "C>A C>B B>A") so that the pairwise
combinations can be combined into a linear order (i.e. there are no cycles).

Then let X be stronger than Y if: X's first comparison has a stronger
defeat strength than Y's first, or if they're both equal and X's second
comparison has a stronger defeat strength than Y's, and so on (leximax).
Missing entries count as 0, so a list of defeat strengths (20 10 5) is
stronger than one of (20 10) but not one of (20 11).

Let such a list be maximal if no other list is better than it.
Clearly, when not further constrained, the maximal list gives the
orderings to be reassembled to find the Ranked Pairs winner in a
single-winner election[1].

The idea for multiwinner is then pretty simple, on a high level:

Let a particular ballot subset of size k be maximal if its
maximal list (when only considering the votes in this subset) is no
weaker than any maximal list from any other ballot subset of size k.
(Here, comparing lists from different subsets implies comparing defeat
strengths calculated from the respective subsets.)

Then:

1. Randomly pick a maximal Hare quota-sized subset of the ballots.
2. Feed the associated ordering for the maximal Hare subset to
Ranked Pairs, conducting an RP election on that subset of ballots.
3. Elect the winner and eliminate him from every ballot.
4. If the council is full, we're done.
5. Otherwise remove the Hare subset in question from the total ballot
set and go to 1.

This is basically the same kind of logic as sequential PAV (or
approximation algorithm A for Monroe here:
http://arxiv.org/pdf/1312.4026.pdf ), but with scoring being based on
maximal lists rather than a simple reweighted sum of ratings.

Note that something alike the elimination in step 3 is forced. To see
why, consider an election where everybody agrees A is best. If we don't
eliminate A, every subset's MAM election will choose A.

The "ideal gerrymander" interpretation is also pretty easy to understand
for this method: step one finds the best district to give a
representative. Step two then proceeds to find who that representative
should be, and then all voters in that imaginary district are removed
from consideration and the process continues with what's left.

-

All the magic resides in step 1. We have to find some way of finding and
picking a maximal subset. This is easy if there are no ties at each
level. Suppose for instance that a Hare quota is 100, and A>B is the
highest defeat strength pair we know of with 80 voters saying A>B. Then
we automatically know that all those A>B voters are part of the maximal
subset, along with 20 more we don't know anything about. No matter what
the other pairs in the maximal subset is going to be, A>B has to be in
it for the subset to be maximal to begin with.

Having locked down the A>B voters, we could then look for which other
pairwise preferences are stronger than any others, subject to the
constraint that we can only pick 20 voters outside the already locked-in
subset. And so it continues until the 100 voters have all been locked in.

The snag lies in that I can't see a way of get rid of lookahead, and
with lookahead, having to consider every option may cause an exponential
blowup. Consider this scenario:

At stage 1, A>B and B>C are tied for strongest defeat; say with a Hare
quota's worth of 100 votes.
Suppose it turns out that if we choose B>C, then the next strongest
defeat is C>D with 60 votes, but the A>B majority and B>C majority is
not the same, so if we choose A>B, the next strongest defeat is D>C with 50.
So we should choose B>C rather than A>B because B>C starts a maximal
list while A>B doesn't.
But the method can't know that in advance! So it would presumably have
to consider both A>B and B>C and backtrack once it finds out which are
better. But then we can bury the crucial tie-breaking distinction
beneath enough ties and the cost to try every combination becomes
prohibitive.

Perhaps there is a set covering-esque problem hiding in there somewhere.
Or maybe memoization can somehow help for low numbers of seats by
showing that the Hare quotas are broad enough to exclude many voters in
one swoop, so the combinatorial explosion doesn't occur, or there's
optimal substructure somehow so dynamic programming works... but any
such tricks will make the method very complex.

I don't think that method would be monotone, either, but that's just a
hunch.

-

[1] A similar reduction is possible for River: just state that the lists
must follow River's constraint that no candidate can be on the losing
side of a pairwise comparison more than once.
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steve bosworth | 28 Jun 01:00 2016
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The easiest method to 'tolerate'

 

To everyone:

 

Thank you Kevin for responding to my questions about IRV being nonmonotonic.  I think our dialogue would be assisted by me also understanding your views about the Majority Judgment method.  You said:  All proposed methods are unfair in some way, and people have different views on what is or isn't tolerable’.  Currently I do not yet see how Majority Judgment is in any way ‘unfair’.  MJ seems to resist manipulation more than any one of the other proposed methods.  Also, it seems fully to satisfy what I mean by the ‘one-citizen-one-vote’ principle

for electing a single-winner.  In this context, this principle requires that each citizen’s vote (preferences or ‘grades’) be counted equally as long as technically possible until the single-winner is discovered, i.e. the candidate who has received the highest average intensity available of majority support.

 

Do you agree or do you see a different method as easiest to ‘tolerate’?

 

From: Kevin Venzke <stepjak <at> yahoo.fr>
Sent: Wednesday, June 22, 2016 1:05 AM
To: steve bosworth; election-methods <at> lists.electorama.com
Subject: Re: [EM] Wiki says IRV is monotonic--not fully democratic?

 

Hi Steve,

 

The first one on the list (mono-raise) is what people are referring to when they say IRV (or two-round) violates monotonicity. But certainly there are other ones from the list that it doesn't satisfy either.

 

You used the terms "democratic" and "one citizen one vote" but I don't really know of definitions for these terms at this level.

 

The reason mono-raise failures are criticized is that they involve situations where a candidate (or his supporters) could complain that they are penalized for getting better rankings. A perception of unfairness could undermine perceived legitimacy of the winner. All proposed methods are unfair in some way, and people have different views on what is or isn't tolerable.

 

Kevin

 

 

 

 

 

++++++++++++++++++++++++

To everyone:

Below, Steve is considering the following section of the following June 21, 2016 Wikipedia article:  Monotonicity criterion’.  He will refer to the author of that section as ‘Wiki’:

Instant-runoff voting and the two-round system are not monotonic[edit

Using an example that applies to instant-runoff voting (IRV) and to the two-round system, it is shown that these voting systems violate the mono-raise criterion. Suppose a president were being elected among three candidates, a left, a right, and a center candidate, and 100 votes cast. The number of votes for an absolute majority is therefore 51.

Suppose the votes are cast as follows:

Number of votes

1st preference

2nd preference

28

Right

Center

5

Right

Left

30

Left

Center

5

Left

Right

16

Center

Left

16

Center

Right

According to the 1st preferences, Left finishes first with 35 votes, Right gets 33 votes, and Center 32 votes, thus all candidates lack an absolute majority of first preferences. In an actual runoff between the top two candidates, Left would win against Right with 30+5+16=51 votes. The same happens (in this example) under IRV, Center gets eliminated, and Left wins against Right with 51 to 49 votes.

[STEVE’S Additions:

S: Given these preferences, the Center candidate rather than the Right candidate should get eliminated because he receives fewer 1st preference votes.  Still, the principle of one-citizen-one-vote requires that the preference of each of these supporter be counted until a majority winner is discovered.  Since 16 of them preferred the Left candidate next and 16 preferred the Right candidate next, the Left candidate receive a total of 51 votes and the Right candidate 49.  Given both that only one candidate can win in this election and the principle of one-citizen-one-vote, no citizen would be able to sustain an objection to this result.

Author’s

1st IRV

COUNT

Left

Center

Right

1

35

32

33

2

51

 

49

Wiki: But if at least two of the five voters who ranked Right first, and Left second, would raise Left, and vote 1st Left, 2nd Right; then Left would be defeated by these votes in favor of Center. Let's assume that two voters change their preferences in that way, which changes two rows of the table:

Number of votes

1st preference

2nd preference

3

Right

Left

7

Left

Right

Now Left gets 37 first preferences, Right only 31 first preferences, and Center still 32 first preferences, and there is again no candidate with an absolute majority of first preferences. But now Right gets eliminated, and Center remains in round 2 of IRV (or the actual runoff in the Two-round system). And Center beats its opponent Left with a remarkable majority of 60 to 40 votes.

1-[STEVE’S IRV exploration:

Wiki’s changed preferences (2nd Set of Ballots)

Number of votes

1st preference

2nd preference

28

Right

Center

3

Right

Left

2

Left

Right

30

Left

Center

5

Left

Right

16

Center

Left

16

Center

Right

 

2nd IRV

COUNT

Left

Center

Right

1

37

32

31

2

40

60

0

3

 

60

 

S: These 28 make the Center candidate’s total of 60 (and the winner) while the 2 make the total of the Left candidate 40.  While it is true that this change in preferences changes the win for the Left candidate to a defeat, they still helped the Left candidate both by increasing the number of first preferences he received and the average intensity of preference given to him.  At the same time, he could not expect to win because he had received only a total of 40 to the total of 60 votes received by the Center candidate.

Consequently, currently I do not yet see this example as containing any anti-democratic element. As I see it, the principle of ‘one-citizen-one vote’ only requires that each citizen’s vote (preferences) be counted equally as long as technically possible until the single-winner is discovered, i.e. the candidate who has received the highest intensity possible of majority support.  Accordingly, before the 2 preferences were changed by Wiki, the Left candidate won with 51 votes with an average intensity of 9.76 on a scale of 10.  After the change, the Center candidate won with 60 votes with an average intensity of 9.53. 

Intensity of support calculations:

1st Set of Ballots

35X10 +16X9=350+144=494

494 divided by 51=9.76

2nd Set of Ballots

32X10 +28X9=320+252=572

572 divided by 60=9.53

In contrast, the intensity of support for a forced win by the Center candidate from the 1st Set of Ballots would only be 9.36:

32 X 1st preferences and 58 X 2nd preferences for the Center candidate:

32X10+58X9=320+522=842

842 divided by 90= 9.36

S: Again, using IRV, the originally winning Left candidate was defeated after the author changed the two voters’ preferences.  This happened even though the Left candidate was now given two 1st, rather than two 2nd, preferences.  Wiki sees this as a violation of the ‘mono-raise criterion’: ‘giving higher preferences to a candidate should never harm him’.  However, at least in some senses, these two higher preferences did help the Left candidate, i.e. they gave him two more 1st preferences. They also helped him by reducing the intensity of 2 preferences given to one of his competitors, i.e. by giving the Right candidate two 2nd rather than two 1st preferences.  By themselves, these changes would make it more likely that the Left candidate would win.  It is only because more other citizens gave their 1st preference to the Center candidate over the Right candidate that the Right candidate correctly had to be eliminated in the second count.  In turn, this appropriately required candidate Right’s 2nd preferences to be transferred:  28 to the Center candidate and 3 to the Center candidate.  Given these two change made by these two citizens, the particular preferences given by the other voters required that the Left candidate not be elected.  Consequently, it was not the isolated giving of two higher preferences to the Left candidate that ‘harmed’ him.  It was how these preferences had to be combined with the preferences of all the other citizens that required the Left candidate to be defeated.  This follows from the principle of one-citizen-one-vote.  Again, given both this principle and the fact that only one candidate can win in this election, no one would seem to be able to sustain an objection to this result.

S: Nevertheless, Wiki claims that IRV is not monotonic (i.e. violates the mono-raise criterion).  Does Wiki have Woodall’s definition of a mono-raise random criterion (see below) in mind [Douglas R. Woodall Discrete Applied Mathematics 77 (1997) 81-98]?

In the light of the above discussion and the following definitions, I would very much appreciate it if anyone could explain why they might still want to criticize IRV for being nonmonotonic.  Is IRV fully democratic in the sense defined above?

Section 1.3 in Woodall’s article defines how a nonmotonic set of rules might ‘harm’ or ‘help’ candidate x:  ‘We shall say a candidate x is either helped or harmed by a change in the profile if the result, respectively, is to increase or decrease [the probability of electing x, i.e] PE(x). The following two properties are well known to hold for STV [which reduces to IRV in a single-winner raced].

  • Later-no-help:  Adding a later preference to a ballot should not help any candidate already listed.

  • Latter-no-harm:  Adding a later preference to a ballot should not harm any candidate already listed.’

Next, Woodall goes on to define nine different ‘versions of monotonicity.  The basic theme is that a candidate x should not be harmed by a change in the profile that appears to give more support to candidate x.

Monotonicity:

1-(mono-raise) x is raised on some ballots without changing the orders of other candidates;

2-(mono-raise delete) x is raised on some ballots and all the candidates now below x on those ballots are deleted from them;

3-(mono-raise random) x is raised on some ballots and the positions now below x are filled (or left empty) in any way that results in a valid ballot;

4-(mono-append) x is added to the end of some ballots that did not previously contain x;

5-(mono-sub-plump) some ballots without x are replace by ballots with x placed top and with no second choice;

6-(mono-sub-top) some ballots that do not have x placed top are replaced with ballots that do place x top (and are otherwise arbitrary);

7-(mono-add-plump) further ballots are added that place x top and with no second choices;

8-(mono-sub-top) further ballots are added that place x top (and are otherwise arbitrary);

9-(mono-remove-bottom) some ballots are removed, all of which have x at bottom, below all other candidate.’

I look forward to any of your replies.

Steve

 


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Richard Lung | 25 Jun 14:44 2016

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Thankyou for your time.
Richard Lung.



 
-- Richard Lung. E-books (mostly available free or reader-sets-price) http://www.voting.ukscientists.com/colverse.html Includes the series of books on: Democracy Science (starting with electoral reform and research); Commentaries (literature and liberty; science and democracy); Collected verse (in five books).
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Forest Simmons | 22 Jun 03:18 2016

question about electoral college in the USA

In a recent counterpunch article Dave Lindorff suggested that Sanders should go ahead and run on the Green ticket, but with the following agreement:  if Trump gets more electoral votes than either Clinton or Sanders, then (of these two) the one with lesser support should withdraw from the race and direct his electors (in the electoral college) to vote for the other.

It seems reasonable, but I wonder if the rules really do allow that.


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steve bosworth | 22 Jun 00:07 2016
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Wiki says IRV is monotonic--not fully democratic?

 

To everyone:

Below, Steve is considering the following section of the following June 21, 2016 Wikipedia article:  Monotonicity criterion’.  He will refer to the author of that section as ‘Wiki’:

Instant-runoff voting and the two-round system are not monotonic[edit

Using an example that applies to instant-runoff voting (IRV) and to the two-round system, it is shown that these voting systems violate the mono-raise criterion. Suppose a president were being elected among three candidates, a left, a right, and a center candidate, and 100 votes cast. The number of votes for an absolute majority is therefore 51.

Suppose the votes are cast as follows:

Number of votes

1st preference

2nd preference

28

Right

Center

5

Right

Left

30

Left

Center

5

Left

Right

16

Center

Left

16

Center

Right

According to the 1st preferences, Left finishes first with 35 votes, Right gets 33 votes, and Center 32 votes, thus all candidates lack an absolute majority of first preferences. In an actual runoff between the top two candidates, Left would win against Right with 30+5+16=51 votes. The same happens (in this example) under IRV, Center gets eliminated, and Left wins against Right with 51 to 49 votes.

[STEVE’S Additions:

S: Given these preferences, the Center candidate rather than the Right candidate should get eliminated because he receives fewer 1st preference votes.  Still, the principle of one-citizen-one-vote requires that the preference of each of these supporter be counted until a majority winner is discovered.  Since 16 of them preferred the Left candidate next and 16 preferred the Right candidate next, the Left candidate receive a total of 51 votes and the Right candidate 49.  Given both that only one candidate can win in this election and the principle of one-citizen-one-vote, no citizen would be able to sustain an objection to this result.

Author’s

1st IRV

COUNT

Left

Center

Right

1

35

32

33

2

51

 

49

Wiki: But if at least two of the five voters who ranked Right first, and Left second, would raise Left, and vote 1st Left, 2nd Right; then Left would be defeated by these votes in favor of Center. Let's assume that two voters change their preferences in that way, which changes two rows of the table:

Number of votes

1st preference

2nd preference

3

Right

Left

7

Left

Right

Now Left gets 37 first preferences, Right only 31 first preferences, and Center still 32 first preferences, and there is again no candidate with an absolute majority of first preferences. But now Right gets eliminated, and Center remains in round 2 of IRV (or the actual runoff in the Two-round system). And Center beats its opponent Left with a remarkable majority of 60 to 40 votes.

1-[STEVE’S IRV exploration:

Wiki’s changed preferences (2nd Set of Ballots)

Number of votes

1st preference

2nd preference

28

Right

Center

3

Right

Left

2

Left

Right

30

Left

Center

5

Left

Right

16

Center

Left

16

Center

Right

 

2nd IRV

COUNT

Left

Center

Right

1

37

32

31

2

40

60

0

3

 

60

 

S: These 28 make the Center candidate’s total of 60 (and the winner) while the 2 make the total of the Left candidate 40.  While it is true that this change in preferences changes the win for the Left candidate to a defeat, they still helped the Left candidate both by increasing the number of first preferences he received and the average intensity of preference given to him.  At the same time, he could not expect to win because he had received only a total of 40 to the total of 60 votes received by the Center candidate.

Consequently, currently I do not yet see this example as containing any anti-democratic element. As I see it, the principle of ‘one-citizen-one vote’ only requires that each citizen’s vote (preferences) be counted equally as long as technically possible until the single-winner is discovered, i.e. the candidate who has received the highest intensity possible of majority support.  Accordingly, before the 2 preferences were changed by Wiki, the Left candidate won with 51 votes with an average intensity of 9.76 on a scale of 10.  After the change, the Center candidate won with 60 votes with an average intensity of 9.53. 

Intensity of support calculations:

1st Set of Ballots

35X10 +16X9=350+144=494

494 divided by 51=9.76

2nd Set of Ballots

32X10 +28X9=320+252=572

572 divided by 60=9.53

In contrast, the intensity of support for a forced win by the Center candidate from the 1st Set of Ballots would only be 9.36:

32 X 1st preferences and 58 X 2nd preferences for the Center candidate:

32X10+58X9=320+522=842

842 divided by 90= 9.36

S: Again, using IRV, the originally winning Left candidate was defeated after the author changed the two voters’ preferences.  This happened even though the Left candidate was now given two 1st, rather than two 2nd, preferences.  Wiki sees this as a violation of the ‘mono-raise criterion’: ‘giving higher preferences to a candidate should never harm him’.  However, at least in some senses, these two higher preferences did help the Left candidate, i.e. they gave him two more 1st preferences. They also helped him by reducing the intensity of 2 preferences given to one of his competitors, i.e. by giving the Right candidate two 2nd rather than two 1st preferences.  By themselves, these changes would make it more likely that the Left candidate would win.  It is only because more other citizens gave their 1st preference to the Center candidate over the Right candidate that the Right candidate correctly had to be eliminated in the second count.  In turn, this appropriately required candidate Right’s 2nd preferences to be transferred:  28 to the Center candidate and 3 to the Center candidate.  Given these two change made by these two citizens, the particular preferences given by the other voters required that the Left candidate not be elected.  Consequently, it was not the isolated giving of two higher preferences to the Left candidate that ‘harmed’ him.  It was how these preferences had to be combined with the preferences of all the other citizens that required the Left candidate to be defeated.  This follows from the principle of one-citizen-one-vote.  Again, given both this principle and the fact that only one candidate can win in this election, no one would seem to be able to sustain an objection to this result.

S: Nevertheless, Wiki claims that IRV is not monotonic (i.e. violates the mono-raise criterion).  Does Wiki have Woodall’s definition of a mono-raise random criterion (see below) in mind [Douglas R. Woodall Discrete Applied Mathematics 77 (1997) 81-98]?

In the light of the above discussion and the following definitions, I would very much appreciate it if anyone could explain why they might still want to criticize IRV for being nonmonotonic.  Is IRV fully democratic in the sense defined above?

Section 1.3 in Woodall’s article defines how a nonmotonic set of rules might ‘harm’ or ‘help’ candidate x:  ‘We shall say a candidate x is either helped or harmed by a change in the profile if the result, respectively, is to increase or decrease [the probability of electing x, i.e] PE(x). The following two properties are well known to hold for STV [which reduces to IRV in a single-winner raced].

  • Later-no-help:  Adding a later preference to a ballot should not help any candidate already listed.

  • Latter-no-harm:  Adding a later preference to a ballot should not harm any candidate already listed.’

Next, Woodall goes on to define nine different ‘versions of monotonicity.  The basic theme is that a candidate x should not be harmed by a change in the profile that appears to give more support to candidate x.

Monotonicity:

1-(mono-raise) x is raised on some ballots without changing the orders of other candidates;

2-(mono-raise delete) x is raised on some ballots and all the candidates now below x on those ballots are deleted from them;

3-(mono-raise random) x is raised on some ballots and the positions now below x are filled (or left empty) in any way that results in a valid ballot;

4-(mono-append) x is added to the end of some ballots that did not previously contain x;

5-(mono-sub-plump) some ballots without x are replace by ballots with x placed top and with no second choice;

6-(mono-sub-top) some ballots that do not have x placed top are replaced with ballots that do place x top (and are otherwise arbitrary);

7-(mono-add-plump) further ballots are added that place x top and with no second choices;

8-(mono-sub-top) further ballots are added that place x top (and are otherwise arbitrary);

9-(mono-remove-bottom) some ballots are removed, all of which have x at bottom, below all other candidate.’

I look forward to any of your replies.

Steve

 


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Ralph Suter | 18 Jun 22:05 2016
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Re: French Region uses Condorcet Voting

I wish the focus of this list was broader than just elections.

Condorcet and other kinds of alternative voting methods could also be 
used in legislative bodies and organizations as well as informal groups 
to decide among three or more alternative proposals, making it possible 
to avoid or bypass the kinds of parliamentary and informal voting rules 
that now prevent consideration more than two alternatives at a time.

Furthermore, as the use of alternative methods in non-election 
situations became more frequent and (I hope) more popular, it would 
become much easier to advocate their use for elections, since far more 
people would have become familiar with them and comfortable using them.

-Ralph Suter
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Markus Schulze | 17 Jun 22:40 2016
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French Region uses Condorcet Voting

Hallo,

on 1 January 2016, the French regions Midi-Pyrenees
and Languedoc-Roussillon have been united to form
a new region. Between 9 May and 10 June 2016, there
was a referendum on the new name for this region.
The voters could choose between five alternatives:

* Languedoc
* Languedoc-Pyrenees
* Occitanie
* Occitanie-Pays Catalan
* Pyrenees-Mediterranee

The voters could rank these alternatives in order of
preference. And Condorcet voting was used to determine
the winner.

Here is the final result:

    There have been 203,993 valid ballots.

    Occitanie : Occitanie-Pays Catalan = 75% : 25%
    Occitanie : Languedoc = 69% : 31%
    Occitanie : Pyrenees-Mediterranee = 62% : 38%
    Occitanie : Languedoc-Pyrenees = 58% : 42%
    Languedoc : Occitanie-Pays Catalan = 50% : 50%
    Languedoc-Pyrenees : Languedoc = 71% : 29%
    Languedoc-Pyrenees : Occitanie-Pays Catalan = 64% : 36%
    Languedoc-Pyrenees : Pyrenees-Mediterranee = 57% : 43%
    Pyrenees-Mediterranee : Languedoc = 60% : 40%
    Pyrenees-Mediterranee : Occitanie-Pays Catalan = 59% : 41%

    Therefore, Occitanie is a Condorcet winner.

To the best of my knowledge, this was the largest
Condorcet poll ever.

Markus Schulze

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Gmane