Dick Burkhart | 16 Sep 05:40 2014
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A "top 3" to replace the "top 2"

Oregon is considering a "top 2" primary, a very regressive move in my opinion.

So I thought what would be simplest "top 3" method that would give voters more choices, especially in regard
to independent or minority candidates or parties. Less partisanship would be an added bonus.

Below is a draft answer. Effective and simple, except for the modest complexity needed to counter
strategic voting.

Dick Burkhart, Ph. D., President, Democracy Works
4802 S Othello St,  Seattle, WA  98118
206-721-5672 (home)  206-851-0027 (cell)
dickburkhart <at> comcast.net

There is a better way than the top two primary. The top two effectively eliminates third party and
independent candidates, sometimes even the second party candidate, as in Washington State’s 4th
congressional district in 2014. In fact we could get rid of the primary altogether. Just rank your top 3
candidates and tally the corresponding points.

How would this work? In the standard case, a voter’s top candidate gets 3 points, the second place
candidate 2 points, and third place 1 point. So imagine a Democrat, a Republican, and an Independent
running against each other. Then a well regarded independent could win with only 25% backing. 

How?  Democrats would rank the Democratic candidate first, the Independent second, and the hated
Republican third. Republicans would do the same, except putting their candidate on top, with the hated
Democrat last. Independents would rank their candidate first and split their second and third choices
between the Democrat and the Republican (so each would get an average of 1.5 points per ballot). Then if the
Democrats and the Republicans split the vote with 37.5% each, the number of points counted for the
Democrat would be 3*.375 + 1*.375 + 1.5*.25 = 1.875 times the size of the electorate. The Republican would
have the same point total, whereas the Independent would win with 2*.375 + 2*.375 + 3*.25 = 2.25 times the
size of the electorate.
(Continue reading)

DNOW1 | 6 Sep 07:56 2014
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Top 5 P.R. method 26 Aug 2014

The gerrymander CRISIS in the U.S.A. is N-O-W.
Advanced P.R. will require a bit of public education -- regardless of the armies of math MORONS in the courts, in legislative bodies and esp. in the brain dead media and polisci depts in colleges and universities.
The top [5] below is of course arbitrary -- BUT something MUST BE done to get SOME sort of P.R. into the U.S.A. before the gerrymander robot party hacks [aka powermad OLIGARCHS] start Civil War II and/or World War III.
--------
Reality check -- The U.S.A. is as *democratic* as a rock on Mars --
 
i.e. Democracy is *ALMOST* gerrymander D-E-A-D in the U.S.A.
-----   
AUTOMATIC ANTI-Democracy indirect minority rule in all legislative bodies having single member districts (subareas) since 4 July 1776 -- with or without intentional gerrymanders --

-- BOTH houses of the U.S.A. Congress, ALL houses of ALL 50 State legislatures and many, many local govt legislative bodies (whole or part). 

INTENTIONAL Gerrymanders (based on prior election results) =

(A) The most political enemies possible are PACKED into the fewest gerrymander districts possible = political concentration camps.

(B) The rest of the area is CRACKED into friendly gerrymander districts -- with the friendly party hack candidates trying to get a majority / plurality of the votes in such districts -- at least 55 percent to be in a *safe seat* district -- i.e. a *safe* 10 percent winning margin [NOT so safe after the 2006-2008-2010 *wave* elections ???].

Results --

1. Half [a plurality - near 1/2] of the votes in a bare majority [1/2 plus 1] of the gerrymander districts [political concentration camps] for 1 party control = about 25 percent ANTI-Democracy indirect MINORITY RULE in ALL 50 States.

1/2 votes x 1/2 gerrymander districts = 1/4 CONTROL = pre-school STONE AGE minority rule math -- with or without intentional gerrymanders.

Much, much worse minority rule math in primary elections -- with the winners elected in the gerrymander districts in general elections.

2. UNEQUAL votes for each gerrymander district winner -- i.e. a de facto POWERMAD legislative monarch in each political concentration camp.

3. UNEQUAL total votes in each gerrymander district -- i.e. political concentration camp.

See ALL of the SUPER-MORON gerrymander math opinions in Vieth v. Juberlier, 541 U.S. 267 (2004) [PA] and L.U.L.A.C. v. Perry, 548 U.S. 399 (2006) [TX] due to MANY, MANY, MANY lawyer and amicus prof MORONS

-- unable to detect the above 3 math items in their New Age ignorant MORON brains

-- and especially the district AREA FIXATION in gerrymanders -- i.e. regardless of the number of ACTUAL voters in each gerrymander district ON ELECTION DAYS - regardless of any obsolete Census stats.

http://en.wikipedia.org/wiki/Gerrymandering

Each gerrymander is an Act of W-A-R against REAL Democracy.

The persons making the gerrymanders are ANTI-Democracy W-A-R criminals.

Again -- there is AUTOMATIC 25 percent indirect minority rule just by having districts.

Result -- the business-as-usual nonstop brain dead ANTI-Democracy minority rule gerrymander *politics* in the Congress and ALL States in the U.S.A. since 4 July 1776 -- i.e. gerrymander monarchs / oligarchs making special interest gang monarchy / oligarchy laws.
------
Computerized minority rule gerrymanders 2010 Census

http://www.caliper.com/mtredist.htm

http://www.caliper.com/Redistricting/state_edition.htm

Anything new and different since the 1964-1966, 1972, 1982, 1992 and 2002 minority rule gerrymanders -- except even better and better ANTI-Democracy computerized gerrymander programs to even better and better identify the political prisoners (i.e. Electors-Voters) in each political concentration camp (i.e. gerrymander district) using the 2010 Census stats in 2011-2012 ???
---------
ATTACK the ANTI-Democracy gerrymander systems in the media and the courts.

U.S.A. Const. Art. IV, Sec. 4 [Republican Form of Government -- NO monarchy / oligarchy (minority rule) regimes allowed to control a State directly or indirectly] and 14th Amdt, Sec. 1 [Equal Protection Clause].

See about 25 paragraphs in the 1787-1788 Federalist about the RFG in Art. IV, Sec. 4 --

I.E. RFG starts with D and ends with Y -- direct or indirect.

REAL Democracy begins at home.

*******
SAVE Democracy NOW 26 Aug 2014
   Current ANTI-Democracy gerrymander math in many governments in the U.S.A. --
1/2 (or less) votes x 1/2 (bare majority of) rigged pack/crack gerrymander districts (concentration camps) = 1/4 (or less) CONTROL indirectly.
   Blatant subversions of USA Const. Art. IV, Sec. 4 (Republican Form of Government) and 14th Amdt, Sec. 1 (Equal Protection Clause).
-------------------------------
Basic Democracy Reforms
26 Aug 2014  [optional language]
1. ONE election day. NO caucuses, primaries and conventions.
2. Proportional Representation in all legislative body elections. ALL voters get represented with BOTH majority rule and minority representation = DEMOCRACY.
3. NONPARTISAN nominations and elections of all elected executive officers and all judges.
------------------------------
Sec. 1. An election shall only be held on [date] of each year [(except for recall elections)].

Sec. 2. (1) All elected officers of any type shall be registered Electors in the election area involved in addition to any other qualifications in this constitution.
(2) All election laws and districts shall exist by [210] days before the election involved.
(3) No change in any election area shall reduce the terms involved.
(4) Any incumbent seeking re-election to the same office shall file an affidavit of candidacy provided by law by [203] days before the election.
(5) The names of other candidates shall by law be put on the ballots by (a) nominating petitions signed by Electors in the area involved equal to [0.2] percent of the number of Electors who voted at the last regular election [for governor] in such area and filed by [98] days before the election, or (b) filing fees equal to such [0.2] number multiplied by a uniform money amount and filed by [196] days before the election.
(6) Each Elector may sign 1 or more petitions for the same office.
(7) No filing shall be withdrawn.

Sec. 3. (1) The Electors shall elect the members of each legislative body for [1] year terms.
(2) As nearly as possible, each legislative election district shall be 1 or more [local governments] or a part of 1 [local government] (using major roads and rivers for internal boundaries), have the same number of Electors who voted at the last regular election [for governor] and be contiguous and square.

Sec. 4. (1) Each legislative body candidate shall receive a list of all other candidates in all districts by [56] days before the election.
(2) Each candidate shall rank such all other candidates (using 1 (highest), 2, etc.) and file such list by [49] days before the election.
(3) The lists shall be made public on the next day.
(4) If a valid list is not filed, then the candidate’s name shall be removed from the ballots.

Sec. 5. (1) Each Elector may vote for 1 candidate for each legislative body.
(2) The [5] candidates getting the most votes in each district shall be elected.
(3) The votes for each losing candidate shall be moved to the elected candidate in any district who is highest on the losing candidate’s rank order list.
(4) Example- 100 Votes. Elect 5.
A 20 Elected
B 18 Elected
C 15 + 9 = 24 Elected
D 13 + 8 = 21 Elected
E 10 + 7 = 17 Elected
X 9 - 9 = 0 Loses, Votes to C
Y 8 - 8 = 0 Loses, Votes to D
Z 7 - 7 = 0 Loses, Votes to E
Total 100
(5) Each member shall have a voting power in the legislative body equal to the final votes that he/she gets.
(6) A fractional part of a legislative body shall mean the members having such fractional part of the total voting powers.

Sec. 6. (1) A legislative body candidate or member may file a written rank order list of persons to fill his/her vacancy (if any) which shall be made public immediately.
(2) The qualified person who is highest on the list shall fill such vacancy.
(3) If the preceding does not happen, then the legislative body shall fill such vacancy with a person of the same party (if any) immediately at its next meeting.
[i.e. NO more vacancy special elections for legislators.]

Sec. 7. The Electors shall elect all elected executive officers [(at least a chief executive, a clerk and a treasurer)] in each government for [1] year terms and all judges [for [6, 4 and/or 2] year terms as provided by this constitution and law] at nonpartisan elections.

Sec. 8. (1) Each Elector may vote for 1 or more candidates for each executive or judicial office (including 1 write-in vote for each position).
(2) The candidate(s) getting the most votes shall be elected (for the longest terms respectively).
[This is the Approval Voting method.]

Sec. 9. Terms of office involved shall end on election days and start the next day.
[To END after election lame duck stuff. Elections would use ALL paper mail ballots to be counted not later than Election days.  See Oregon elections.]
---------
Advanced (more complex) P.R. would have Condorcet head to head math (using Number Votes) and YES/NO votes as a tiebreaker.
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Kristofer Munsterhjelm | 3 Sep 20:10 2014
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Whoops! Correction to Statistical Condorcet

Apparently the unconstrained MLE for the multinomial distribution with 
given probabilities isn't the Sainte-Laguë or Webster apportionment, but 
the D'Hondt or Jefferson apportionment[1].

This came as quite a surprise to me, given that the chi-squared and 
G-tests are claimed to approach the exact test as n goes to infinity. I 
may look into this in detail later, but I suspect the situation is that 
although the exact test value, call it x, and the G-test value, call it 
y, obey lim n->inf x_n-y_n = 0, for any finite n, the exact test will 
give the D'Hondt assignment a greater value (more likely draw) than the 
Sainte-Laguë one, whereas it's the other way around for the G-test (or 
chi-squared test).

I am not a formal statistician, though! And since I got the implications 
of the convergence wrong, I might be wrong about this as well.

For clarification purposes, letting s be the number of seats, the exact 
test for the multinomial distribution is: given a draw vector x, (i.e. 
so many of x_1, so many of x_2, etc) and a probability vector p = (p_1, 
p_2, ...), and the multinomial pmf P

Pr(x) = sum [for all y so that P(y; s, p) <= P(x; s, p)] P(y;s,p)

And letting s be the number of seats, define chi-squared test statistic as

chi(x, p) = SUM i=1...n (x_i/s - p_i)^2/(p_i)

Then, say, for the following votes: (10, 9, 8, 5, 4) and 5 seats, we have:

p-vector: 0.28, 0.25, 0.22, 0.14, 0.11

Sainte-Lague: (1, 1, 1, 1, 1)
D'Hondt:      (2, 1, 1, 1, 0)

Exact test value for Sainte-Lague: 0.899
Exact test value for D'Hondt: 1.0

multinomial pmf for the Sainte-Lague assignment: 0.028
multinomial pmf for the assignments with greater probability than this:

0.03234 for [1, 2, 1, 1, 0]
0.03622 for [2, 1, 1, 1, 0]
0.03234 for [2, 2, 1, 0, 0]

But the chi-squared statistic for Sainte-Lague is 0.13403 while the one 
for the D'Hondt apportionment is 0.19896, thus ranking the former higher 
than the latter.

This is true even for large s, e.g.:
	p = (0.3786, 0.245265, 0.1846, 0.06637, 0.06583, 0.059335)
	150 seats
	Sainte-Lague: [56, 37, 28, 10, 10, 9]
	D'Hondt: [57, 37, 28, 10, 9, 9]
	pmf for Sainte-Lague: 1.64*10^-5
	pmf for D'Hondt: 1.66*10^-5
	chi-square for Sainte-Lague: 0.00012
	chi-square for D'Hondt: 0.00058

-

Of course, if you like D'Hondt (for stability reasons or otherwise), you 
don't need to do anything to Statistical Condorcet to fix the above. 
Because it's Condorcet-based, it should also favor compromise parties 
rather than parties that get large numbers of first preference votes, so 
it is better than ordinary D'Hondt in that respect.

But if you don't, then the elegance of maximizing the pmf falls. So we'd 
have to find some way of using, say, the global optimality properties 
mentioned in http://rangevoting.org/Apportion.html directly. But this is 
tricky because they are all minimization properties, which means that 
the optimizer might just decide to set zero voters to participate and 
thus get a perfect zero every time.
That is again something to investigate later. Perhaps taking the area of 
the chi-squared distribution above the point given by the chi-squared or 
G-test would work: that turns it into a maximization problem again. But 
since the cdf for chi-squared involves gamma functions, optimizing that 
might be rather difficult.

Alternatively, we might go deeper. Why choose Sainte-Laguë to begin 
with? Because it's unbiased: it doesn't consistently favor small or 
large parties (and, because it's a divisor method, it has certain 
favorable properties we'd like to carry over). So find something that is 
unbiased. But the problem with that is that we might lose the "reduction 
to Webster when everybody plumps" property.

-

[1] I uncovered this when reading "A fast and simple algorithm for 
finding the modes of a multinomial distribution" by White and Hendy. It 
gives an algorithm for finding a mode of the multinomial, i.e. an 
apportionment that maximizes the exact test value. The paper is 
paywalled, but the algorithm is essentially a combination of Jefferson 
and D'Hondt: first they get a Jefferson solution for a number of seats 
that's close enough to the number of seats specified, and then they run 
D'Hondt either forwards or in reverse until they get the number of seats 
you want. The authors don't appear to recognize the solution as D'Hondt, 
though.
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Kristofer Munsterhjelm | 31 Aug 12:08 2014
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A simple Random Ballot proportional method

And here's a simple method I thought of for a multiwinner method. Would 
it be any good?

- Draw k assemblies using Random Ballot.
- Gather everybody who were selected in at least one of these draws, and 
set a deadline.
- If, after negotiations, at least 90% (or some high supermajority) of 
the gathered people agree on one of the k assemblies drawn, that outcome 
is chosen.
- Otherwise, if the deadline passes without agreement, draw another 
assembly using Random Ballot. That outcome is then chosen.

The idea is to exclude unlucky draws by using a negotiation phase. Yet 
there's little incentive to stall in the hope of getting a favorable 
outcome to oneself, because the post-deadline default isn't status quo 
but simply another random ballot council.

I suppose the main risk would that not enough people agree and then the 
final outcome turns out to be quite disproportional due to bad luck. The 
risk would be greater for smaller assemblies. Perhaps it could be 
lessened by running n different instances of the above in parallel, and 
as long as one of them decide upon an outcome, that outcome is picked. 
(If multiple do so, draw one at random.) But I'd have to consider it in 
greater detail to find out if that would be proportional.
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Kristofer Munsterhjelm | 30 Aug 18:06 2014
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Statistical Condorcet: Combining Schulze STV and Webster

Some days ago, I thought more about the relation of chi-square to the 
Sainte-Lague index and Webster as a MLE for the multinomial (for large 
seat assemblies), and after considering this further, I think I have 
found a way to combine Schulze STV and Webster to make a more fair party 
list method. Unfortunately, unless the structure of the thing permits 
massive pruning, it will be much too slow to run on a national scale. 
But perhaps it could be used in local elections.

The method goes like this: The meta-system is like Schulze STV. Define a 
contest function c(sA,sB) where sA and sB are sets of candidates that
differ from each other by just one candidate. Contests between sets that 
differ by more than one candidate are handled through strongest path, as 
in ordinary Schulze STV.

Since voters vote for parties, a contest may also contain numerous 
copies of the same "candidate". For instance, [AAAB] is a set with 3 
members from party A and one from B.

The main difference between this method and Schulze STV is in what c(sA, 
sB) is. Let sA and sB be council assignments that differ by a single 
candidate which we'll call C. C is present in sB but not in sA, so c(sA, 
sB) returning a higher score means sA is better than sB.

As in Schulze STV, in a given contest, each voter may give his vote to
any candidate he prefers to C. But how is this assignment to be guided? 
Well, that's where the difference comes in. Let x_j be the number of 
seats given to the jth party in the set sA.
Let f(x_1, ..., x_n, n; p_1, ..., p_n) be the multinomial pmf for n 
draws where the probability of drawing an item from category j is p_j, 
and x_j is the number of items drawn. Let p_j be the fraction of the 
voters' support that goes to the jth party. Then the voter-party support 
assignment is done so as to maximize f. So in this particular contest, 
the voters are engaging in a kind of maximum-likelihood cumulative vote 
DSV against C.

Some voters may not be able to contribute to this - for instance, if
they rank C on top. Let nv be the number of voters who did contribute.
Then c(sA, sB) = nv * f(x_1, ..., x_n, n; p_1, ..., p_n).

There is one other quirk to iron out. Since parties may have multiple
candidates in the running, C might be a member of a party that's also 
present in sA. In that case, since voters directly vote for parties, 
they are also allowed to support the party C is a part of if sA contains 
at least one member of that party. This doesn't directly help C because 
if the supporters of C's party were to dump too much support into that 
party, the fit that is optimized by f would decrease. Yet it's only 
permitted if at least one candidate of that party is present on the left 
side; otherwise, single-winner won't reduce properly. (It can also be 
seen by considering party support for A>B>C as 
A1>...>An>B1>...>Bn>C1>...>Cn and then using ordinary Schulze STV rules)

====

Note that it's conceptually easy to alter this system to take other
factors into account. Just alter the distribution and the pmf. For 
instance, if you want to incorporate that some parties may only have a 
few members (not enough to fill the council), then replace the 
multinomial with the multivariate hypergeometric distribution.

Also, the method above converges to Sainte-Lague/Webster when everybody
plumps for one party each, and the council size is large. This is 
because Sainte-Lague/Webster optimizes the Sainte-Lague index, which, 
through its connection to the chi-squared test, finds the council that 
optimizes f above when the council size is large enough.

The mathematical simplicity of the thing might mean that one can 
optimize it to run on large instances. In particular, dealing with it on 
a candidate by candidate basis rather than a party-by-party basis is 
designed to make full use of excess votes so they may add up to give a 
seat to a compromise party. Perhaps one could determine the number of 
safe seats for each party in a per-party manner and then hone the result 
afterwards.

One could also imagine an Approval variant of the concept: voters 
approve of one or more candidates or parties. Then the method picks the 
council that maximizes nv * f as above where each voter's support is 
distributed over the candidates or parties he approved, cumulative 
voting style. But I have a hunch that such a method would reduce to 
Monroe's method or a variant of it.

As for applying MJ to this idea... perhaps robust estimators? I don't know.

I could write something about how to find the optimal vote supports as 
well, but this post is long enough. Tell me so if you think I should. 
The short of it is that it comes down to optimizing a weighted sum of 
logarithms under linear constraints.
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Jameson Quinn | 25 Aug 23:47 2014
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Fwd: Empirical voting experiment: first numbers



2014-08-22 15:44 GMT-04:00 Kristofer Munsterhjelm <km_elmet <at> t-online.de>:
On 08/22/2014 01:05 AM, Jameson Quinn wrote:
Here I am surprised that Condorcet was considered more easy to understand than IRV. IRV advocates often say that the "remove the loser from the ballots and run again until someone gets a majority" is a very simple phrasing, and it certainly seems simpler than explaining Minmax. Did you explain the actual Minmax method or just Condorcet (the candidate that would beat every other candidate one-on-one wins)?

My explanation was just for Condorcet, though it did mention the word "minimax" in parentheses.


If you did explain Minmax itself, I am indeed surprised. I'm not going to complain, though! If the results are representative, that would be a serious counter to the "IRV is so easy" argument. The method itself is harder to understand according to your numbers, and if the advocates try to shift the goal to "as easy as 1-2-3", well, then Condorcet is just as easy because the front-end is the same.

I've actually contacted Fair Vote to get a new explanation for IRV. They've agreed to give me one, and I'll rerun a few sessions of the experiment with their wording, so that I can be accused of biasing the experiment with an intentionally poorly-written explanation.

...

However, that may also show that the Turkers aren't good at evaluating fairness. They consider Borda among the best, but we know about its extreme teaming incentive. OTOH, they also consider IRV in the Plurality class. I could understand either judgement, but both at the same time is quite unexpected.

Yes, you can certainly criticize their judgment here. Still, their perception is a fact we have to deal with.
 


I think these numbers are certainly interesting. To me, they clearly
bolster the case for joining forces behind approval activism, and for
eschewing IRV as an activist strategy; even for the majority of us who
see some other system as ultimately better than approval.

Right. Approval is a simple fix on Plurality, gives the best bang for the buck, and is easily understood. I think the greatest risk to Approval is a scenario where it is implemented, the chicken dilemma makes it dangerously unstable, and after having gone the wrong way a few times due to voters mis-anticipating each other, it is repealed in a similar way to how Burlington repealed IRV.

I'd agree that that's probably the biggest risk (besides "nobody pays any attention and it never happens"). How big is it? This experiment can help us see.

Note that this experiment is 100% in a chicken dilemma situation, with an unrealistically tiny number of voters, so insofar as the pathologies are avoided and/or accepted by the voters in the experiment, they'd be even less likely to be an issue in real life.


Maybe your strategy data will provide information on how realistic that scenario is.

It will certainly help us understand this question. I'll post about that as soon as I'm confident in my analysis.

Cheers,
Jameson

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Kristofer Munsterhjelm | 25 Aug 22:44 2014
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Re: Empirical voting experiment: first numbers

On 08/22/2014 01:05 AM, Jameson Quinn wrote:
> As many of you know, I've been running an online voting experiment using
> human subjects from Amazon Mechanical Turk. I'm using a 3-candidate,
> 9-voter "chicken dilemma" scenario, with factions of 4, 2, and 3 voters:
> Cand:        X  Y  Z
> Faction:
> Red   4      3  1  0
> Green 2      0  3  2
> Blue  3      0  2  3
>      Size     payoffs
>
> Each group of 9 gets assigned factions and a voting method, and runs the
> election 3 times, with monetary payoffs proportional to the numbers
> above in the last two rounds. Then they answer a survey about how fair,
> easy to vote, and easy to understand they found the method, plus some
> demographic questions.
>
> The voting systems I have tested so far include approval, Borda,
> Condorcet (minimax), IRV, MAV (medians), plurality, and score. I plan to
> also test SODA very soon.
>
> My analysis of the outcomes and strategies is not yet ready to share
> here. However, I have some numbers on the survey results. I used a
> Kruskall-Wallis comparison test, appropriate for Likert-scale results
> like these. Here are the results for the question "How easy was it to
> *understand* {{methName}} (the voting system you used)?":
>
>
>          trt    means   M
> 1 approval  231.2388   a
> 2 borda     229.7286   a
> 3 score     205.4898  ab
> 4 MAV       195.5761 abc
> 5 plurality 172.9545  bc
> 6 condorcet 165.3897   c
> 7 IRV       118.8281   d
>
> The important thing about the above table are the letters at the end. If
> two systems share at least one letter in common, the differences between
> those systems are not statistically significant. So we can safely say,
> for instance, that Approval and Borda are easier to understand than
> Condorcet, but we can't tell whether MAV is as understandable as the
> former or as confusing as the latter.

Here I am surprised that Condorcet was considered more easy to
understand than IRV. IRV advocates often say that the "remove the loser
from the ballots and run again until someone gets a majority" is a very
simple phrasing, and it certainly seems simpler than explaining Minmax.
Did you explain the actual Minmax method or just Condorcet (the
candidate that would beat every other candidate one-on-one wins)?

If you did explain Minmax itself, I am indeed surprised. I'm not going
to complain, though! If the results are representative, that would be a
serious counter to the "IRV is so easy" argument. The method itself is
harder to understand according to your numbers, and if the advocates try 
to shift the goal to "as easy as 1-2-3", well, then Condorcet is just as 
easy because the front-end is the same.

> Now, one thing in this table gives me pause: the result for plurality.
> Sure, approval and Borda are simple and intuitive for most people; but
> are they really more so than plurality? I suspect that this may reflect
> a flaw in my experiment. People assigned to plurality may, as they take
> the survey, still be very hazy on what "voting method" means. If all
> they've ever seen is plurality, it's hard for them to imagine something
> different. So they may effectively be answering a different question...
> something like, "How easy was it to understand this experiment as a whole?"
>
> However, I think that the rest of the numbers here are reliable. So
> clearly, IRV is hard to understand, and Approval and Borda are easy.
>
> Now, for the question "How easy was it to figure out *how to vote* in
> {{methName}}?":
>
>          trt    means  M
> 1 approval  214.8881  a
> 2 score     211.1531  a
> 3 borda     206.8429 ab
> 4 MAV       195.7717 ab
> 5 plurality 190.6970 ab
> 6 condorcet 167.6250  b
> 7 IRV       163.4531  b
>
> Generally, rated methods are at the top, ranked ones are at the bottom;
> though Borda may be (perceived to be) an exception. Again, we can't
> entirely rely on the number for plurality.

Seems reasonable. I find ranking easier than rating (less to worry about 
whether I got the scale wrong), but I might well be in the minority.

> Finally, the question "How *fair* did {{methName}} seem to you?":
>
>          trt    means  M
> 1 borda     209.0000  a
> 2 MAV       206.8587  a
> 3 approval  206.0571  a
> 4 condorcet 200.2721  a
> 5 score     189.3776 ab
> 6 plurality 158.3939  b
> 7 IRV       157.6094  b
>
> Again, Approval comes in among the best, and IRV among the worst.
> Surprisingly, score is not significantly better than plurality/IRV
> (though it also isn't significantly worse than the best). In this case,
> though we still have to take the plurality numbers with a grain of salt,
> I think it's fair to give them some credence. Even if people were
> answering the question "How fair did the results of this experiment seem
> to you?", it's not unreasonable to lay whatever unfairness they saw at
> the feet of plurality.

However, that may also show that the Turkers aren't good at evaluating
fairness. They consider Borda among the best, but we know about its
extreme teaming incentive. OTOH, they also consider IRV in the Plurality 
class. I could understand either judgement, but both at the same time is 
quite unexpected.

> I think these numbers are certainly interesting. To me, they clearly
> bolster the case for joining forces behind approval activism, and for
> eschewing IRV as an activist strategy; even for the majority of us who
> see some other system as ultimately better than approval.

Right. Approval is a simple fix on Plurality, gives the best bang for 
the buck, and is easily understood. I think the greatest risk to
Approval is a scenario where it is implemented, the chicken dilemma
makes it dangerously unstable, and after having gone the wrong way a few 
times due to voters mis-anticipating each other, it is repealed in a 
similar way to how Burlington repealed IRV.

Maybe your strategy data will provide information on how realistic that
scenario is.
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Jameson Quinn | 22 Aug 01:05 2014
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Empirical voting experiment: first numbers

As many of you know, I've been running an online voting experiment using human subjects from Amazon Mechanical Turk. I'm using a 3-candidate, 9-voter "chicken dilemma" scenario, with factions of 4, 2, and 3 voters:
           
Cand:        X  Y  Z
Faction:   
Red   4      3  1  0
Green 2      0  3  2
Blue  3      0  2  3
    Size     payoffs

Each group of 9 gets assigned factions and a voting method, and runs the election 3 times, with monetary payoffs proportional to the numbers above in the last two rounds. Then they answer a survey about how fair, easy to vote, and easy to understand they found the method, plus some demographic questions.

The voting systems I have tested so far include approval, Borda, Condorcet (minimax), IRV, MAV (medians), plurality, and score. I plan to also test SODA very soon.

My analysis of the outcomes and strategies is not yet ready to share here. However, I have some numbers on the survey results. I used a Kruskall-Wallis comparison test, appropriate for Likert-scale results like these. Here are the results for the question "How easy was it to understand {{methName}} (the voting system you used)?":


        trt    means   M
1 approval  231.2388   a
2 borda     229.7286   a
3 score     205.4898  ab
4 MAV       195.5761 abc
5 plurality 172.9545  bc
6 condorcet 165.3897   c
7 IRV       118.8281   d

The important thing about the above table are the letters at the end. If two systems share at least one letter in common, the differences between those systems are not statistically significant. So we can safely say, for instance, that Approval and Borda are easier to understand than Condorcet, but we can't tell whether MAV is as understandable as the former or as confusing as the latter.

Now, one thing in this table gives me pause: the result for plurality. Sure, approval and Borda are simple and intuitive for most people; but are they really more so than plurality? I suspect that this may reflect a flaw in my experiment. People assigned to plurality may, as they take the survey, still be very hazy on what "voting method" means. If all they've ever seen is plurality, it's hard for them to imagine something different. So they may effectively be answering a different question... something like, "How easy was it to understand this experiment as a whole?"

However, I think that the rest of the numbers here are reliable. So clearly, IRV is hard to understand, and Approval and Borda are easy.

Now, for the question "How easy was it to figure out how to vote in {{methName}}?":

        trt    means  M
1 approval  214.8881  a
2 score     211.1531  a
3 borda     206.8429 ab
4 MAV       195.7717 ab
5 plurality 190.6970 ab
6 condorcet 167.6250  b
7 IRV       163.4531  b

Generally, rated methods are at the top, ranked ones are at the bottom; though Borda may be (perceived to be) an exception. Again, we can't entirely rely on the number for plurality.

Finally, the question "How fair did {{methName}} seem to you?":

        trt    means  M
1 borda     209.0000  a
2 MAV       206.8587  a
3 approval  206.0571  a
4 condorcet 200.2721  a
5 score     189.3776 ab
6 plurality 158.3939  b
7 IRV       157.6094  b

Again, Approval comes in among the best, and IRV among the worst. Surprisingly, score is not significantly better than plurality/IRV (though it also isn't significantly worse than the best). In this case, though we still have to take the plurality numbers with a grain of salt, I think it's fair to give them some credence. Even if people were answering the question "How fair did the results of this experiment seem to you?", it's not unreasonable to lay whatever unfairness they saw at the feet of plurality.

I think these numbers are certainly interesting. To me, they clearly bolster the case for joining forces behind approval activism, and for eschewing IRV as an activist strategy; even for the majority of us who see some other system as ultimately better than approval.

I'll be sharing more numbers from this experiment as I have them ready. Also, if anybody here wants access to my raw data, I'd be happy to share; though of course, I'd want you to duly cite me if you use them for anything.

Cheers,
Jameson
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Jameson Quinn | 10 Aug 17:33 2014
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New paper: "~25% intrinsic-honest voters"

Kawai and Watanabe 2013 uses what looks to me to be pretty reasonable statistical methods and assumptions to estimate that voters for the Japanese House of Representatives (plurality single-member districts) are between 68% and 83% intrinsically strategic. Crucially, their methods can estimate the number of intrinsically "strategic" voters who end up voting honestly because that was the best strategy for them; it turns out that they estimate that 92-98% of intrinsically "strategic" voters in this sense actually vote honestly (that is, 95-98% of all voters are voting honestly in their data).

In order for their model to work, they need to be comparing the results of similar sub-regions (like precincts; actually, they use small municipalities) in different electoral districts. They must also assume that different candidates from the same party are essentially similar. There must also be sufficient votes for more than 2 parties for their model to work with. I doubt that they could have gotten a worthwhile estimate if they'd used US data.

I haven't read the paper carefully enough to be 100% sure, but based on a quick skim, it appears that they're assuming that the proportion of strategic voters is constant across ideological groups. That's probably necessary in order for their parameters to be identifiable/estimable for the data they have, and close enough to true for their results to be valid. However, this does mean that their work doesn't give any evidence one way or the other about how or whether strategic proportion varies across ideology.

Still, these numbers seem pretty reasonable to me. It's certainly useful to have an "empirical" number that I can plug into my VSE (aka BR) simulations. In particular, the most realistic scenarios are in the range from 75% strategic/25% honest, 50% strategic/50% one-sided strategic. That's a considerably narrower range than if you have to consider any combination of strategy, honesty, and one-sidedness. Someday soon I'll re-run my VSE sims focusing on these numbers and report what I find here. 

If anybody wants to read the PDF of this paper but doesn't have access, email me privately, and I'll send you a copy.


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robert bristow-johnson | 24 Jul 20:05 2014

Re: Voter strategising ability


Jameson, i am assuming you meant this for the list.

*wow*!  i would have never expected a real-world election where it would 
have mattered (in the outcome) whether it was a Shulze or Ranked-Pairs 
Condorcet method.  not that the Romania 2009 was *any* Condorcet, but 
was it STV and is the ballot data available?  otherwise i would ask, how 
do we know how be the Smith set was?

bestest,

r b-j

On 7/24/14 12:31 PM, Jameson Quinn wrote:
> I believe that cycles in real-life, contentious Condorcet elections 
> would be rare — on the order of 1-2% of elections, or a bit lower if 
> your data include "elections" with only one serious candidate. 
> However, when a Condorcet cycle does happen, it basically implies the 
> existence of at least three separate, more-or-less coherent factions 
> in the electorate. In that case, there's no particular reason that 
> there shouldn't be 2 "quasi-clone" candidates from one of those 
> factions. Thus I'd expect 4-member Smith sets to be almost a third of 
> all Smith sets larger than 1; not "*never*" as Robert suggests. In 
> fact, it is possible that Romania 2009 
> <http://rangevoting.org/Romania2009.html> had a 4-member Smith set.
>
>
> 2014-07-24 0:11 GMT-04:00 robert bristow-johnson 
> <rbj <at> audioimagination.com <mailto:rbj <at> audioimagination.com>>:
>
>     On 7/23/14 2:17 AM, Juho Laatu wrote:
>
>         On 20 Jul 2014, at 22:48, Kristofer
>         Munsterhjelm<km_elmet <at> t-online.de
>         <mailto:km_elmet <at> t-online.de>>  wrote:
>
>             Discussion about which kind of strategy is most likely to
>             happen can go on forever without data. Even if there is
>             data, it is quite easy and/or tempting to explain it away
>             as not being representative of what would happen under an
>             ordinary election. As long as that's possible, it's really
>             hard to convince someone who is worried about burial not
>             to be, or vice versa.
>
>         Unfortunately we don't have data from very many Condorcet
>         elections.
>
>
>     but the *data* doesn't give a rat's ass *how* it's counted or
>     tabulated.  can't we use the data from all ranked-choice elections
>     (which, in government, would be IRV or RCV or AV or STV or Hare)
>     and see how they would work out with Condorcet-compliant rules?
>      like we did for Burlington 2009.  that was a 4-way election close
>     enough that the Plurality (of 1st choice votes) winner, the IRV
>     winner, and the Condorcet winner were three different candidates.
>      and yet there was *no* cycle.  not even close to a cycle.
>
>     are there any other ranked-choice elections where media or
>     research could access the anonymous ballot data and see if there
>     would have been a cycle and then see how Shulze and Tideman and
>     Minimax and Kemeny would have been different?  i think we would
>     virtually never see a cycle.  and *more* than virtually, i think
>     we would *never* see a cycle with more than 3 in the Smith set.
>
>
>           And those elections have been quite non-competitive. So we
>         don't know very well what would happen (in different
>         societies) in competitive Condorcet elections.
>
>
>     but with ballot data in public records (and a little bit of
>     computer programming), we *should* be able to use all that IRV
>     ballot data and see what might happen in hypothetical
>     Condorcet-compliant elections.
>
>
>     -- 
>
>     r b-j rbj <at> audioimagination.com <mailto:rbj <at> audioimagination.com>
>
>     "Imagination is more important than knowledge."
>
>
>
>     ----
>     Election-Methods mailing list - see http://electorama.com/em for
>     list info
>
>

--

-- 

r b-j                  rbj <at> audioimagination.com

"Imagination is more important than knowledge."

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Jameson Quinn | 18 Jul 00:40 2014
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Request: Voting method blurbs for research

I am continuing my research on voting methods on Amazon Mechanical Turk. I'm currently looking at 8 voting methods:
approval, Borda, "Condorcet" (minimax), IRV, MAV (Majority Approval Voting; that is, Bucklin/Medians with ABCDF grades, breaking ties by above-median votes), plurality, score (0-10), and SODA.

The full protocol is outlined below, but one aspect is that, at the end of the experiment, each subject takes a quick survey, including their feelings about the voting system they used. I'd like to test out different system descriptions, to see if how the description impacts those feelings. So, I'd like blurbs to describe how you'd vote, and how votes are counted, in each of these systems. Of course, clarity and brevity are desirable.

So, I have my own blurbs already, but anybody else who can write alternate blurbs for me, I'd appreciate it. You don't have to cover all 8 systems if you don't want, but please do as many as you can; at least 5. You can use html trickery (collapsible sections, popups, tables, images), or not; however you want.

Here's how the experiment works, as described on the landing page:

Please do not take this HIT until you are told to. Press "Next" below when you're ready to.

Voting Experiment

This is an experiment on voting. 18 voters like you, divided into three groups, will decide between three options. Depending on the winning option, participants will earn extra pay of up to $2.40 (paid within hours as a "bonus" in AMT). The average pay for each participant will be at least $2.67, and depending on your luck and skill you may earn up to $4.00 in total. We will be running this experiment several times, using different voting systems, but you may only participate once.

In order to ensure enough simultaneous participants, we will be starting this experiment at a defined time. Until the countdown finishes, you can only view steps 0 (this screen) and 1 (consent form). Press "next" below to see the consent form and countdown. If you leave this window open, when the countdown completes, a sound will play ("voting experiment starting") and a "consent and join" button will appear. At that point, we will accept only 18 subjects per experiment run, on a first-come first-served basis. We ask that you only "accept" the HIT with Amazon after you are allowed into the experiment. (But we have made more than 18 HITs available for idiot-proofing.) Only the 18 workers allowed in will be paid for each run of the experiment.

Process

Step Name Time Payout Explanation

0

Overview

0-0.5 mins See an outline of the experiment (this stage).

1

Consent

0-2.5 mins Understand your rights, wait for the experiment to begin, and informed consent.

2

Scenario

1-15 mins Understand how much you and other voters will earn depending on which of the virtual candidates wins.Also, wait until the experiment fills up before proceeding (a sound will play when ready).

3

Election method practice

1-1.5 mins Learn and practice the election method to be used.

4

Practice results

1-0 mins See results of the practice election: the winner and how much you would have been paid.

5

Voting round 1

0.5-1 mins Vote. You will be paid based on results.

6

Payout round 1

0.5-0.5 mins $0-$1.20 See results of the round 1 election: the winner and how much you will be paid. (Payments will arrive within 1 day)

7

Voting round 2

0.5-1 mins Vote. You will be paid again based on results.

8

Payout round 2

0.5-0.5 mins $0-$1.20 See results of the round 2 election: the winner and how much you will be paid. (Payments will arrive within 1 day)

9

Survey

2-5 mins $1.60 4-5 simple questions each about:
  • you (gender, country, etc)
  • the voting system you used (on a 0-7 scale)
  • your general comments about the experiment

10

Debrief

0-0.5 mins Thanks for participating, and a simple explanation of what we hope to learn from this study. Submit job and receive base pay.

Total

7-16 mins $1.60-$4.00 The total time will mostly depend on how quick the other turkers in the experiment are. (15 minutes are allowed on step 2 for the experiment to fill, but that is usually much quicker.)

Press the button below to see the consent form and wait for the experiment to start.



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Gmane