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@yahoo.fr
Sent: Wednesday, June 22, 2016 1:05 AM
To: steve bosworth; election-methods@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[edithttps://en.wikipedia.org/w/index.php?title=Monotonicity_criterion&action=edit§ion=1
Using an example that applies to instant-runoff votinghttps://en.wikipedia.org/wiki/Instant-runoff_voting (IRV) and to the two-round systemhttps://en.wikipedia.org/wiki/Two-round_system, it is shown that these voting systems violate the mono-raise criterion. Suppose a presidenthttps://en.wikipedia.org/wiki/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
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.
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.
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.
My main distaste for median rating comes from my feeling that in most scenarios (i.e. availability of information on others' rating intentions) strategic-minded voters would only use the top and bottom ratings. This is because (as we see from the Later-no-harm example) median rating doesn't really offer guarantees about how your ratings will be used in relation to each other. The rating/grade values have no independent, practical meaning. If voters have this perception and respond with this behavior, then the method is just an overly complicated form of approval voting. In that case I'd rather just use approval, because it's clearer what's going on. (There are arguments about whether median rating voters would actually try to be so strategic, and about whether it would be bad if they did, but I will skip over that.)
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 might be another way of describing what is problematic about it.
I find a lot of methods tolerable, and I've designed a lot of methods too (most of them tolerable). I care about certain properties more than others, but the ones I like aren't even all compatible with each other. In general I feel that election methods should produce an outcome that would be plausible if the voters had been able to gather and vote in person, just as a legislature.
Kevin
De : steve bosworth <stevebosworth@hotmail.com>
À : "election-methods@lists.electorama.com" election-methods@lists.electorama.com; "stepjak@yahoo.fr" stepjak@yahoo.fr
Envoyé le : Lundi 27 juin 2016 18h00
Objet : [EM] The easiest method to 'tolerate'
Sent: Wednesday, June 22, 2016 1:05 AM
To: steve bosworth; election-methods@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[editUsing an example that applies toinstant-runoff voting (IRV) and to thetwo-round system, it is shown that these voting systems violate the mono-raise criterion. Suppose apresident 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’s1st IRVCOUNT | 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 IRVCOUNT | 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 Ballots35X10 +16X9=350+144=494494 divided by 51=9.762nd Set of Ballots32X10 +28X9=320+252=572572 divided by 60=9.53In 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=842842 divided by 90= 9.36S: 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 amono-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 orharmed 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
Election-Methods mailing list - see http://electorama.com/em for list info
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
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[1.2sqrt%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.
Instead, 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.
I have no hard proof that this is the case, and as I mentioned in
another post, there might very well be cultural differences. An
electorate accustomed to FPTP and the pervasive strategy there might be
more inclined to be strategic by default. I also seem to recall that the
parties in New York under STV almost immediately tried to game STV
through vote management, whereas according to Schulze's paper on vote
management, other countries' STV elections seem to be relatively free of
strategy.
This is another one of those questions that ultimately have to be
answered by practice. My point is that MJ has a pretty broad
not-affected threshold, but Range is more like the continuous function
above up to Approval, so if thresholds protect against strategy, MJ
would be better protected.
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
might be another way of describing what is problematic about it.
To repurpose a quote, "I do indeed concur. Wholeheartedly!". In my
opinion, criteria should say something about the results, not about how
the algorithm works.
It's always advantageous if the method also makes sense based on how it
works, but I'd rather have an opaque method with good compliance than
vice versa. Borda is very simple, but its extreme teaming incentive
makes it of little use in competitive elections.
That doesn't mean it's impossible to rephrase seemingly obvious
algorithm-based criteria to be more algorithm-agnostic. My post on
qualitative vote-wasting is an example of that.
If I recall correctly, Steve has stated that Nanson/Baldwin fail his
OCOV because Borda's points system takes later preferences into account.
However, it does "treat all preferences equally". If anything, IRV fails
to do so because it only looks at first preferences, yet IRV appears to
pass that OCOV criterion.
Hi Kristofer,
De : Kristofer Munsterhjelm km_elmet@t-online.de
À : Kevin Venzke stepjak@yahoo.fr; steve bosworth stevebosworth@hotmail.com; EM list election-methods@electorama.com
Envoyé le : Mercredi 29 juin 2016 6h19
Objet : Re: [EM] The easiest method to 'tolerate'
See also, from a Range perspective: http://rangevoting.org/MedianVrange.html
Unrelated: That link says Chris Benham invented MCA. I'm pretty sure that's wrong, and that it was either Forest, or else it didn't have a clear inventor. But I am struggling to find any archives for this list older than 2015. Hopefully we have not managed to lose nearly 20 years of posts...?
I'm trimming the below because I can't figure out how to make yahoo quote this:
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.
Instead, 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.
I have no hard proof that this is the case, and as I mentioned in
another post, there might very well be cultural differences. An
electorate accustomed to FPTP and the pervasive strategy there might be
more inclined to be strategic by default. I also seem to recall that the
parties in New York under STV almost immediately tried to game STV
through vote management, whereas according to Schulze's paper on vote
management, other countries' STV elections seem to be relatively free of
strategy.
If we are reading the same paper, that's not my impression of what it said. I thought it said that vote management in particular was widespread.
I don't disagree with your statements on median rating, but I don't quite see the point of messing around with a method like that, whose benefits are undone if human nature isn't what we think. Even if you manage to adopt it successfully for e.g. a school board election, who's to say it will continue to work properly as political stakes increase (e.g. moving on to adopt the method for a gubernatorial election). It seems hard to advocate.
Generally I don't think that much is based on culture when it comes to comparative politics. If something is at stake, one should look and keep looking for the practical reasons why actors do what they do.
Certainly I have an ulterior motive for thinking this way: If we can introduce roles for culture, or the inherent sincerity of voters, then it becomes even harder to create a meaningful simulation to try to forecast methods' properties.
It's always advantageous if the method also makes sense based on how it
works, but I'd rather have an opaque method with good compliance than
vice versa. Borda is very simple, but its extreme teaming incentive
makes it of little use in competitive elections.
I feel like the value comes not just from understanding how it works but being comfortable with how the method behaves as an agent for the voter. I've been wanting to write a post for several months on a few topics but I haven't found an excuse or even an overarching idea. This is one piece though. It's common to think of the method as an agent representing the entire electorate, which figures out the best possible result for everybody. But we could also try to imagine a given method's rules in terms of how we would define an agent representing an individual voter, such that the interactions of the agents produce the method's results. Think of the agents as legislators talking among themselves before making a final vote.
In this framework I find IRV pleasing and natural. Your agent advocates for a single best candidate and will abandon that candidate given the quite logical trigger that he's the weakest of whatever candidates remain. Everything seems great except, say, that the ultimate winner may lack a full majority and yet suffer a majority pairwise defeat that never gets explored in the process.
I feel like MinMax (etc.) doesn't compare so well. Say that the agents do a full set of round-robin voting to make the pairwise matrix. The potential for mischief and accidents related to LNHarm and LNHelp failures immediately occurs to me. Not only would some agents (ideally) not want to give up certain preference information prematurely, but the agents should also be suspicious of the information they receive from this process. Certain candidates will have a "superficial viability" and the lower preferences of their supporters are less likely to be something we want to look at.
Consider this standard cycle:
40 A>C
35 B>A
25 C>B
MinMax drops B>A, and people like me will historically say that if those A>C voters are lying, then it's the B>A voters responsibility and option to not give a preference for A, given that A is probably known to be viable ahead of time, and B's primary competitor. But maybe our agents should be somehow noticing the viability of A and saying to themselves that that C lower preference is suspect as long as A is in the running. Maybe it's C>B that should be thrown out. I haven't explored the implications of this idea though, or fully defined it even.
There are obvious reasons why we wouldn't want to just use first preferences to tell us about apparent viability. But the first preferences are the ones we can definitely trust. If we were to accept that as important (even if just for sake of argument) I wonder if it would lead somewhere.
Just a tangent.
Kevin
On 07/01/2016 12:44 AM, Kevin Venzke wrote:
Hi Kristofer,
De : Kristofer Munsterhjelm km_elmet@t-online.de
À : Kevin Venzke stepjak@yahoo.fr; steve bosworth stevebosworth@hotmail.com; EM list election-methods@electorama.com
Envoyé le : Mercredi 29 juin 2016 6h19
Objet : Re: [EM] The easiest method to 'tolerate'
See also, from a Range perspective: http://rangevoting.org/MedianVrange.html
Unrelated: That link says Chris Benham invented MCA. I'm pretty sure
that's wrong, and that it was either Forest, or else it didn't have a
clear inventor. But I am struggling to find any archives for this list
older than 2015. Hopefully we have not managed to lose nearly 20 years
of posts...?
http://permalink.gmane.org/gmane.politics.election-methods/184
says it's Forest.
I'm trimming the below because I can't figure out how to make yahoo quote this:
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.
Instead, 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.
I have no hard proof that this is the case, and as I mentioned in
another post, there might very well be cultural differences. An
electorate accustomed to FPTP and the pervasive strategy there might be
more inclined to be strategic by default. I also seem to recall that the
parties in New York under STV almost immediately tried to game STV
through vote management, whereas according to Schulze's paper on vote
management, other countries' STV elections seem to be relatively free of
strategy.
If we are reading the same paper, that's not my impression of what
it said. I thought it said that vote management in particular was widespread.
I must have remembered incorrectly. On a second reading of the paper
(http://m-schulze.9mail.de/schulze2.pdf), I see that he gives general
examples where the voters learn to manage their votes. I was thinking of
the more specific examples he gave in sections 3.1-3.2. where he found
no evidence of Woodall free riding in the Cambridge School Council
elections and no evidence of Hylland free riding (under certain
assumptions) in the same ballot data. However, in section 3.3. Schulze
also says:
On the other side, we quoted several empirical papers on STV that
demonstrate that Hylland free riding is a frequently used strategy (Berger,
2004; Harris, 1930; Johnston, 2000; Pilon, 1994).
and in section 4, he gives examples of vote management in various
countries where STV has been used. So I was wrong; I must have only
remembered the Council free-riding examples.
I don't disagree with your statements on median rating, but I don't
quite see the point of messing around with a method like that, whose
benefits are undone if human nature isn't what we think. Even if you
manage to adopt it successfully for e.g. a school board election, who's
to say it will continue to work properly as political stakes increase
(e.g. moving on to adopt the method for a gubernatorial election). It
seems hard to advocate.
Generally I don't think that much is based on culture when it comes
to comparative politics. If something is at stake, one should look
and keep looking for the practical reasons why actors do what they
do.
Certainly I have an ulterior motive for thinking this way: If we can
introduce roles for culture, or the inherent sincerity of voters, then
it becomes even harder to create a meaningful simulation to try to
forecast methods' properties.
Yes, I understand that, and I would be inclined to believe that voters
generally won't employ strategy in the kind of thresholded utility
setting I mentioned in the previous post (independent of culture). I'm
mostly mentioning culture because my inclination seems to be greatly at
odds with, say, Ossipoff's. He focuses a lot on compromising strategy,
as well, which seems (sort of) to be based on how prevalent
lesser-of-two-evils voting is in the US. Also, Norway uses party list PR
and I have the impression that tactical voting isn't really a thing here
when talking about parties above the threshold, even though
Plurality-based party list PR has a compromise incentive between seats.
So I could be wrong about culture playing a part. But then some other
explanation has to account for my observations, or I have to be wrong
about some of them as well.
If, on the other hand, voters generally do strategize in threshold
scenarios where there's nothing to lose or gain until a certain level of
strategy, then we're in rather more trouble. One could easily argue that
Condorcet would lead to inferior outcomes because voters would betray
their favorites in that manner. See e.g.
http://rangevoting.org/IRVStratPf.html :
"Strengthening: If could, however, be argued that if the CBA voters are
convinced C cannot win, then their betrayal by switching to BCA cannot
hurt them but with 8.78% probability will help them. I.e, if convinced C
cannot win, then this betrayal is a strategically sometimes-wise and
never-unwise move with 100% probability. "
It's always advantageous if the method also makes sense based on how it
works, but I'd rather have an opaque method with good compliance than
vice versa. Borda is very simple, but its extreme teaming incentive
makes it of little use in competitive elections.
I feel like the value comes not just from understanding how it works
but being comfortable with how the method behaves as an agent for the
voter. I've been wanting to write a post for several months on a few
topics but I haven't found an excuse or even an overarching idea. This
is one piece though. It's common to think of the method as an agent
representing the entire electorate, which figures out the best possible
result for everybody. But we could also try to imagine a given method's
rules in terms of how we would define an agent representing an
individual voter, such that the interactions of the agents produce the
method's results. Think of the agents as legislators talking among
themselves before making a final vote.
I see what you mean. IRV fits well as an individual DSV method. It's
much harder to do that with Condorcet because Condorcet is "global". I
imagine you could make a sort of probabilistic variant where you vote on
candidates in turn, legislature style, but it wouldn't be strategically
resistant.
E.g. something like
1000 times:
- order the candidates in random order
- ask "do you prefer X or Y" where X is the first candidate and Y is the
second - whoever wins is then compared to the third in line, and so on.
Pick the winner who won most often.
Then each agent participates by voting for the proper candidate in each
proposal, and the agenda is set to be random so that nobody has an
unfair advantage. But this would most likely reduce to Copeland and so
be full of ties.
Another option is BTR-IRV where the two last by Plurality count get an
elimination round and the pairwise loser is eliminated.
Bucklin could be considered a method where each voter has a reluctance
to voice his support for candidate X, and then as time passes, he adds
inn support he's more reluctant to voice until someone gets a majority.
I suppose that Borda-elimination doesn't feel as well-suited as an
individual DSV method because it's not clear why one is using Borda. If
IRV proponents are coming from Plurality, it makes sense to use
Plurality logic, even though from a logical perspective, it is not
altogether clear why Plurality should be good at finding losers if it's
bad at finding winners.
It's too bad we can't just search over the whole space of
"natural-sounding" rules and find the best one. What does or doesn't
constitute a natural-sounding or pleasing rule is not very clearly
defined, though I do think you're onto something with the DSV explanation.
There are obvious reasons why we wouldn't want to just use first
preferences to tell us about apparent viability. But the first
preferences are the ones we can definitely trust. If we were to accept
that as important (even if just for sake of argument) I wonder if it
would lead somewhere.
My brute force attempt to find strategically resistant Condorcet rules
for three-candidate elections did find something that used first
preferences.
If there's no cycle, elect the CW. Otherwise, let A>B>C>A and call the
candidate we're considering A without loss of generality. Then A's score
is fpA - fpC. The candidate with highest score wins.
First preferences can be important since you can't bury with them.
They're not all that important under honesty, however.
Hi Kristofer,
----- Mail original -----
De : Kristofer Munsterhjelm km_elmet@t-online.de
À : Kevin Venzke stepjak@yahoo.fr; EM list election-methods@electorama.com
Envoyé le : Vendredi 1 juillet 2016 10h48
Objet : Re: [EM] The easiest method to 'tolerate'
Unrelated: That link says Chris Benham invented MCA. I'm pretty sure
that's wrong, and that it was either Forest, or else it didn't have a
clear inventor. But I am struggling to find any archives for this list
older than 2015. Hopefully we have not managed to lose nearly 20 years
of posts...?
says it's Forest.
Ok, good that that is there.
Generally I don't think that much is based on culture when it comes
to comparative politics. If something is at stake, one should look
and keep looking for the practical reasons why actors do what they
do.
Yes, I understand that, and I would be inclined to believe that voters
generally won't employ strategy in the kind of thresholded utility
setting I mentioned in the previous post (independent of culture). I'm
mostly mentioning culture because my inclination seems to be greatly at
odds with, say, Ossipoff's. He focuses a lot on compromising strategy,
as well, which seems (sort of) to be based on how prevalent
lesser-of-two-evils voting is in the US. Also, Norway uses party list PR
and I have the impression that tactical voting isn't really a thing here
when talking about parties above the threshold, even though
Plurality-based party list PR has a compromise incentive between seats.
So I could be wrong about culture playing a part. But then some other
explanation has to account for my observations, or I have to be wrong
about some of them as well.
My inclination would be to ask whether the stakes are high enough. A party list's share of the vote is the main thing that will have any consequence, isn't it?
(I recognize that "stakes aren't high enough" would be an argument in favor of tolerating some vulnerability.)
If, on the other hand, voters generally do strategize in threshold
scenarios where there's nothing to lose or gain until a certain level of
strategy, then we're in rather more trouble. One could easily argue that
Condorcet would lead to inferior outcomes because voters would betray
their favorites in that manner. See e.g.
http://rangevoting.org/IRVStratPf.html :
Yes but I think there's a qualitative difference between Condorcet's compromise incentive and the way that individual ratings under median/mean rating mean nothing to the would-be strategist. Under Condorcet your relative rankings at least get counted. Under median rating you're just trying to pull numbers up or down, and you probably will never have adequate information to say e.g. that the rating you need a candidate to hit is 7/10.
It's always advantageous if the method also makes sense based on how it
works, but I'd rather have an opaque method with good compliance than
vice versa. Borda is very simple, but its extreme teaming incentive
makes it of little use in competitive elections.
I feel like the value comes not just from understanding how it works
but being comfortable with how the method behaves as an agent for the
voter. I've been wanting to write a post for several months on a few
topics but I haven't found an excuse or even an overarching idea. This
is one piece though. It's common to think of the method as an agent
representing the entire electorate, which figures out the best possible
result for everybody. But we could also try to imagine a given method's
rules in terms of how we would define an agent representing an
individual voter, such that the interactions of the agents produce the
method's results. Think of the agents as legislators talking among
themselves before making a final vote.
I see what you mean. IRV fits well as an individual DSV method. It's
much harder to do that with Condorcet because Condorcet is "global". I
imagine you could make a sort of probabilistic variant where you vote on
candidates in turn, legislature style, but it wouldn't be strategically
resistant.
E.g. something like
1000 times:
- order the candidates in random order
- ask "do you prefer X or Y" where X is the first candidate and Y is the
second - whoever wins is then compared to the third in line, and so on.
Pick the winner who won most often.
Then each agent participates by voting for the proper candidate in each
proposal, and the agenda is set to be random so that nobody has an
unfair advantage. But this would most likely reduce to Copeland and so
be full of ties.
I see the eliminations in IRV (in this DSV conception) as representing that the agent has permission to give up on a candidate and propose the next compromise. I think we can interpret that to exist in some sense in Condorcet methods (like when MAM locks defeats) but it fails somewhat for me that a 90:10 A>B win is taken as lack of viability for B without any comment intended on the viability of A. That seems different from IRV, and prone to mischief.
I think a method with constantly adjusting approval cutoffs would probably satisfy Condorcet and also make intuitive sense. Not a very novel idea I know.
Another option is BTR-IRV where the two last by Plurality count get an
elimination round and the pairwise loser is eliminated.
Bucklin could be considered a method where each voter has a reluctance
to voice his support for candidate X, and then as time passes, he adds
inn support he's more reluctant to voice until someone gets a majority.
Yes Bucklin works really well in this context. I probably prefer Bucklin to median rating purely because it (and its shortcomings) feel more clear.
I suppose that Borda-elimination doesn't feel as well-suited as an
individual DSV method because it's not clear why one is using Borda. If
IRV proponents are coming from Plurality, it makes sense to use
Plurality logic, even though from a logical perspective, it is not
altogether clear why Plurality should be good at finding losers if it's
bad at finding winners.
Actually I think Borda-elimination is fine in this context, and Borda alone is a fine estimate of strength. (That doesn't mean some of the side-effects are tolerable.) I feel similarly about Plurality: I don't think that an IRV advocate should say that Plurality is bad at finding winners but good at finding losers. I think he would want to say that Plurality is a meaningful measure and it's improved by taking the measure more than once.
It's too bad we can't just search over the whole space of
"natural-sounding" rules and find the best one. What does or doesn't
constitute a natural-sounding or pleasing rule is not very clearly
defined, though I do think you're onto something with the DSV explanation.
There are obvious reasons why we wouldn't want to just use first
preferences to tell us about apparent viability. But the first
preferences are the ones we can definitely trust. If we were to accept
that as important (even if just for sake of argument) I wonder if it
would lead somewhere.
My brute force attempt to find strategically resistant Condorcet rules
for three-candidate elections did find something that used first
preferences.
If there's no cycle, elect the CW. Otherwise, let A>B>C>A and call the
candidate we're considering A without loss of generality. Then A's score
is fpA - fpC. The candidate with highest score wins.
First preferences can be important since you can't bury with them.
They're not all that important under honesty, however.
Hmm I didn't remember the exact rule you found. I think the rule I just suggested is more like 0 - fpC. I can't see a "philosophical" reason not to bring in fpA though. And both methods elect B in my example.
Sort of wondering whether I could come up with an iterating method that would pick B, or if this burial idea is a completely separate thing. I feel like it is: i.e. if you just use a constantly adjusting approval cutoff (based on tentative winners) then there isn't a natural means of discovering which preferences might be bogus.
--
Totally unrelated but one thing I think about is two-round methods and whether we can do anything interesting with them, by "sharpening the questions" for voters. Here's a method that doesn't quite work for me, but it's really close:
1: Have a first round vote. Ideally this doesn't collect full rankings but is still a decent estimate at finding the best candidate. Approval is probably best. Call the winner X.
2: Don't eliminate anybody. Have a second round with an approval ballot and all voters do is vote for candidates they think are better than X. Alternatively they can check a box saying nobody is better than X. But X does not themselves receive any votes.
3: If anybody gets majority approval, the candidate with the most approval wins. Otherwise X wins. Effectively, X has an assumed approval score a bit less than the barest (mathematically possible) majority.
The (obvious) point over some other methods is that it's trying a little harder to find a majority. And more importantly, trying to make sure the winner wouldn't be voted down by any majority. It's also burial-proof (if you don't count first-round push-over as burial). We (try to) avoid majority cycle controversy by not collecting a full pairwise matrix.
Downsides are: by electing a candidate who beats the tentative winner, one can perceive a disadvantage to being the tentative winner, even if we don't know exactly what the sincere rankings were: A monotonicity issue. And secondly, I'm concerned that in sufficiently simple scenarios it could frequently happen that the second round just reverses the outcome of the first round, due to variations in turnout.
(I'd also say I'm disappointed that the second round's purpose could be defeated by chicken dilemma issues, and that even the second round considered independently can't be said to satisfy FBC.)
Kevin