[EM] Condorcet/Score

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[EM] Condorcet/Score

Curt

Hi, I was wondering what you all thought of the following reasoning.

1) Start with the assumption that for a single-winner election, if one candidate would defeat all others head-to-head, that candidate must be the winner. This requires the method to be Condorcet-compliant, and, I believe, disregards the later-no-harm criterion.

2) Acknowledge the “one-person one-vote” principle that means that if, in a two-candidate election, candidate A has 50 votes and candidate B has 49 votes, then candidate A *must* win, even if B’s voters are wildly more enthusiastic.

3) Acknowledge that score or range voting *does* have an advantage in recognizing overall utility society when taking into account voter enthusiasm - *if* the enthusiasm is scored/recorded honestly.

4) Acknowledge the occasional (and probably rare) phenomenon of A->B->C->A loops in Condorcet-style voting, which must be resolved somehow.

5) Accept that the presence of such loops is not a “bug”, but instead the measurement of some level of indecisiveness among the electorate, such that further voter data is required.

And end up with the following:

1) Present the ballots as score/range ballots
2) When tabulating, use the scores/ranges to deduce an ordinal (ranked-choice) ranking for each ballot, ignoring the scores/ranges otherwise
3) Use the rankings to determine if there is a Condorcet Winner. If so, STOP HERE. This makes the voting method Condorcet-Compliant.
4) If not, determine the Smith Set
5) Use the scores/ranges to determine the winner from within the Smith Set. This makes the method Smith-compliant.

I am not well-versed in voting criteria, but it seems to me this bypasses the worst criticisms of score/range voting, while also taking in account some of their advantage. While score/range voting is susceptible to strategic voting, there should be little incentive for a voter to strategically adjust their scores *to the point of changing their ordinal ranking*, due to the emphasis on finding the Condorcet Winner first. And so then, since people will be scoring/rating relatively honestly, greater social utility is met in the case where there is not a Condorcet Winner. Finally, we know that the winner is (ordinally) preferred over all other candidates outside of the Smith Set, making it Smith-compliant. Score/Range/Star voting are not Condorcet-compliant (nor Smith-compliant, I think), but this voting method is.

I conjecture that if scores/rankings were measured for all other Condorcet methods (and then similarly ignored to deduce ordinal rankings), this method would offer greater social utility as measured by the scores, by definition. And, I believe this is superior to pure range/score/star voting *when* starting with the axiom that the voting method must be Condorcet-compliant.

Thanks,
Curt

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Re: [EM] Condorcet/Score

robert bristow-johnson



---------------------------- Original Message ----------------------------
Subject: [EM] Condorcet/Score
From: "Curt" <[hidden email]>
Date: Fri, January 4, 2019 2:47 pm
To: "EM" <[hidden email]>
--------------------------------------------------------------------------

>
> Hi, I was wondering what you all thought of the following reasoning.
>
> 1) Start with the assumption that for a single-winner election, if one candidate would defeat all others head-to-head, that candidate must be the winner. This requires the method to be Condorcet-compliant, and, I believe, disregards the later-no-harm criterion.
>
> 2) Acknowledge the “one-person one-vote” principle that means that if, in a two-candidate election, candidate A has 50 votes and candidate B has 49 votes, then candidate A *must* win, even if B’s voters are wildly more enthusiastic.
>
> 3) Acknowledge that score or range voting *does* have an advantage in recognizing overall utility society when taking into account voter enthusiasm - *if* the enthusiasm is scored/recorded honestly.
>
> 4) Acknowledge the occasional (and probably rare) phenomenon of A->B->C->A loops in Condorcet-style voting, which must be resolved somehow.
>
> 5) Accept that the presence of such loops is not a “bug”, but instead the measurement of some level of indecisiveness among the electorate, such that further voter data is required.
>
> And end up with the following:
>
> 1) Present the ballots as score/range ballots
> 2) When tabulating, use the scores/ranges to deduce an ordinal (ranked-choice) ranking for each ballot, ignoring the scores/ranges otherwise
> 3) Use the rankings to determine if there is a Condorcet Winner. If so, STOP HERE. This makes the voting method Condorcet-Compliant.
> 4) If not, determine the Smith Set
> 5) Use the scores/ranges to determine the winner from within the Smith Set. This makes the method Smith-compliant.
>
> I am not well-versed in voting criteria, but it seems to me this bypasses the worst criticisms of score/range voting, while also taking in account some of their advantage. While score/range voting is susceptible to strategic voting, there should be little incentive for a voter to strategically adjust their scores *to the point of changing their ordinal ranking*, due to the emphasis on finding the Condorcet Winner first. And so then, since people will be scoring/rating relatively honestly, greater social utility is met in the case where there is not a Condorcet Winner. Finally, we know that the winner is (ordinally) preferred over all other candidates outside of the Smith Set, making it Smith-compliant. Score/Range/Star voting are not Condorcet-compliant (nor Smith-compliant, I think), but this voting method is.
>

it's not a bad idea.  i had, some time ago, thought of simply deriving ordinal ranking from the score ballot.

doing what you suggest (using Score Voting to resolve a Condorcet paradox or cycle) would require two passes over the voting data or, if it's a single pass, maintaining both the defeat matrix for ranked-choice/Condorcet and for Scoring later if necessary.

i think the Score ballot imposes a burden of tactical voting on the voter.  How much should a voter score their second choice?  (Approval Voting has a similar problem, when should a voter approve their second choice?)

Approval Voting (as well as FPTP) gets too little information from the voter, while Score Voting requires too much.  Voters aren't the same as Olympic judges at a skating competition.


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Re: [EM] Condorcet/Score

Magosányi Árpád
In reply to this post by Curt
I am thinking about similar lines. The preferential voting methods undoubtedly have a presentation problem: it is hard to sort a lot of candidates, especially on paper.
Cumulative/approval voting is easily presented, and can be used to give preferences (at least partially).
I would throw the following into the mix however:
- to avoid the effect tht rage voting reduces to plural voting when voters vote fully tactically (I know, that IRL they do not. not all, and not yet), I would use cumulative vote
- to handle not just the positive preferences, but also the negative ones, I would allow for negative votes.

So the ballot would look like:

Please distribute at most 6 marks at likes, and at most 1 mark at dislike..
likes  candidate   dislike
OOO candidate 1 O
OOO candidate 2 O
OOO candidate 3 O
...

the overall number of likes would be sum(1 to n) where n is the max likes per one candidate, and n < number of candidates.
number of dislikes would be similar, with n << number of candidates, probably only one.

This would be useable o reconstruct a partial preference. My suspicion is that psychology could prove that what someone actually knows for sure (if anything) is whom they prefer most and whom they dislike most), so not much information actually lost.
Using the preferences, a Condorcet method can be run.



Curt <[hidden email]> ezt írta (időpont: 2019. jan. 4., P, 20:47):

Hi, I was wondering what you all thought of the following reasoning.

1) Start with the assumption that for a single-winner election, if one candidate would defeat all others head-to-head, that candidate must be the winner. This requires the method to be Condorcet-compliant, and, I believe, disregards the later-no-harm criterion.

2) Acknowledge the “one-person one-vote” principle that means that if, in a two-candidate election, candidate A has 50 votes and candidate B has 49 votes, then candidate A *must* win, even if B’s voters are wildly more enthusiastic.

3) Acknowledge that score or range voting *does* have an advantage in recognizing overall utility society when taking into account voter enthusiasm - *if* the enthusiasm is scored/recorded honestly.

4) Acknowledge the occasional (and probably rare) phenomenon of A->B->C->A loops in Condorcet-style voting, which must be resolved somehow.

5) Accept that the presence of such loops is not a “bug”, but instead the measurement of some level of indecisiveness among the electorate, such that further voter data is required.

And end up with the following:

1) Present the ballots as score/range ballots
2) When tabulating, use the scores/ranges to deduce an ordinal (ranked-choice) ranking for each ballot, ignoring the scores/ranges otherwise
3) Use the rankings to determine if there is a Condorcet Winner. If so, STOP HERE. This makes the voting method Condorcet-Compliant.
4) If not, determine the Smith Set
5) Use the scores/ranges to determine the winner from within the Smith Set. This makes the method Smith-compliant.

I am not well-versed in voting criteria, but it seems to me this bypasses the worst criticisms of score/range voting, while also taking in account some of their advantage. While score/range voting is susceptible to strategic voting, there should be little incentive for a voter to strategically adjust their scores *to the point of changing their ordinal ranking*, due to the emphasis on finding the Condorcet Winner first. And so then, since people will be scoring/rating relatively honestly, greater social utility is met in the case where there is not a Condorcet Winner. Finally, we know that the winner is (ordinally) preferred over all other candidates outside of the Smith Set, making it Smith-compliant. Score/Range/Star voting are not Condorcet-compliant (nor Smith-compliant, I think), but this voting method is.

I conjecture that if scores/rankings were measured for all other Condorcet methods (and then similarly ignored to deduce ordinal rankings), this method would offer greater social utility as measured by the scores, by definition. And, I believe this is superior to pure range/score/star voting *when* starting with the axiom that the voting method must be Condorcet-compliant.

Thanks,
Curt

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Re: [EM] Condorcet/Score

Abd ul-Rahman Lomax
In reply to this post by Curt


On 1/4/2019 2:47 PM, Curt wrote:
Hi, I was wondering what you all thought of the following reasoning.

1) Start with the assumption that for a single-winner election, if one candidate would defeat all others head-to-head, that candidate must be the winner. This requires the method to be Condorcet-compliant, and, I believe, disregards the later-no-harm criterion.

Actually, you are starting with a prior assumption, perhaps several of them. You assume a deterministic voting system, you assume a fixed candidate list. Then "must be the winner" may allow a candidate to win without being specifically approved for that by a majority of the electorate, which is a basic principle of democracy for *any decision binding on the membership.* It's where democracy begins.

I have never seen a study of when and where this was abandoned. It is still followed in deliberative bodies

LNH is a voting system criterion, that, if passed, disallows compromise. Imagine neighbors voting to decide what colors to paint fences. Neighbor A has a favorite. The voting system they use satisfies LNH. LNH compliant systems must hide all lower preferences from consideration until the first preference is actually eliminated. Then and only then can another color be voted for. In fact, neighbors will probably use an ancient system, negotiation, and will seek supermajority, not mere majority. Majority is a fall-back position, but if majority decisions are not at least accepted at some level, the neighborhood will be in trouble.

People will agree, in real situations, that such a winner is not always the best choice. And this points to a possible fundamental voting system criterion: can the system distinguish preference level from acceptance, which is binary, and there is a simple way to do this with score voting, which is to define a particular score or above as the minimum acceptance level.

In promoting Approval Voting, votes have been called, no surprise, "approvals." "Do you approve of candidate A?" That is an ontological error, where "approve" has a narrow meaning, different from the emotional reaction. In a runoff voting system (which I argue is fundamentally necessary), approval means "do you prefer the election of this candidate over the election being repeated?" That is a binary choice.


2) Acknowledge the “one-person one-vote” principle that means that if, in a two-candidate election, candidate A has 50 votes and candidate B has 49 votes, then candidate A *must* win, even if B’s voters are wildly more enthusiastic.

Which, of course, makes sense only because we are accustomed to voting systems that don't consider preference strength, except in one way: turnout. Turnout is biased in some election by the level of preference the voter actually holds. "Wildly more enthusiastic" does not encompass the possibilities. How about "49 people are ready to destroy the organization if the candidate mildly preferred by 50 is elected?" Preference strength matters. Only if the two factions are similarly "enthusiastic" would choosing a bare majority candidate make sense. In reality, the probability is high that the best person for the office was not on the ballot. A simple vote-for-one ballot seems simple, but does not collect enough information to allow better social choices to be made.\

So, then, should B win? No, of course not, not just with that information. However, I suggest this basic principle, to make *and continue* any decision, majority approval is required. This can be expressed as a ratification or the lack of a motion for reconsideration.

3) Acknowledge that score or range voting *does* have an advantage in recognizing overall utility society when taking into account voter enthusiasm - *if* the enthusiasm is scored/recorded honestly.

This issue of "honesty" vastly distorts the reality. Voting is like tossing weights on a balance. Score voting is just voting, tossing weights on a balance. Generally, score systems do not reward reversal of preference, optimal strategy will rank candidates in order of preference, but, then, the decision of how to rate those candidates (equally or not, or with what difference in score) is made generally, and optimally,. according to the voters' estimation of the effect of the vote. There may be such a thing as absolute preference strength, but it's quite a complex issue. To test it requires some kind of metric. Bottom line and in practice, people have varying preference strength and it is expressed according to probabilities, not according to absolutes.

When there is a real-world consequence, affecting the voter, that leads the voter to make accept/reject choices, this can nail the score votes to a minimum of three levels. Suppose there is a score system allowing three ratings: Prefer, Accept, and Reject. "Prefer" has an obvious meaning, Accept means "prefer the election of this person to a repeated election," and Reject again has an obvious meaning: "I prefer another election."

Ballots, I suggest, as far as is practical, should collect preference information and acceptance information. So I would have a score ballot with enough rating resolution to allow meaningful preferences to be expressed. Below a certain level of preference strength, votes are not particularly meaningful. My general sense is that ratings of 0-9 would be quite adequate. Then 5 could represent acceptance. Because equal rating would be allowed, the voter would still have 4 acceptance levels and 6 rejection levels.

But such systems require very substantial voter knowledge and participation. There is a far easier solution that hybridizes voting with represented voting, first suggested by Charles Dodgson (Lewis Carroll) in the 1880s, for use with Single Transferable Vote, now called Asset Voting, the term invented, if I'm correct, by Warren Smith. More about that below.

4) Acknowledge the occasional (and probably rare) phenomenon of A->B->C->A loops in Condorcet-style voting, which must be resolved somehow.

Once we accept that an election can fail, which is standard democratic process in voluntary organizations, there is no "must be resolved." Does the voting system allow explicit acceptance, in addition to mere preference? If so, that is a possible resolution. This is approached and possibly implied by the use of a score ballot. This would be handled in a ranked ballot by having a dummy candidate called "Repeat the election," which the voter would rank at the appropriate position in the list of candidates.

And compared to Asset, it's all unnecessary complication, that perpetuates the isolation between voters and the collective. Asset creates public voters (I call them electors) and the collection of electors fully represents the entire voting electorate. The electors then make the necessary compromises, etc,. on behalf of the electorate. Contrary to what is often assumed, these are not necessarily "candidates" for the office. This is like the original U.S. electoral college, but the writers of the Constitution punted on voting system. It's clear that the intention was not, however, "pledged electors, from a slate pledged, and not even named on the ballot." It became that because of a loophole in the Constitution, allowing each state legislature to determine how the electors from each state would be chosen. Thus, in fact, the Electoral College ended up representing the States, not the voters. They did not factor for the development of the party system.

5) Accept that the presence of such loops is not a “bug”, but instead the measurement of some level of indecisiveness among the electorate, such that further voter data is required.
Indeed. What is missed is "a better list of candidates."

And end up with the following:

1) Present the ballots as score/range ballots
Score ballots allow ranking. If the score resolution is limited, not full ranking, but full ranking with small preference strength (or donkey voting in systems that require full ranking, as in some Australian elections) is largely meaningless. If there are as many ratings as candidates, it allows full ranking. Such ballots would collect valuable information, even if it is not used for the instant election. It could, for example, provide for ballot eligibility, it could affect campaign funding. I am opposed to public campaign financing (but in favor of measures that would reduce or even eliminate the need for major election spending, which are possible, and Asset would do it), but if there is such financing, ratings could affect it. At substantial cost and effort, information is gathered from the voting electorate, but it's primitive, black and white, unsophisticated.
2) When tabulating, use the scores/ranges to deduce an ordinal (ranked-choice) ranking for each ballot, ignoring the scores/ranges otherwise
Yes, basic in designing a hybrid system. This was proposed long ago.
3) Use the rankings to determine if there is a Condorcet Winner. If so, STOP HERE. This makes the voting method Condorcet-Compliant.

I would not stop there. I would require explicit approval. This can be easily specific on a score ballot as a particular rating. On a score 9 ballot, half rating would be 4.5 which can't be expressed, so 5 becomes the accepted rating level. The actual rules could be come quite sophisticated, with practice and experience. I would "err" in the direction of repeated election where there is doubt about the result.

I would have write-in votes be allowed in all elections (which is standard practice in many places in the U.S.), including run-offs. I would then use an "advanced ballot" for both a primary and a runoff. The runoff ballot would then have at least two candidates on it, plus write-in. Under some conditions, it might have three on the ballot.

A Condorcet winner, if not winning directly, would be on the runoff ballot, for sure. This is why "must win" is a Bad Idea. The runoff will test preference strength! If you voted for the CW, but it was a weak preference, you might not turn out to vote in runoff, because *you don't care enough to spend the time.* So the "enthusiastic" Score voting winner might well prevail. There are indications from study of runoff election results to indicate that this effect actually happens. A dark horse becomes the runner-up in a primary and then goes on to win in the runoff. That rarely happens with IRV.

4) If not, determine the Smith Set
5) Use the scores/ranges to determine the winner from within the Smith Set. This makes the method Smith-compliant.

The Score voting winner would also be on a runoff ballot.

If the Score winner is the same candidate as the Cordorcet winner, and if a majority of the electorate has also approved of the candidate, there is no runoff.

Then we start to deal with rarer situations: my view is that no election should complete without majority approval. A point to keep in mind, mentioned by Roberts' Rules of Order, is that repeating the election would allow new nominations. In fixed runoff systems, this is still respected by allowing write-in votes in the runoff. (and it has happened that a write-in candidate won a runoff.) Ah, but can a candidate win a runoff with a mere plurality? This is at the edge of democracy, and it's hazardous to discard the majority principle. But the example I know of, it was very clear that the winner was the choice of the electorate, given the obstacles she faced and overcame.

The runoff ballot should also allow multiple "accept" votes, in addition to ranking. This would allow a write-in to also express an opinion on the frontrunners.

Asset trumps all this complication. Asset shines with proportional representation, with the entire assembly being a single district, which, then allows flexible and full representation. I would expect that electors would mostly be elected locally, so they would, to that extent, represent districts. And then the Assembly would elect officers, i.e,. a parliamentary system, the officers serving at the pleasure of the public, expressed through the Assembly, elected by the Electoral College, each set representing a quota of votes, all traceable to electors, and voters know whom they voted for.

However, the Electoral College could also elect officers, single-winner. Simple. Ballots could even be vote-for-one, majority required. But there is no reason to avoid more sophisticated, more efficient ballot designs, expecially given that the electors are public voters. So the standard result that a decision can be moved for reconsideration by anyone who supported it can function (with a secret ballot, there is no way to know). A motion for reconsideration must be seconded and is then put to a vote immediately. No debate, no discussion. Thus every election must, in effect, be, at least, implicitly approved.

I am not well-versed in voting criteria, but it seems to me this bypasses the worst criticisms of score/range voting, while also taking in account some of their advantage. While score/range voting is susceptible to strategic voting, there should be little incentive for a voter to strategically adjust their scores *to the point of changing their ordinal ranking*, due to the emphasis on finding the Condorcet Winner first.
Right. Equal ranking must be allowed, though. It means "no *significant* preference.
 And so then, since people will be scoring/rating relatively honestly, greater social utility is met in the case where there is not a Condorcet Winner. Finally, we know that the winner is (ordinally) preferred over all other candidates outside of the Smith Set, making it Smith-compliant. Score/Range/Star voting are not Condorcet-compliant (nor Smith-compliant, I think), but this voting method is.

But it does not satisfy the generalized "negative majority criterion" (for lack of a better name, "if a candidate does not receive an acceptance vote from a majority of voters, the candidate cannot win.". Even though this is standard practice in deliberative bodies, voting systems theorists, designing voting systems criteria, have apparently neglected it.

Task for a student: how did we end up in this fix?

The most advanced voting system in current practice in the U.S. is runoff voting. It has a problem, for sure, center squeeze. Curt should look at Bucklin voting, which was almost what he wants. A Score ballot could be used for Bucklin. Bucklin was rejected, in the end, because not many voters in primary elections still using it, were adding additional approvals. It's obvious why. It was a friggin' *primary*. It was replaced by runoff voting, if I'm correct, instead of keeping the Bucklin ballot for the primary and using it to feed a runoff if there was no majority winner, they dropped the advanced ballot.

So FairVote is going around, killing the most advanced method in use (runoff voting), in favor of the "instant" version that then fails to allow flexibility in runoffs. Even with top-two runoff, the runner-up in the primary often wins, about a third of the time, whereas it is rare with "instant runoff." FairVote then argues that this result is "unfair," because of lower turnout in runoffs, which is a knee-jerk response that assumes there is something wrong with low *voluntary* turnout.

I conjecture that if scores/rankings were measured for all other Condorcet methods (and then similarly ignored to deduce ordinal rankings), this method would offer greater social utility as measured by the scores, by definition. And, I believe this is superior to pure range/score/star voting *when* starting with the axiom that the voting method must be Condorcet-compliant.

The Condorcet criterion is intuitively satisfying only in a world which does not consider *actual preference strength. The negative majority criterion is more fundamental. I agree that hybrid systems are the possible future of voting systems, but the fact is that very primitive voting systems work with the negative majority criterion respected.

For the present, the most obvious voting system reform is what I call "Count All the Votes." This slogan or name for it represents how simple the system is, it requires no ballot changes except a changed instruction. This is what is more commonly called Approval Voting, and it is a Score voting system, Score 1, i.e, votes from 0-1, with 0 being assumed if the voter does not mark the candidate. It is then a simple step to add more score levels, Score 2 having obvious meaning, as stated above. (but I defined a vote of 1 as being "accept." It could be neutral, an abstention, which then would be more likely to require a runoff.)

Asset's slogan could then ride on this: "Make All Votes Count." Asset wastes no votes, period.

Asset is radical, it would, my opinion, transform politics entirely, into the science of how we communicate, collaborate, and cooperate.

The system is the message.


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