[Election-Methods] Corrected "strategy in Condorcet" section

[Juho]

On Jul 29, 2007, at 20:09 , Abd ul-Rahman Lomax wrote:

> At 02:46 AM 7/29/2007, Juho wrote:
>>  > 49 A
>>  > 24 B
>>  > 27 C>B
>>
>> The numbers of this example are so unlikely to occur in real life
>> that I modified the example a bit to get values that would be more
>> probable. This was the first one that I found to be close enough to
>> be realistic (maybe not yet fully realistic, maybe there are others
>> that serve the strategic needs better).
>
> It's a bit difficult to judge what is "realistic" without looking  
> at real election data, and we are short of real data even from  
> polls, since most polls are asking the question "Who's your favorite?"
>
> I'm not familiar with what *is* known about real voting behavior,  
> beyond a few points. Real voters vote many different kinds of  
> ballots. In a large real election, there will be ballots that are  
> totally blank, and ballots with all choices filled in. Even if the  
> rules prohibit overvoting, there will be overvotes, and some of  
> them will be deliberate, either due to a misunderstanding of the  
> rules or a deliberate voiding of the vote. Faster than running back  
> and getting another ballot, and voters can be in a hurry to get  
> back to work or whatever. An absentee voter marks the ballot wrong  
> and, oops! Can't get another so easily....

Yes, in normal public elections people will vote in many ways,  
including ways that others may not even consider rational.

>
> Like many election examples, the imagined data has itself been  
> truncated. If we are showing actual vote counts, we are showing a  
> very small election, and small elections have different  
> characteristics than large ones. The possibility of ties or near- 
> ties is increased, for example, and this affects strategy. The  
> voters and candidates tend to know each other, and there is less  
> polarization.
>
> And if we are showing percentages in a large election, they'd  
> better not add up to 100% unless we are including all the  
> reasonable cases we would see. The first example is oversimplified,  
> for sure. Let's look at how Juho has extended it.
>
> I'm going to take Juho's example and edit it to add the complete  
> preferences, he omitted the equalities and I like to be explicit.  
> Truncating is the same as rating all the other candidates equal  
> last. I'm also spreading out the fields and putting them in columns  
> so that rank is clearly indicated
>
>> 30 A > B=C
>> 9  A > B   > C
>> 6  A > C   > B
>> 14 B > A=C
>> 8  B > C   > A
>> 2  B > A   > C
>> 25 C > B   > A
>> 5  C > A=B
>> 1  C > A   > B
>
> I'm now quoting Juho out of sequence.
>
>> I tried to keep the original number of first place supporters of each
>> candidate. => 49/24/27. But I had to assume that some C supporters
>> will truncate (since some B voters did so too) and as a result the
>> number of A supporters had to be dropped to 43. In order to make C
>> win B I donated these votes to C. => 45/24/31.
>
> What is truly odd about this is the high number of truncations from  
> B supporters. It's the third most common vote.
>
> Let's assume that the candidates are on some single axis. In major  
> elections, this is likely to be true, it is a simplifying first  
> assumption. In reality, there is more than one axis, and so  
> candidates who are, for an individual voter, close on one axis may  
> be far on another, and how the voter votes may thus seem  
> inconsistent. A otherwise-liberal who is morally opposed to  
> abortion, for example, may neglect the abortion axis except within  
> pairs where the candidates have the same position, in which case  
> the liberal-conservative axis comes into play.

Yes, a more detailed analysis should not rely on one axis only.

>
> Nevertheless, barging ahead with a single-axis assumption, who is  
> the centrist?
>
> Aside from sheer laziness -- and we've already selected out much of  
> that since truly lazy voters don't vote except where it is illegal  
> to not vote (a concept I detest, since not voting can be presumed  
> to be a vote equating all candidates, and there are non-coercive  
> methods of making sure that this is truly the case) -- truncation  
> indicates a strong preference between the marked candidate and the  
> other two, with a weak preference between them.
>
> I've been contending for some time that in order to understand  
> election methods, even if they do not collect preference strength  
> information, we should posit it. Otherwise vote patterns are rather  
> arbitrary. We see, in places, comparisons of election methods that  
> are utterly concerned about what might be called the Satisfaction  
> Sum criterion (the method chooses the candidate who maximizes  
> overall satisfaction with the result) or the Satisfaction Count  
> criterion (the method chooses the candidate who maximizes the  
> number of voters who are at a chosen level of satisfaction or  
> higher, also called Approval). For brevity, we could call these the  
> Range Criterion and the Approval Criterion, but they should not be  
> confused with the methods.
>
> The reason why these criteria aren't mentioned and considered in  
> evaluating election methods is that we are accustomed to studying  
> methods by positing votes. And so we don't have any information  
> about these criteria. Except that, for example, with the Majority  
> Criterion, most writers *do* assume some kind of invisible  
> preference. But what is lacking is the far more informative  
> assumption of preference *and* preference strength. Otherwise,  
> without preference strength information, the analyst is equating a  
> strong, maximal preference, unshakeable, with an extremely weak  
> preference, so weak that the voters' vote is really a random choice  
> made at the time of voting. There is actually no preference at all.
>
> There are those who claim that Range Voting is problematic because  
> there is no way of comparing the "utilities" expressed by the  
> voter, between voters. However, we can posit utilities just as  
> easily as we can posit votes, and we can posit them on an absolute  
> scale that *is* commensurable. Yes there is an assumption  
> underneath that which may not be true, but it is an assumption that  
> democracy depends on. It is the assumption that the opinion of  
> every voter is equally valuable; underneath this must be an  
> assumption that the *range of welfare possibilities* for every  
> voter is equal.

The additional (utility/preference strength related) information that  
range style ballots provide is excellent information. The only  
problem is that we don't have a voting method that would both take  
that information properly into account and be resistant to strategic  
voting at the same time.

>  	
> In my writing on this, I call it the "first normalization." When we  
> select the utilities for candidates in preparing a study, we would  
> place these utilities on a scale where one end is "the worst  
> possible thing that could ever happen," and the other end is like  
> that, only the best." In real elections, generally, the absolute  
> utilities will be clustered in the middle somewhere, usually. And  
> then there will be, in the votes cast, some kind of normalization,  
> which may or may not be full.
>
> We will see Range ballots where the voter votes low scores, for  
> example, for all candidates. Ballots like these will produce  
> different results with the Range Criterion and Approval Criterion,  
> if the approval cutoff is set at the mean rating for all  
> candidates. So a vote of Bad will be considered "Approval," by this  
> criterion. There are arguments that this is, indeed, what we should  
> do.
>
> When we are studying election methods, we are usually judging them  
> by some standard we presume best, such as maximizing the number of  
> people who prefer the candidate. Certainly we should include the  
> Range Criterion and Approval Criterion in our consideration.
>
> Ranked methods without preference strength information inherently  
> will fail Participation, because if the voter expresses a  
> preference that is actually weak, it is treated as strong, or as  
> being of middle strength, and thus can warp the outcome such that  
> it worsens for the voter by voting. If I've got this right, the  
> problem of Participation is inherent with ranked methods for the  
> reason described.
>
> With the truncated votes here, the expressed vote is then treated  
> as having maximal strength. This is almost certainly overstated,  
> yet the ranked method leaves the voter with no alternative. If the  
> voter's normalized utilities for ABC are 910 in Range 9, the  
> truncation is a very reasonable vote, but if the voter does not  
> truncate and votes A>B>C, the voter is effectively voting as if the  
> rating for B were 5. That's a large distortion. And ranked methods  
> do encourage this distortion. The voter *does* prefer B to C.
>
> Whether or not to use Range methods in public elections is a  
> complex question, particularly because of the possible problem of  
> strategic voting (though that appears overstated) and of  
> normalization as well (the alleged incommensurability of the  
> utilities), but this is quite different from avoiding its use in  
> comparing election methods. Whether in simulations or in exact  
> studies, utilities must properly underlie the value of election  
> methods.

Condorcet votes are relatively expressive (less than Range but more  
than most) and at the same time they are relatively resistant to  
strategic voting. That's why they are interesting and why they may be  
a good or the optimal method for many uses.

>
> Back to the question of "Who is the centrist?"
>
> We have here a disagreement by the electorate as to who is in the  
> middle. This is completely normal, because supporters of the middle  
> candidate will not agree on who is in the middle (in their own  
> rankings).
>
> If the election were choosing the "middle" candidate, who would it  
> pick? Consider it an approval election, with = votes being votes  
> for both candidates as in the middle.
>
> We have
>         A       B       C
> A:              39      6
> B:      16              22
> C:      1       30
> -------------------------
> tot:    17      69      28
>
> If we use the standard that equalities are not votes for middle,  
> then we get
>
>         A       B       C
> A:              9       6
> B:      2               8
> C:      1       25
> ------------------------
> tot:    3       34      14
>
> Now, supporters of the middle candidate will disagree on who is in  
> the middle, because their judgement, inherently, will be  
> individual. If we assume an exact centrist candidate, half the  
> voters will consider the left to be the middle candidate, and half  
> will consider the right to be the middle.
>
> The single vote from a C supporter that B is in the middle is  
> anomalous and relatively unrealistic, and this shows, actually, how  
> the original rankings were even more unrealistic. While real  
> elections will have anomalous votes, its introduction here, to  
> assume that a C voter will truncate because some B voters did,  
> ignores the fact that supporters of a centrist candidate can still  
> have a large distance from one side, if that candidate is closer to  
> the other side. The B truncations are realistic, the C not.
>
> Clearly B is the middle candidate, overall, it's not even close,  
> and we can infer, further, from the B votes, that B is closer to C  
> than to A.
>
>> Vulnerability to the margins strategy was kept => similar cycle with
>> appropriate differing strengths with margins and with winning votes.
>> One C>B voter can change the result by voting B>C.
>
> Thus reversing preference, considered undesirable. However, ranked  
> methods provide only one way to raise a candidate up in the vote,  
> and that is to reverse preference. In Range, as an example, a  
> rating for a candidate can be raised up to the level of another  
> candidate, without reversing preference. While this is not  
> considered "sincere," neither is it "insincere," in that it is only  
> asserting a smaller preference, something that ranked methods don't  
> even allow. Rating B=C means that "Compared to my preference for  
> both A and B, my preference for B>C is negligible. If I think the  
> real pairwise election is between A and B, then my vote for C is  
> really moot, unless it harms B. Range methods would allow the voter  
> to vote for C without harming B. Ranked methods typically don't  
> allow that.
>
> To understand voter strategy and election methods, we must  
> understand how underlying satisfaction expectations relate to  
> votes, and we must also integrate how election probabilities relate  
> to votes. Using the Range or Approval Criteria allow these things  
> to be quantified, and without quantification, deciding what is  
> "better" boils down to trying to satisfy a list of criteria, known  
> to be incompatible with each other (and they are, if we restrict  
> ourselves to ranked methods and single ballot elections), without  
> any objective standard for rating the criteria themselves.
>
> It's a formula for endless argument.
>
>> It looks to me that B must be more centric than C.
>
> Well, from the votes, it is totally obvious and clear. The division  
> of the A voters on this question is a bit puzzling, but it is  
> explained by the introduction of another axis of comparison that is  
> driving it. This axis does not affect the C voters, because they  
> align with B, relatively, over it.
>
> I think looking at three-candidate elections as containing votes  
> for who is in the middle is interesting.
>
>>  I expect A voters
>> to truncate since they are not interested in the right wing internal
>> battle.
>
> This was the comment that first motivated me to respond here. At  
> first I thought it unreasonable, but, in fact, it is reasonable. B  
> is some distance to the right of center, so Juho's description is  
> accurate. For many A voters, B and C are both far to the other  
> side. In a method which allows the expression of preference  
> strength, I think we would see this clearly, if voters didn't  
> exaggerate.
>
>>  B voters truncate since many of them are so close to the left
>> wing that A and C are about equal in preference to them. C voters do
>> not truncate much since for them the other right wing candidate B is
>> clearly better than A.
>
> Yes.
>
>> The most unrealistic point in this (one step more realistic) scenario
>> is maybe the fact that so few A supporters find B better than C
>> (although as I said, B appears to be closer to the centre than C).
>> But let's go forward.
>
> Yes. However, the introduction of another axis explains that. There  
> is some other issue on which B and C disagree that is of importance  
> to a subset of the A voters. And the A voters disagree among  
> themselves on this issue.

If B and C are clearly different kind of candidates, then I'd expect  
many more A supporters to have an opinion on which one of B and C is  
better, i.e. less truncation.

>
> I gave an example above, abortion. Perhaps B is libertarian,  
> really, and opposes coercion, whereas C is more traditionally  
> "conservative," which can be just as coercive as the supposedly  
> high-tax big-government position of the liberals.
>
> And then we have the left divided into those who dislike coercion  
> and those who are quite willing to impose it for the public  
> betterment. (In reality, this is usually an argument over what  
> coercion is *necessary,* the libertarian position tending toward a  
> stricter definition of necessity, the authoritarian one toward an  
> easier assumption of necessity.)
>
> So it's not only realistic that factions truncate, thus equating  
> two candidates to bottom place, but that they also disagree as to  
> who is in the middle. A two-party system makes this more rare,  
> because the big parties have amalgamated positions and thus define  
> a major axis: which party do you support, with lots of consequences  
> for the answer, because of how power is exercised.
>
> When we get multiparty systems, it gets hopelessly complicated.  
> Some think that an argument against multiparty systems, but it  
> isn't. Reducing the complex choices of modern life to Party A or  
> Party B creates chaos on another level, the chaos of major effects  
> from minor causes. It's inherently unstable, though it can appear  
> otherwise. If the parties are really quite close to each other, if  
> they are really, in the universe of parties, quite centrist, then a  
> flip from one party to another has less effect, making the system  
> more stable, but also making the parties into Tweedledum and  
> Tweedledee for a significant number of voters, who then express  
> their utilities by not voting, it isn't worth it. Of if they vote  
> for other reasons, such as local elections that they care about,  
> then their vote in the election of concern is useless, chaotic, or  
> can harm the outcome, if they cannot express real preference  
> strengths or participate in a way that makes their vote count.
>
> And a strong two-party system avoids the real question by deferring  
> it. How does society make decisions about how to coordinate and  
> cooperate for the common welfare? Putting the decisions into the  
> hands of two parties defers the question and makes it into "How  
> does the majority party make decisions about...." and "How do the  
> two major parties come to agreement to truly maximize common  
> welfare?" So, then, if we consider each party, how does *it* make  
> decisions? Does it do so democratically? What methods does it use?

Theoretically, in a two party system the opinions of the two parties  
should change in time so that the average voter opinion would lie  
approximately between the two parties.

>
> Very few methods, I'd say. Primary elections have become common; it  
> is not clear to me that this is any better than the old smoke- 
> filled rooms, except for health reasons. Primary elections, indeed,  
> would tend toward radicalizing the parties, making them no longer  
> centrist, increasing the differences between them, bringing each  
> party into the center *of its wing* or even toward the more radical  
> side of the wing, because that side tends to be more motivated.
>
> It's a mess, and we often think of, as solutions, proposals that  
> actually make things worse, because we don't understand how to  
> evaluate elections. We think that primaries are "more democratic,"  
> yet the result can be seriously harmful effects on the overall  
> satisfaction of the public. If we use the Approval criterion, this  
> is obvious. It we have two large parties roughly at parity, if the  
> rightist party nominates a candidate who is "centrist" on the  
> right, this candidate is at 25% on a scale, and this is quite  
> "democratic." And if the left party nominates a candidate centrist  
> on the left, this candidate is at 75% on that scale. (This is  
> assuming equal distribution. It isn't quite that bad, actually,  
> because the distribution will be, probably, a bell curve weighted  
> toward the overall center ... but the increased motivation to vote  
> and campaign from extremists can still push toward this position,  
> effectively).
>
> And then, no matter what candidate wins, 75% of the electorate  
> considers this candidate relatively undesirable, out of the  
> universe of possible candidates.
>
>
>> [...]
>
>> This kind of observations apply to many strategic examples, not only
>> this margins based strategy. The vulnerability of Condorcet methods
>> to strategic voting is a fact but in most cases the vulnerabilities
>> are quite marginal and seldom (or in some cases practically never)
>> occur in real life.
>
> That's not necessarily true. Truncation is a kind of strategic  
> voting, and it affects outcomes. Will voters reverse preference,  
> however?

Truncation can be used for strategic or sincere (equal candidates at  
the bottom) reasons. Therefore I see truncation and strategies as  
separate concepts.

Juho

>
> They do under plurality, and it is normal.
>
> Consider this: if an election allows write-ins, voting the ranks in  
> the election is bottom-ranking every other possible candidate.  
> There are really, in public elections that allow write-ins, a very  
> large number of "candidates." Because of political realities,  
> voters don't write them in, they consider it a waste of time, and  
> in a ranked method, a wasted vote is possible. (In plurality, the  
> waste is guaranteed; allow overvoting, this changes.)
>
> So almost every ballot, we can predict, incorporates preference  
> reversal!
>
> This could be changed! Suppose we have a Range election, and write- 
> ins are allowed, and so are runoffs under some circumstances. There  
> is a debate among Range advocates over how to treat specific  
> abstentions, that is, the voter votes, rating one or more  
> candidates, but does not rate all. Alignmnt with existing practice  
> indicates that you would min rate them. However, currently the  
> default Range proposal is a little more complicated than that. It  
> is definitely interesting to, at least for some purposes, exclude  
> abstentions from determining the average Range rating of a  
> candidate. To allow this candidate to therefore win has some  
> obvious problems, starting with a write-in candidate who gets 100%.
>
> But what if we have a write-in candidate who gets 100%, and he is  
> written in by a very substantial chunk of the voters, say 25%. That  
> this candidate is not on the ballot, giving him a huge  
> disadvantage, he really should be there, but the process excluded  
> him. Holding a runoff between this candidate and the sum of votes  
> Range winner would make sense.
>
> (I'm not sure if this could be made compatible with my other  
> proposals to hold a runoff with a pairwise preference winner. True  
> democratic process does not limit the number of questions to be  
> asked the electorate, the electorate itself decides when it is  
> ready to make a final decision, and, unless there are special rules  
> -- which are generally compromises intended to speed up decision --  
> the final decision is necessarily ratified by a majority. No matter  
> what the method used to get to that final nomination of a single  
> candidate, it is impossible not to get a majority winner, for the  
> majority can still reject the candidate if something went wrong  
> with the process.)
>
> (This inherent superiority of full democratic process over election  
> methods must be understood; election methods are compromises,  
> intended to make a decision out of a single snapshot of the  
> electorate, yet, in the real world, people make, when they have the  
> option, decisions over time as various options are weighed. People  
> who make major decisions in a snap without having reflected on the  
> options, which includes a kind of back-and-forth, are actually  
> disabled. But note that what can appear to be a snap decision can  
> reflect a long unconscious process, and it is only the final  
> decision point that is quick, where "intuition" leads the person to  
> make a choice.)
>
>


	
	
		
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