[EM] C//A (was: Remember Toby)

[Juho Laatu]

On 9.6.2011, at 4.54, Kevin Venzke wrote:

> Hi Juho,
> 
> --- En date de : Mer 8.6.11, Juho Laatu <juho.laatu at gmail.com> a écrit :
>> I was busy with other activities for a while but here are
>> some comments.
>> 
>>> 
>>> --- En date de : Mer 1.6.11, Juho Laatu <juho4880 at yahoo.co.uk>
>> a écrit :
>>>>> I agree with Kevin that "elect the CW if there
>> is one,
>>>> else elect the 
>>>>> candidate ranked (or ranked above last) on
>> the
>>>> greatest number of ballots" is plenty simple, and
>> is much 
>>>>> more satisfactory than MinMax or Copeland in
>> other
>>>> respects.
>>>> 
>>>> In what sense is the above mentioned "implicit
>> approval
>>>> cutoff" + Approval to resolve is the best "simple"
>> method?
>>>> If compared to MinMax, is it maybe easier to
>> explain to the
>>>> voters, more strategy free, or yields better
>> winners? Would
>>>> an explicit approval cutoff be fine (to allow full
>> rankings
>>>> to be given)?
>>> 
>>> It is surely easier to explain than MinMax,
>> 
>> If we talk about the sincere voting procedure, then MinMax
>> voter only needs to rank candidates, but if loops are
>> resolved using implicit Approval, then the voter should know
>> in addition to the idea of ranking that truncation means
>> that the remaining candidates are not approved. The voter
>> needs to decide where to truncate. Or alternatively one
>> could let the voters vote without knowing that truncation
>> means disapproval. That would give more power to those that
>> have the knowledge (although not very much if approvals are
>> expected to come into play only seldom). I note also that if
>> we don't tell to the voters how their ballots will be
>> interpreted, then all Condorcet methods become very similar
>> from the sincere voting procedure point of view (just rank
>> the candidates sincerely and that's it).
>> 
>> If explanation to regular voters should contain strategic
>> voting aspects, then the methods become more complex to the
>> regular voter. I don't know if voters should be trained to
>> use of approval as a tie breaker or if those properties
>> should be hidden from the voters as discussed above. Burial
>> would be even more difficult to explain (but maybe not
>> recommended to the voters). In Approval all voters are
>> expected to vote strategically (=decide where to put the
>> cutoff), but if one uses approval only for tie breaking then
>> one need not be as careful as with normal Approval.
> 
> I don't recommend that voters not be instructed on how the method is
> supposed to work.
> 
> I think with C//A it is easier to explain how to find the winner, and
> the strategy becomes obvious. No defeat strengths are involved. MinMax
> has its strategy too, and this is harder to perceive because the method
> rules are harder to understand.

If we are taking about simple explanations to regular voters then maybe all the strategy related aspects should be considered not-simple.

C//A's counting process is quite simple (to explain) although its counting process has two phases that differ from each others. I don't think e.g. the "elect the candidate that needs least number of additional votes to beat all others" would be more complex.

> 
>> If we talk about the vote counting process (with sincere
>> votes) and how to explain it, then we have a two phase
>> explanation (=Condorcet winner, and alternatively sum of all
>> the ticks in the ballots if there is no Condorcet winner)
>> vs. a one or two phase MinMax explanation (elect the
>> candidate worst worst defeat is least bad. MinMax(margins)
>> is quite simple since it is enough to refer to the number of
>> additional votes each candidate would need to win all others
>> (if doesn't already). None of the explanations is quite
>> obvious to average voters if one has to explain the
>> difference between having a Condorcet winner and not having
>> a Condorcet winner. The MinMax(margins) specific explanation
>> is maybe easiest (and still fair, clear and exact enough) to
>> present without talking about the probabilities of having or
>> not having a top cycle.
> 
> You have to explain CW either way.

Not necessarily, but that need might pop up. For example in the MinMax(margins) explanation above ("elect the candidate that needs least number of additional votes to beat all others") CW is not mentioned. Some voters might however start wondering in what kind of situations the winner does not win all others. In that case that individual voter might need someone to explain that sometimes there is a CW and sometimes not.

> 
>> If we seek simplicity, I'd be happiest to explain the
>> voting procedure simply "just rank the candidates" and use
>> the MinMax(margins) "additional votes" explanation if the
>> voters need to know how the votes are counted.
> 
> When I think of "simplicity" I mean that the voters would actually 
> understand how the method works.
> 
> I don't think you will have much luck proposing methods if you don't
> think voters need to understand them. Can you find an angle / sales 
> pitch that dodges this?

I believe most people are not interested in the vote counting process. The voting procedure and general idea of the method must be easy to understand (but no mathematically exact description is needed). People are happy enough if the method seems good enough and experts and their own party are not complaining about its possible problems.

If we take for example a country that uses D'Hondt to allocate seats, only some voters are able to explain how the D'Hondt allocation is actually counted. Most voters vote happily despite of this and have considerable trust on the method.

It is possible that the complexity of a method will be used against it in some reform campaigns but maybe that's a different story. This is not really a problem of the regular voters but just a campaign strategy. Defendability in campaigns is a valid separate topic for discussions though.

> 
>>> has more obvious burial 
>>> disincentive (especially if the comparison is to
>> margins),
>> 
>> All Condorcet methods have a burial incentive with some
>> variation between different methods. I don't know why
>> margins would be more problematic than winning votes. 
> 
> The theoretical reason is that the offensive and defensive strategies
> look exactly the same. It's analogous to Borda. You cannot tell whether
> somebody is trying to steal an election or just cover themselves.

I'm living in the hope that strategic voting would not be widely spread in Condorcet methods. If strategic voting (offensive and defensive) becomes the norm, Condorcet methods might well lose their attractiveness. If regular voters have to start thinking about offensive and defensive strategies instead of just indicating their preferences they might get fed up pretty quickly.

> 
>> I mean
>> that they have different kind of vulnerabilities and
>> disincentives, and it is not straight forward to say which
>> ones are more problematic. 
> 
> It is not straightforward but one can certainly make an effort. It is
> not clear to me what strategic benefit margins is even supposed to have.

Maybe e.g. the fact that they lack some of the weaknesses of winning votes.

> So it wants to make equality of ranking unattractive...

In what sense? I guess the basic assumption is that voters will cast sincere votes.

> where does this 
> get us? It isn't IRV, there is no guarantee that the truncations turn 
> into sincere rankings. If someone wanted to tell you a half-truth why 
> would you guess that they won't decide to just lie now instead? You 
> would have to presume that all would-be truncators are just lazy.
> 
>> Also Condorcet with approval as a
>> tie-breaker has its own burial problems, although the
>> approval cutoff introduces also some risk to the burying
>> strategy. I'll give one example of a burying strategy when
>> approval is used for tie-breaking.
>> 
>> 49: A>B
>> 02: B>A
>> 49: C
>> 
>> A wins. But if the two B supporters vote B>C, then there
>> is a cycle, implicit approvals will be used, and B wins.
>> 
>> One possible comment to this strategy problem is that A
>> supporters could truncate and not approve B (that seems to
>> come from the same party or the same coalition at least). In
>> that case all the big groupings could simply bullet vote and
>> only the small ones would rank their second favourites. That
>> approach could kill the chances centrists that are not the
>> first candidates of one of the major groupings as potential
>> compromise candidates and Condorcet winners.
> 
> This last scenario doesn't seem to be a problem experimentally. I have
> usually found that Approval over-selects the centrist.

Yes. But my concern was that if people are given arguments and guidance on how and when to truncate, they will truncate more, and thereby they will not give full rankings, and that tends to favour major candidates (leads to stronger bullet voting and plurality orientation).

> That is, the
> centrist will be one of the two winners during the pre-election polling,
> and the third candidate who lost out then can't win the election even if
> they turn out to be sincere majority favorite.
> 
> If the centrist is seen as worse than expectation, then sure, they won't
> get many votes.
> 
> Anyway, I know that C//A is not immune to burial.
> 
>> It seems I have to give one more example to cover also
>> cases where the difference between major an minor candidates
>> is not that clear.
>> 
>> 26: A>B
>> 25: B>A
>> 49: C
>> 
>> Again, if two of the B supporters vote B>C, then B wins.
>> If some A and B supporters truncate in order to defend
>> against burying or as a general safety measure against the
>> other competing grouping (A and B supporters may not guess
>> right which one of them will have more votes), then C wins.
>> Before the election A and B groupings could both claim that
>> they are bigger and therefore they should truncate, and all
>> the voters of the other grouping should rank also the
>> candidate of the other grouping.
>> 
>> This second example comes close to the traditional Approval
>> strategy related problems where near clone
>> parties/candidates fight about who must approve whom. The
>> strategic problems of approval as a tie-breaker and winning
>> votes are also quite closely related.
> 
> The method isn't perfect, no.
> 
> I don't believe this kind of scenario has a good resolution. I think in
> practice one of those candidates will drop out, and while that's bad,
> I don't think we can do much about it.

If we want the majority side (A+B) to win, the voters should be given strict advice not to truncate. In that sense they should forget the approval part. And voters should be warned that although there is a potentially successful strategy available they should not use it.

(It is very easy to make the strategy work (only few strategic voters needed) but the risks are quite high if the A+B camp hates C. Voters that feel e.g. A>>>B>C would be more tempted to use the strategy. This set-up is thus quite unstable and therefore not a nice situation to be in.)

> 
>> Although use of approval as the tie-breaker has some
>> disincentive against burial in the sense that approving some
>> unwanted candidate increases the risk of electing that
>> candidate, in these examples burial works anyway. Plain
>> Approval method is free of the burial strategy but that does
>> not mean that this property can be carried also to Condorcet
>> methods that use approval for tie-breaking.
> 
> Maybe so, but it appears to be true anyway. I ran a few simulations
> recently, on a 1D spectrum. I don't expect anyone to take it as gospel
> or even as fully explained, I just offer it as evidence that I'm not a
> total fool when I make claims. In these simulations, here were the
> percentage of voters that wanted (after learning the method and playing
> against the other voters) to use burial strategy on average:
> WV 3.3%. Margins 3.4%. C//A (implicit) 1.9%. C//A (explicit) 7.0%.
> 
> I also explained on EM why C//A might have better resistance than WV,
> years before I wrote and ran these sims.
> 
> Voters wanting to compromise?
> WV 0.1%. Margins 1.6%. C//A (implicit) 0.3%. C//A (explicit) 1.2%.
> 
> My point? I am actually trying to learn things, and to some extent I
> guess I'm probably succeeding. I don't view EM as purely an art project.

Yes, simulations offer good support. They of course show only what is written in their parameters. Often they are theoretical in the sense that they observe the situation after knowing the votes accurately and asking a question, what if someone had voted in a different way. In practical elections the situation looks quite different from an individual voter's point of view. Maybe one could model also that situation and run simulations that tell more facts on how regular voters see the game. I'm not sure what parameters you had in the simulations. I'm thinking about parameters like uncertainty of the polls, risk of backfiring, need to coordinate the behaviour of the similar minded voters.

(I note also here that I would like to see rules for regular Condorcet voters (or parties) on how to cheat the system (or how to advice the party supporters to cheat the system). That (and some successful implementations in real life elections) would demonstrate that Condorcet methods are indeed in trouble with strategic voting.)

> 
>>> and, in my
>>> view, gives comparably good winners to WV,
>> 
>> Did you mean "when compared to WV"?
> 
> No, I meant I think it's about the same. Though in the sims above it
> was the best of those methods according to sincere Condorcet efficiency.
> 
>> The approval
>> tie-breaker version clearly assumes an implicit approval
>> cutoff, so in that sense it may collect more information
>> than basic ranking based Condorcet methods. But on the other
>> hand an implicit approval cutoff cuts away some ranking
>> information that could have been useful. Since approvals are
>> used only when there is a top cycle, that approach may lose
>> more ranking information (due to truncation) than it gives
>> additional approval information. Picking good winners would
>> benefit of collecting lots of sincere information. (There
>> may also be different opinions on what kind of candidates
>> would be good winners.)
> 
> Yes. Lots of theory in that paragraph. May be right, may be not, may
> vary based on the circumstances. It often happens with election methods
> that things don't work the way one would expect. Regarding the last
> parenthetical I'm willing to go with sincere Condorcet efficiency.
> 
>>> but more attention may need to
>>> be placed on where to stop ranking than under WV. (In
>> practice, I would
>>> not plan to rank any lower than could possibly help me
>> in WV, so I would
>>> probably vote the same under both methods.)
>> 
>> This sounds like voters would need to use some (cutoff
>> placing) strategy while voting. That does not make the
>> methods simpler to the voters.
> 
> I didn't say it did. I say it's unfortunate but still simpler on the
> whole.
> 
>>> The favorite betrayal incentive is worse than WV
>> though. (This is where
>>> I should plug my ICA method, which satisfies FBC. But
>> it's more
>>> complicated.)
>> 
>> I'll skip this part since the mail is about to become so
>> long (and this one would require more work from me :-).
> 
> I am sure that is true; what I find myself wondering is whether and why
> you might be confident that you would have an argument on this topic. 
> Have you thought about it? Or you think I haven't done any homework?

I have many things to say on this topic but maybe nothing that would be very useful to others. I believe you have at least done your homework well (existence of ICA as an answer or discussion point that addresses some of the key problems demonstrates that).

> 
> I mean, this is a fairly obscure issue that is a *downside* to the method
> I am advocating here.

I see this area as a game where one needs to find a good balance between various vulnerabilities and various positive targets. ICA is one rather complex point in this space. That makes it more difficult to give stable and meaningful comments on it - when compared to the ease of commenting some very basic stuff like Approval and Condorcet. ICA puts some special emphasis on equal ranking with the first preference candidate. On the other hand typical voters often have strongly "patriotic" feelings like A>>>B>C>D. I mean that all this complexity makes it hard to find comments that would address the method as a whole. ICA is to me actually a theoretical point in space, demonstrating how one can develop methods that meet some selected target criteria. I tend to like methods that are simple and sincere voting oriented. From that point of view ICA and other more complex approaches set the limits on what one can do if one needs to patch the simpler methods somehow.

> 
>>> An explicit approval cutoff in this method is not fine
>> at all: You will
>>> lose the burial disincentive. You would be able to try
>> to stop your
>>> opponents from winning as CW without hurting your own
>> candidate's odds
>>> to win that way, and then in the approval count you
>> would not have to
>>> stand by the pawn candidates you voted for. This
>> strategy would only
>>> backfire when too many voters try it and make a pawn
>> candidate the CW.
>> 
>> Yes, some of the disincentive is lost. But there are also
>> other reasons why burial may backfire. You may not manage to
>> create a loop and the pawn candidate might win.
> 
> Yep, I said that one. That's the scenario where multiple factions are
> trying to cheat on the first phase.
> 
>> If voters manage to create a cycle, the end result could be
>> a quite sincere Approval election, i.e. not an outright
>> victory to the ones who created the cycle (=some
>> disincentive). In that election those voters that falsified
>> their preferences e.g. from A>B>C to A>C>B would
>> still have a dilemma of being forced to (explicitly) approve
>> also C if they want to (explicitly) approve B (in addition
>> to the obvious A) (=some disincentive).
> 
> I'm not sure I follow that. Since nobody's going to be approving the
> pawn candidates in phase 2, who can win other than a frontrunner? You're
> not going to pairwise beat your own candidate by burying, you can only
> sink the other guy. If he wins on approval, that's just the same outcome
> you were going to get anyway.
> 
> But sure, yes, there is "some" disincentive. What I meant was, the
> disincentive is no longer very good. It's no longer something to brag
> about. It's *vastly* worse than margins in my opinion. In margins it is 
> at least confusing to think through the burial issues. To my eye the
> brokenness of C//A (explicit) is hard to miss.

My interest in explicit cutoffs comes from the interest to get full sincere rankings (that implicit approval / truncation may easily erase). If we assume that strategies are not a problem, then explicit approvals could be sincere, and sincere cyclic opinions could be solved in a way that could be even better (?) than what plain rankings can offer. The question is thus if use of strategies is so marginal that also explicit approval would work.

> 
> Maybe you want to say that any disincentive is good enough. I'm not sure
> why that would surprise me.

I'm studying also the possibility that no additional disincentive is needed. At least some societies could work this way.

> 
> You may as well consider me to be in agreement with statements like "X
> might be good enough in some situations." Why not. Can't really argue
> about that.

Maybe Condorcet methods are good in general. One could look at this problem also from the point of view that in some societies with tendency to resort to strategies some defensive add-ons might be needed.

Well, I think we should be prepared for both approaches. Time will tell us how people will react to use of Condorcet methods in real elections.

> 
>>> Also, the reason I don't need to see Smith in this
>> method is that unlike
>>> MinMax, where there isn't an obvious justification for
>> failing Smith,
>> 
>> I think there is an obvious justification for failing
>> Smith. If one of the candidates outside the Smith set is
>> less controversial (in terms of number of votes needed to
>> become a Condorcet winner, or in terms of size of opposition
>> planning to work against the elected candidate in favour of
>> some other candidate vs. number of supporters) then why not
>> elect that candidate. This is one very rational way of
>> measuring which candidate should be elected. There may be
>> other criteria too, but not necessarily any better than this
>> one.
> 
> For me "controversial" is an art project term. So is "rational." I wish I
> could get it in practical terms. The first one is so close to being one,
> too.

I'm interested in getting definitions on which candidate should be elected if we can assume 100% sincere votes. Would it be someone with lots of first preference support, someone that would have smallest opposition while in power, or would we maybe like to measure the level of happiness of all voters and then try to find a solution that gives highest average happiness or maybe highest minimum happiness. There are many alternatives. And different elections have different needs. We might measure the quality of single candidates one by one, or we might try to establish a linear order among the candidates (maybe to demonstrate to the audience that the electorate had a rational will). I'm thus talking about performance with sincere votes. And my claim was that there are viewpoints to this question where Smith set is not a valid way to measure the quality of the candidates.

> 
> If you look at a standard 4-candidate Smith failure example I see
> remorseful voters. I can count them, and your argument still works. I
> have to ask how I should differentiate different "degrees" of remorse,
> if I want to say that sometimes more remorseful voters is OK, if Smith
> is involved. I'm not sure how to do that.

Let's say there is a top loop of 3 (A, B, C) and D outside the loop. Defeats between A, B and C are strong. All defeats of D are weak.

If we elect A, then there are (say) B supporters that say that there was a strong opinion that B is better than A.

If we elect D, then there are B supporters that say that there was a marginal opinion that B is better than D. In this case there is also a marginal opinion in favour of A, and a marginal opinion in favour of C. We can say that in many elections D is a good choice since there would be only marginal forces of opposition against him.

Probably you should not draw a picture with Smith set drawn above the D candidate. That could give the audience false impression that all the candidates in the Smith set are clearly better than D. And they might think that candidates in the Smith set must be clones (in which case two of them could have withdrawn and donated the victory to the remaining one).

I must also add that of course this kind of situations where someone outside the Smith set wins in MinMax are very rare and probably will "never" happen in real elections. But if they do happen, then there are also explanations why this choice was correct.

Unfortunately cyclic group opinions are not an easy task to explain to anyone, not even to experts. I personally am not too much fond of the Smith set as a philosophy to explain cyclic opinions since, as I said already earlier, it looks to me like an artificial attempt to establish a linear order and thereby explain the cyclic group opinions using terminology that is valid only for linear/transitive opinions. Explanations to regular voters are of course another game.

> 
>> (Actually I think the popularity of Smith set comes
>> partially from the temptation of forcing the circular
>> preferences to a linear order. In that case the natural
>> position of the top cycle may appear to be ahead of the
>> other candidates. This approach can however be considered
>> irrational since it completely hides away the defeats within
>> the cycle. Forcing cyclic preferences to linear ones is thus
>> the dangerous (and irrational) part. The opinions are cyclic
>> and there is no need to establish a linear order. Other
>> criteria may work better, like e.g. the the opposition
>> against the elected candidate. Another reason behind the
>> popularity of Smith set is the interest to make a method
>> clone proof. That is a positive target. But it may violate
>> other criteria, like making the least controversial
>> candidate win. In the case of MinMax and possibility of
>> electing outside the top cycle, violation of the clone
>> criterion is not very critical, i.e. the number of
>> candidates that parties nominate may not change despite of
>> not meeting this criterion 100%.)
> 
> The question I have is, is the *only reason* that clone independence is
> desirable, that it may prevent aberrations in the candidate nominations?
> Maybe Smith has a justification here. I don't have an answer.

My thinking is such that since we can not make a fault free system, it is possible that the ideal method for our needs (in some particular single case) may well be a method that violates numerous criteria, but each criterion is violated only so little that it does not have any practical meaning. As an end result the method with many marginal vulnerabilities may not have any major vulnerabilities, and in real life elections that could mean "fault free". In addition to this the method should also achieve the intended targets with sincere votes (and these targets may again be in conflict with other criteria).

In this particular case I don't expect MinMax to violate clone independence so seriously that it would stop people nominating candidates (nor nominate numerous candidates). There are MinMax strategies that attack on known sets of clones, but also those strategies may be just theoretical threats, not practical ones.

Juho



> 
> Kevin Venzke
> 
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