[EM] Ordering defeats in Minimax

[Juho Laatu]

Also this mail is a late rely. This time I had some additional problems since I didn't receive this mail in my unbox at all. I found it in the electorama mail archives. The mail traffic between electorama and me doesn't always work perfectly.

> On 28 Apr 2017, Kevin Venzke wrote:
> 
> Hi all,
> Kristofer wrote:>Do you consider Plurality a strategic criterion? It seems to me to be>more of a "natural behavior" criterion
> FWIW I don't consider Plurality a strategy criterion.

I already answered Kristofer's question once, but I was maybe not as clear as I should have been. I agree that Plurality can be classified as a criterion that is intended to be a "natural behaviour" criterion. I used term "heuristic", that os close to "intended to be a natural behaviour". Plurality is however often linked with winning votes, that I consider to be a very "strategic behaviour" related comparison method.

> We can bring up strategy criteriaif we wanted to, but they are more obscure than the Woodall criteria. The best knownone worth bringing up is favorite betrayal, but WV methods don't completely satisfy it,so I would be stuck talking about simulations instead of firm guarantees.
> (You may ask why does favorite betrayal come into it? Because the same incentives thatare supposed to discourage margins voters from truncating at the bottom, also discouragethem from equal-ranking a set of favorites at the top. And there isn't a mechanism ensuringthat ideal strategy is to simply rank them sincerely.)
> I would say margins' largest issues are strategy-related, but its most obvious issuesaren't, so I prefer to talk about "natural behavior" when I have a choice.
> To Juho:
> You feel criteria are "too far from practical election method considerations to be applieddirectly on them as viability criteria"; that is actually very close to how I view yourcriteria (even if you don't use the term "criteria"). You say the "strongest argument" formargins is that it is a relatively natural and continuous preference function.
> I guess that you don't say that this involves "practical considerations," and it's justan aesthetic preference.

I often talk about performance with sincere votes when I'm not talking about performance against strategies. That is practical (although also aesthetic, like many things in formal systems :-) ).

> I give you credit for consistency in not even mentioning mono-add-top, which could easily be argued to be a practical consideration. On the otherhand you seem to believe WV has effective strategy incentives that result in things you don't like, so you don't seem to completely dismiss practical considerations either.

My thinking is often based on the assumption that in typical large public elections with independent voters strategic risks are not very high. I'd expect almost all Condorcet elections to be quite strategy free in practice. In most countries people would vote for the best candidates, not in some other way, trusting that giving false rankings or omitting preferences would help them in the election.

For this reason my practical considerations often tend to focus on the above mentioned performance with sincere votes. I tend to "like" margins more than winning votes not because of differences in their behaviour in the presence of strategic voting, but because of their differences in performance with sincere votes. For example with votes 51: A, 40 B>C I like more the margins thinking that C is 48 (sincere) votes away from winning the election than the winning vote thinking that C is 3 (sincere) votes away from winning the election. If we can afford to use a natural pairwise comparison method, why not use it.

> I find it more accurate when you complain that WV seems like an approval hybrid thanwhen you suggest that interest in WV stems from strategic defense concerns. When peopleinvent random new methods on EM they frequently behave like WV (or IRV); it's very hard toemulate margins' results without actually being margins. Methods that show approval-likebehavior stem from a relatively common expectation that expressed votes are a goodindication of viability/merit.

Yes, I'm looking forward to such use of Condorcet methods where voters rank multiple candidates, to rank all the potential winners, in the hope of allowing the fair algorithm to pick the best winner. I hope people will understand that most likely their best strategy is to do just that.

> There may be good historical reasons to portray WV as ahorrified reaction to margins... And I can imagine the FPP supporter who says interest inIRV "comes mainly from strategic defense reasons."

One reason behind the popularity of IRV, when compared to Condorcet, could be its tendency to favour large incumbent parties. (Another one is its interesting dramatic elimination process that appears more natural than it is.)

> But that seems like a limited way oflooking at it.
> You write:>I think Plurality is a bit strange. Actually it is not even a criterion >of ranked methods. It is a criterion for ranked methods with implicit>approval cutoff. It makes the assumption that a voter that casts a short>vote has somehow approved those candidates that he marked, and not approved>the others. In different elections the behaviour of voters with respect>to which candidates will be marked on the ballot may vary a lot, and that>may have nothing to do with how much the voters support or approve those >candidates. In order to make any sense of the Plurality criterion we are >thus tied to having an assumption of implicit approval in the ballots, >where marking a candidate means approving that candidate at some level.
> I think voters expect this behavior, and that's why it's important, for example, forthe long-term viability of the method's adoption. Now, you may say that we could convince voters not to expect this.

Yes, they should be educated if they ever get that kind of ideas somewhere.

> You might even (though I'm still not 100% sure)manage to do this by forbidding voters from truncating at all. In that case, I woulddrop all my objections dealing with naturalness and what voters expect. My remainingcomplaints at that point would be the strategy-related ones.

I don't want to forbid truncation because I want voting to be easy and pleasant, and I want to have a reasonably high number of candidates. If insincere truncation turns out to be a problem that threatens the soundness of the results in some elections, maybe one could try other tricks first, like e.g. completing the vote with random candidates or using some party preference list to complete the vote. I'm however living in the hope that in most cases none of these tricks are needed.

> >
> One reason why I don't like implicit approval in general (as a fact that>is known by the voters) is that it encourages voters not to rank candidates>that they don't like.
> 
> Sure, I would rather criticize how margins addresses this than the fact that it triesto address it. IRV does this, for instance: You can rank the worse frontrunner in asincere way and you know that it won't hurt you. In margins we "want" you to rank theworse frontrunner, but it's not expected to be of any use to you, and it can hurt thebetter frontrunner by making "worse" look like your compromise choice.

Yes, but what is the probability of hurting one's targets by ranking numerous candidates in a Condorcet election with a bunch of potential winners and few additional candidates that are unlikely to win? And what are the benefits of ranking all the potential winners?

> A few comments on your Plurality example:
> >
> I'm not well prepared to comment how margins can handle Plurality>criterion but I'll address one basic (but theoretical and extreme,>i.e. unlikely to happen in typical elections) example. 35:A, 34:B>C,>31:C. A has more first preferences than B has ballots where B is>marked. B's worst defeat margin is however smallest (1), so it will>win in typical margins based methods. Plurality criterion says that B>should not win. B is however two votes short of being a Condorcet>winner, so it can't be the worst of the worst. What if A would win?>Plurality criterion pays special attention to A's high number of first>preferences. But on the other hand voters would like to elect C>instead of A with large majority (C>A voters would not be happy with>the result). How about C then? Plurality criterion accepts C too, but>using the high number of first preference votes of A as an argument >that supports C does not make much sense. My conclusion is that this>is a typical mess that we can get with circular preferences. Our>voters were quite stupid when they didn't sufficiently rank the >potential winners. There are many different possible scenarios on what>the truncated opinions might have been, and different results emerging>from that. In this example my recommendation would be to tell to the>voters that they should rank all potential winners (except maybe the>worst one). I don't see any need to start blaming (or praising) margins>on what happened. Maybe you have some realistic examples in your mind,>that would give better justification to the Plurality criterion.
> 
> 1. I just note that "fewest votes short of being a Condorcet winner" need notstrike one as a particularly less arbitrary standard than Plurality. I do not knowwhat stops one from dismissing yours as a criterion whose "message somehow soundsgood to people that do not regularly deal with election methods." It does "soundgood," I agree with that.

Democracies typically work via majorities, and majorities are generated by voters. To me the required number of additional voters to reach majority is a very natural measure of the popularity of some idea. I'm having hard time trying to invent something that would be a more natural measure.

> 2. I'm not sure what is your basis for calling these voters "stupid." Are you(rhetorically) employing Plurality's assumption that voters didn't like theoutcome? I get the sense that you don't like the outcome yourself.

I referred to truncation of votes that obviously made it impossible for the election method to decide who the ideal winner is. The voters maybe failed to tell whom they would like to elect.

It is also possible that all truncations were sincere (opinions where all the remaining candidates were equally good). In that case any method with good/desired performance with sincere votes would do the job fine. It is however typical that people have clear opinions about the three potential winners, and therefore it is probable that many of the voter that truncated had some opinions that they didn't express. Giving fuller rankings would probably be in their interest (in typical elections).

> 3. I do understand feeling that Plurality is strange. I don't love it. My view isthat Plurality is an easily articulated subset of a larger principle. Essentially,if the voters were instead legislators selecting an outcome, could B ever prevail?It seems quite unlikely, because at the moment that C is the status quo and the Bvoters wish to assert their win over C, they can't because they are outnumbered bythe A voters. The pairwise contest doesn't occur in a vacuum. In this case Pluralityconveys what I would want.

Voting about things vs. persons is about the same. Condorcet is a good method if one wants to elect a good compromise winner. In a small community where people think that they know beforehand how others will vote, and where the party leaders and strategists possibly can force the voters to vote as told, strategic problems are more likely to occur than in large public elections with independent voters. Condorcet could however work well also in such small and strategy prone environments. The problems of cyclic group opinions are incurable. If opinions have a top cycle, there will be a majority that would like to change the outcome to something else. In small political circles the solution could often be to make an agreement with some other party, I will get this and you will get that, and then vote accordingly. This is more probable than leaving uncertain decisions and expected circular opinions to be solved by a rather random outcome of a vote, or even more random outcome of a vote with strategic moves by multiple parties.

> A more thorough version of Plurality (in my opinion, to my taste) wouldn't talkabout first preferences or votes in total. I doubt this language is necessary toexpress the idea. (The criterion we do have is easy to apply, though.)

Yes, Plurality's reference to first preferences is not good. If one wants to say something more generic that is not tied to first preference votes, one should reformulate the criterion. The criterion would not be as sexy that way. Also the use of implicit approval should be made clearer, if the intention is to say something about voters that assume it, or a method that makes some use of it.

Juho

> Kevin

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