[EM] Fwd: Ordering defeats in Minimax

Fri Apr 28 00:37:33 PDT 2017

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. 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 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.
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. 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." 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. 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.
>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.
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.
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.
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.
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.)
Kevin
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