[EM] Fwd: Ordering defeats in Minimax

[Toby Pereira]

I think I basically agree with Juho on this. The plurality criterion sounds like a reasonable criterion on the surface, but think about it more and it's arguably less so. To summarise, in a pairwise method, first place on a ballot doesn't hold any special status, nor does indeed last place (or joint last place or "unranked"). And a criterion shouldn't be used to impose an approval cut-off on a method that doesn't have one in its definition.
So while it sounds like a good criterion, removing the special status of these positions means that we are left with just saying that a candidate who pairwise beats another candidate should finish ahead in the overall ranking. Which is what all Condorcet methods do - except when there's a cycle.
Toby

      From: Juho Laatu <juho.laatu at gmail.com>
 To: Election Methods <election-methods at lists.electorama.com> 
 Sent: Thursday, 27 April 2017, 22:57
 Subject: Re: [EM] Fwd: Ordering defeats in Minimax
   
> On 27 Apr 2017, at 10:25, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:

> Do you consider Plurality a strategic criterion? It seems to me to be
> more of a "natural behavior" criterion: if A gets more first preferences
> than B gets any preferences, then B shouldn't win. This seems reasonable
> from a natural behavior perspective because A dominates B in some
> Approval-ish sense.
> 
> If that's a "natural behavior" criterion, then you could say that
> margins is more natural from a descriptive point of view (no
> discontinuities) while wv is more natural from a criterion point of
> view. Though, if we're to go by the apparent popularity of IRV, it seems
> that descriptive clarity weighs heavier than criterion clarity.

First of all, my thinking when it comes to practical election methods is not very criterion oriented. I tend to see criteria and criterion compatibility as important theoretical results that are mostly too far from practical election method considerations to be applied directly on them as viability criteria. The relevance of different criteria to practical election methods is almost as low as the relevance of latest mathematical inventions to practical everyday economic calculations (well, not quite, but something in that direction). I'm about at the level of accepting Condorcet criterion if we seriously want to have a neutral majority based method for consensus oriented single winner elections. One has to take also into account the fact that all election methods are bound to break some potentially useful criteria. All this means that I classify Plurality and most other criteria as an interesting discussion points but not something to be followed categorically. There are many
  criteria that are useful in the sense that most elections should have strong orientation in the described direction, but no need, or possibly with strong reasons to deviate from some criteria in some special (usually marginal) situations.

I think Plurality is a bit strange. Actually it is not even a criterion of 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.

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. Ranked methods work well only if most voters do rank explicitly at least all the potential winners (or all of them except one). If there is an approval cutoff, it would be better if it was an explicit one (this comment is not Plurality criterion specific but a general one).

Plurality criterion is a "heuristic" criterion in the sense that its message somehow sounds good (e.g. to people that do not regularly deal with election methods and their peculiarities). People would like also criterion "if voters would prefer A to B, then B should not win". But EM experts know that this criterion would not be a very good one, although it states something that we all would like to be true in all elections. What I'm trying to say here is only that we should be careful with cyclic group opinions. They will contain some nasty features. Instead of trying to pick a set of criteria that should be met 100%, my preferred approach is to see what kind of problems each method would be likely to face in real elections (typically but not necessarily large public elections with many different kind of voters that the strategists can not control), and evaluate them based on their performance in such real life situations.

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 c
 ircular 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.

Juho


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