[EM] Ordering defeats in Minimax

[Juho Laatu]

> On 06 May 2017, at 23:26, Kevin Venzke <stepjak at yahoo.fr> wrote:

> It's not whether they are ranked (margins will essentially force me to rank
> them, I think), it's whether I decide to rank them sincerely.

I think all Condorcet methods have a severe incentive to apply one particular strategy. That is the strategy of sincerity, or the strategy if voting / casting one's vote. There is an incentive to rank all the potential winners (one can rank them all by listing all except one of them in the ballot).

All potential members of a top loop are included in the definition of potential winners. Both sincere and strategic potential winners are included in the definition.

Let's assume that in some group of voters all prefer A to B but they don't rank candidates A and B. B wins the election, and A is not too far behind. It is obvious that those voters would have had a better strategy, the strategy of expressing their opinion on whether A or B should win. This is not a rare incident if it is common among the voters not to rank many of the potential winners. This could thus be the most common mistake that a voter might make in an election. It is about as severe as staying home in a Plurality election, and then wondering afterwards, why the favourite of our group did not win.

Wouldn't you call this a strong strategic incentive? :-) The impact of many other strategies could be much weaker and more improbable. Any strategy that includes truncation would force you not to follow this strategy. And strategies that include changing the order of some of the candidates could be even more catastrophic. These effects are particularly strong in large public elections where nobody has accurate prior knowledge on how people are going to vote, or how much and what strategies they might apply.

> Legislators usually don't use election
> methods. I would say essentially they figure out among themselves what
> the outcome likely must be and then "elect" it, typically by a majority
> vote. If voters could do that directly I think that would be the ideal
> situation, as far as minimizing the need for strategy.

That's an interesting viewpoint. I'd like to see Condorcet tested in some parliaments. Although negotiations and Plurality can be used to solve many cases, also Condorcet and the idea of having multiple candidates could have some benefits. The first one in my mind is openness. Even when the "big boys" have agreed something behind the screens, and then bring that decision into a majority vote, some smaller groupings could add some alternatives in the election that they consider better. This would open up the available alternatives to the world (media, public), and all voters would have to take position on the presented alternatives. Small parties or groupings could thus make sensible compromise proposals that might even win, if they are good enough.

> I'm not sure if you thought I was talking about a legislature using
> Condorcet. What I was saying is that I don't think the behavior of a
> legislature would be emulated well by, for example, picking any arbitrary
> option from the top cycle. Some of those options may not be plausible
> outcomes, despite what the pairwise matrix says.

I think what I was thinking wast only that in small closed circles where everyone knows everyone's opinions strategic tricks are easier (but not easy) to apply than in typical large public elections.

I think Condorcet does pretty good job also when there are non-plausible alternatives in the election. If some option is really bad, it would not end up in the top cycle. Or do you expect strategic voting to be so rampant that legislators would use their most disliked options in their strategies and eventually elect them? A sensible voter should rank the non-plausible non-wanted options last.

> >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.
> 
> One idea is that Plurality approximately says that if candidate X wins
> then there should be some way to place approval cutoffs within the
> rankings such that X is the approval winner. (First preferences come
> into play because it's assumed no one would disapprove those.)

That's a good approach. Ability to win an Approval election (without changing the rankings) says pretty much everything that the traditional Plurality definition should say. Maybe it should be called and Approval criterion or something like that instead (word "Plurality" is quite confusing even with the original definition).

First preferences have an impact since they are the extreme top position in the rankings. A good definition should however not include any references to them. One viewpoint to this is that we can always add to an election n new candidates where n = number of voters. Each voter has now his own private candidate that is ranked first in one vote and last in all other votes. The results should still be the same, although all the old candidates now have zero first preference votes.

Juho


-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20170507/076f6c1d/attachment.htm>