[EM] More 0-info pairwise strategy

[Blake Cretney]

On Mon, 20 Mar 2000, "MIKE OSSIPOFF" wrote:

> You're trying to maximize a candidate's chance of losing
> (or the chance of all the sub-mean candidates of losing),
> in case they don't have a majority pairwise defeat, in case
> a majority isn't trying to get that defeat. Fine. I don't have
> a problem with what we have incentive to do non-defensively.
> Maybe I'd vote the strategy Blake suggests, in a 0-info
> election with Condorcet, but I don't regard that incentive as
> a problem for Condorcet.

Your posting makes the case that equal rankings aren't a problem for Condorcet, where, by "Condorcet" you mean a family of methods using winning-votes.

That question is really too broad for me to deal with.  I think everyone would agree that it is at least slightly better when people have reason to vote sincerely, so your statement, that this isn't a problem, really means that you have considered this negative effect, and compared it to the problems of other methods, and found that this is acceptable in contrast.  For me to debate that point would require me to go through a thorough comparison between the winning-votes methods and the marginal methods, something we have all seen before.

However, there are two more precise questions that I think are both answerable, and worth answering:

1.  What is the best strategy in each of the winning-votes methods, given zero strategic information?  I have conjectured based on no real evidence that it might be similar to Average Ratings, that is, to rank as equal all candidates of above mean utility.  The below mean candidates would, of course, be ranked sincerely, or, when no sincere preference exists, randomly.

> Of course defeating your last choice isn't really all that matters
> to you usually, so in Condorcet, you have some reason to want
> to sincerely rank the candidates whom Blake said you'd put
> in 1st place. 

The question isn't whether you have "some reason," it's whether you have a good reason.  That is, what maximizes expected utility?  You are evading the issue of what is the best strategy by suggesting naive strategies.

For example, imagine we are playing a dice game with a standard 6 sided die.  You can choose to play "low", and win $1 if it comes of 1.  You can play "highs" and get $1 if it comes up 5 or 6.

If your goal is to maximize your expected winnings, your best strategy is to play highs.  Of course, you have "some reason" to play lows, that is, it allows you to win on a 1.  But a reason isn't necessarily a good reason.

> And in Margins, since defeating your last choice
> isn't all you want, you'd like to protect your more preferred
> candidates by sharing 1st place position with them. If you don't,
> for instance, one of them could turn out to be a sincere CW who
> lost because of truncation, and because you didn't insincerely
> share 1st place with him.

But can you give an argument for why in a 0-knowledge situation, falsely ranking two candidates as equal can maximize expected utility, in margins?  All you have done is suggested that in some cases, equal ranking can help.  But unless you know that you are dealing with one of those cases, that isn't a good reason to vote a particular way.

2.  Does this affect strategy in real elections?

You weren't directly addressing this question in your 3 points, but the first point has some relevancy.

> 1. Blake's discussion was about a 0-info situation. Never happens
> in public political elections. And even committees should have
> discussion before voting, and then there won't be 0-info.

You probably will never have the perfect situation of zero strategic information.  However, it would be absurd to argue that a single shred of information would suddenly change correct strategy away from the zero-knowledge strategy.  The change will be gradual as more information is accumulated.

Furthermore, when formulating a strategy with some knowledge, it makes sense to start with the zero-knowledge strategy, and modify it based on the additional knowledge.  That's what you would do in approval.  The zero-knowledge strategy in approval is to "approve" candidates who are above your mean utility.  As you get additional knowledge, you try to differentiate between candidates in likely close races.

Similarly, to decide how to vote in winning-votes, you would start with the zero-knowledge strategy, whatever that is, and adjust it, using the normal strategies of order-reversal, but also by differentiating between candidates if you think the race will be between them.

BTW, here's an interesting idea.  What if we asked voters to sincerely rate all their candidates.  Then, a computer program could translate these ballots into the optimal zero-knowledge winning-votes ballot.

This new optimal-winning-vote method would be similar to winning-votes, but would ensure that every voter is given some of the advantages of understanding the potentially very complicated winning-votes strategy.

> I've noticed that some prefer "sincere CW" to mean what I
> meant by "CW". And presumably many would use CW to mean what
> I call "BeatsAll candidate". Ok, I'll use "sincere CW", and
> maybe abbreviate it SCW. I'll still say BeatsAll candidate
> to mean the candidate that beats each one of the others, unless
> it's a sure thing that people prefer CW to have that meaning.
> There's plenty of academic support for CW to mean sincere CW,
> but I'll use SCW if that's preferred here.
> 
> Some authors say "Condorcet candidate" to mean SCW, so that
> usage should be ok here too.

I think that it is less confusing not to have the idea of a CW tied to either the sincere or actual preferences, as other concepts, like plurality winners and Smith sets are not.  I don't consider the use of CW to mean SCW to be actually wrong, though.  I have seen it used both ways.

---
Blake Cretney