[EM] Condorcet Criterion definitions (was Markus' Econometrica reference...)

Blake Cretney bcretney at postmark.net
Wed Jan 30 18:39:33 PST 2002


> Blake continues:
> Another solution to the problem would be to redefine CC to involve the
> idea of voting sincerely. Presumably, sincere votes in a Condorcet
> completion method should result in the sincere Condorcet winner winning.
> But they would not in plurality. So, if we define CC on sincere votes,
> perhaps this would be the best solution.
> It's the one that I like best and use.
> Blake continues:
> In fact, as this list has proven, that solution is far more complicated
> that one might naively imagine. Remember that the previously suggested
> approaches only considered ballots, with methods and criteria based on
> them. The sincerity-based CC involves a theory involving voters having
> mental states that correspond to particular ballots. But it isn't
> always clear in what sense these mental states exist
> I reply:
> What are you talking about?? You can call a preference for chocolate
> over vanilla a "mental state", but it isn't some debatable theory.
> It's known that people have preferences on all sorts of things, 
> including political candidates. A definition of "prefer"? We could
> say that John prefers X to Y if, given the choice, he'd choose X
> instead of Y, if there were no considerations other than having X
> or having Y. But then someone could ask what "choose" means, or
> what "he" means, etc., but we don't have to get into that, at least
> I "prefer" not to.

Theory doesn't necessarily mean debatable.  My point was that we've 
expanded the issue under discussion.  The old theory only considered 
preference orders and methods based on them.  We need a new theory to 
talk about what's going on in people's heads, and how that is reflected 
in sincere ballots.

> Blake continues:
> , and how they
> correspond to "sincere" votes is not obvious either.
> I reply:
> That's why I defined "sincere voting", for the purpose of my
> criteria that refer to sincere voting.
> When it's defined, it's obvious.

Your definition may well be clear and easy to apply.  I don't remember 
your definition.  My point is that it isn't obvious that it is the 
single correct definition of sincerity, since there are multiple 
positions on this subject (and not just mine and yours).

> Yes, there can be different definitions, but not for use with
> my criteria.
> My "sincere" should really be called "sincere & complete", but
> I prefer the briefer "sincere". The fact that there can be many
> different interpretations of what kind of sincerity people are
> talking about when they say "sincere" shouldn't be surprising, and
> it shouldn't discourage us from using the word, provided that we
> define it in a way that's appropriate for the purpose for which
> it's being used.

It's perfectly reasonable for you define sincerity or CC your own way. 
 But then you have to explain why these definitions reveal the truth 
about plurality.  Perhaps you have a great argument to that effect.  But 
I think it would be simpler just to argue why plurality or approval 
isn't acceptable to Condorcet advocates, without having to go into all 
these new definitions.

> Blake continues:
> Some people believe
> that they "approve" only of a fixed number of candidates, and that a
> sincere approval vote is for exactly these candidates. So for them, a
> particular approval ballot corresponds to a particular judgment about
> the candidates, a particular mental state. Personally, I do not
> normally make this kind of judgment about the candidates in an election.
> I reply:
> But anyone who doesn't have any "mental state" about the relative
> merits of the candidates shouldn't vote. You make "mental state"
> sound like some sort of debatable ghostlike concept.

Personally, I have a mental state about relative merits.  I do not have 
a mental state that divides candidates into two different groups, one 
acceptable, the other unacceptable.  I could perform the task of 
dividing candidates into the two groups, but I would need more to go on. 
 For example, I could divide them on the basis of strategy.  Or, I could 
divide them on the basis of falling at below average utility (although 
this would be more difficult).

> Isn't there, for you, such a thing as a set of candidates who
> are absolutely unacceptable, so that voting would be a simple matter
> of voting for everyone else, in order to do all you can to avoid
> victory by an unacceptable?

No.  There are certainly candidates I abhor.  But that doesn't mean that 
voting comes down to keeping them out, as opposed to trying to get who I 
want in.  As well, I may vote for one candidate I abhor to keep another 
candidate I abhor out (in approval or plurality).  In a ranked method I 
would usually rank abhorred candidates to the extent I have a preference 
(unless I'm too lazy and they have no chance of winning).

> Blake continues:
> So although the purpose of the sincerity-based CC was to make it easier
> to explain why a Condorcet advocate would reject plurality. In fact, it
> makes the explanation much more complicated.
> I reply:
> But my definition of sincere voting, for criteria, isn't compliced.

I assumed that you would want to defend your criteria and definition. 
 That makes the explanation more complicated (or at least longer). 
 Maybe there are people who are so in awe of mathematics that when you 
prove that a particular definition (of your own design) applies, they 
feel that you have proven your point.  If I define the "Great Method 
Criterion" and prove that Ranked Pairs passes it, they will take it as 
proven that Ranked Pairs is a great method.

But for reasonable people, the objective proof of a method passing a 
criterion has to be supplemented by an argument for why they should 
care.  So, the question is, if you want to make a Condorcet-based 
argument against plurality, is this simplified by the whole sincere-CC 
issue.  I don't believe it is.  I don't feel that strongly about it, though.

Blake Cretney

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