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

[MIKE OSSIPOFF]

Blake wrote:

[...]

Another way out is to redefine plurality so that it applies to ranked
ballots. The winner is the candidate who gets the most first-place
votes. Now, plurality fails. I suspect that this is the approach most
academics would take. However, it clearly involves a redefinition of
plurality.

I reply:

Yes, and then it isn't Plurality.

Blake continues:

For my web site, I avoid the problem by using a definition of CC that
only applies to ranked ballots, and a definition of plurality that only
applies to lone-mark. So, CC doesn't apply to plurality. In other
words, I avoid the question. Personally, I think that it is obvious
that the goals of the Condorcet advocates are not achieved by plurality.

I reply:

Yes, but Plurality fails my CC for the obvious reason why we
expect Plurality to fail CC: Plurality only allows us to vote
preferences with respect to one candidate.

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.

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.

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.

For instance, Nurmi, if I remember correctly, defines sincere
Approval voting to be voting (only) for the candidates whom one
approves of. Brams & Fishburn define it in a way that's consistent
with my sincere voting definition.

But Nurmi's definition is valid for me, since it's the way I'd
vote in Approval, though I prefer acceptable/unacceptable to
approved/disapproved. Though it's how I'd vote, it isn't what
sincerity means to me when I define my criteria, so I use a
different definition for that purpose.

Blake continues:

I am amazed by all the competing interpretations of sincere votes. Mike
believes that a voter implies acceptance of any candidates she ranks.
I, for one, believe no such acceptance is implied.

I reply:

Well, I personally wouldn't rank anyone I didn't consider acceptable.
Ok, maybe ranking someone doesn't imply acceptance, on everyone's
ballot. Only if you're particular whom you respect enough to honor
them by voting for them.

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.

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?

It's true that our preferences aren't always "dichotomous", but
in our political elections here, the candidates are, for me,
acceptables & unacceptables. Of course you don't vote where I do.

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.

That definition doesn't have to match Nurmi's definition of sincere
Approval voting. There are different ways of talking about sincerity.

A person can vote, in Approval, sincerely by my definition for criteria,
but not by Nurmi's definition. Mine is better for criteria because
it allows for strategy. For instance, if Bush really has an 87%
approval rating, some of those must be Democrats, and presumably
in a 2004 Presidential election by Approval, they'd vote for the
Democrat but not for Bush, if Bush is the Democrat's rival. They're
voting sincerely by my definition but not by Nurmi's definition.
And they're not voting as I would, because I'd vote Nurmi-sincererely
in political Approval elections, if "approved/disapproved" is
replaced by "acceptable/unacceptable".

So, since many people wouldn't vote Nurmi-sincerely, then my
sincerity definition is more realistic for criteria.

Mike Ossipoff


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