[EM] Differences of sincerity definitions

[MIKE OSSIPOFF]

Craig L.--

I've taken a closer look at the 2 definitions of sincere voting,
and would like to comment on the differences:

1. Your definition allows the voter to not vote a sincere preference,
while my definition only allows the omission of a sincere preference
when the method wouldn't allow it in addition to the preferences
actually voted. There's certainly a case for saying that when
you vote 2 candidates equal, you merely aren't expressing a preference
between them, that you're abstaining for that pair. I'd felt that
the voter who votes A=B when he prefers A to B is insincerely calling
them equal, but your interpretation is equally valid. Maybe that voter
just isn't saying anything about which is better. I'm not sure which
way would be better in principle.

But my way serves the purpose of letting me write my criteria more
briefly, and so, for that practical purpose, I like my wording,
both being arguably equally valid.

2. Your definition allows a voter to vote an unfelt preference if
not doing so would prevent voting a felt preference. But that's like
saying that abstaining about a pairing is more insincere than voting
an unfelt preference.

Also, if the preferences that I've voted for A are sincere, and I
sincerely rate B equal to A, then voting B equal to A can't interfere
with the expression of a sincere preference. So that clause of
your definition isn't needed.

3. Your definition, but not mine, takes into account the fact that
a rank-balloting system sometimes doesn't allow someone to rank
candidates equal. But IRV and Borda are the only rank method proposals
that I know of that don't allow equal ranking, and I'm not sure right
now whether allowing for that fact would change their compliance with
any of the criteria that stipulate sincere voting.


On another topic, neither sincerity definiton requires Cardinal Ratings
voters to vote their actual felt ratings. But Cardinal Ratings fails
the criteria that stipulate sincere voting, and still would if
the sincere voting definition required the voter to vote his actual
felt ratings. Aside from that, of course, rank order is much easier
to vote than accurate felt ratings. (I'm avoiding the word "sincere"
here).

A clause could be added to those sincerity definitons to make them
really universal, and make them apply to Cardinal Ratings. That isn't
necessary in a practical way, since they work fine for Cardinal Ratings
with the criteria. And even in their present form, the sincerityd
definitions define a degree of sincerity in Cardinal Ratings. But
maybe, ideally, the definitions should have versions that cover
Cardinal Ratings so as to require complete sincerity with that method,
making them truly universal in application.

You asked Markus if he meant that we assume or simulate sincere ratings
for the voters. Don't let him off so easy: He's saying that the
assumption is that the voters actually _vote_ ratings, which may
be their vN-M utilities, or may be just insincere numbers.

As you suggested, criteria could be written involving voters' sincere
ratings. Some of my criteria speak of sincere pairwise preferences.
As you suggested, a version of IIAC could be written about sincere
ratings. In fact, we often hear IIAC spoken of as if it is about
sincere ratings, and 2 ballotings, one of which has a candidate who
isn't in the other balloting. When people refer to that "version",
they never define it. It would obviously be much wordier and more
complicated than the version that I quote, and which is almost surely
Arrow's version:

Deleting a loser from the ballots and then recounting those ballots
should never change who wins.

A more complicated version could say that no matter what people's
sincere ratings are, and no matter what the relevant probabilities are,
it should be impossible for the addition of a new candidate, in a
new balloting, to change the winner, when everyone votes so as to
maximize their sincere ratings expectation, in each balloting.

I doubt that any method could comply with that though.
Make the new candidate a clone, and the criterion is similar to
the suggested clone criterion replacement that I refer to below.

Maybe that would do for the wording of that criterion that we hear
referred to so much but never defined.

One of my suggested ways of making the clone criterion realistic
involves sincere ratings also. Right now, the unrealisticness of
the clone criterion makes it rather unmeaningful to meet that criterion,
which greatly reduces its usefulness for distinguishing between methods.

Mike

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