[EM] Markus: Your error. My misunderstanding.

[MIKE OSSIPOFF]

Markus--

Again I have to apologize because I misunderstood what you meant.

You'd said:

>[the voter] will probably approve all potential winners, or
disapprove all potential winners...

I thought you were saying that would be a person's _strategy_, to
try to vote for both frontrunners or for neither frontrunner.

Of course that's the opposite of the actual goal. The goal with
Approval is to vote for one of the 2 frontrunners and not for the
other.

When it seems that someone has said something as absurd as that
people's strategy is to vote for both or neither of the frontrunners,
I should reconsider whether they really meant that, before I
say something like calling you an academic :-)

In another of your messages I noticed what your misunderstanding was,
and I'd like to comment on it now:

You'd said:

>In your example, you presume that candidate C is the Condorcet winner
>of the sincere vNM utilities and that as some voters vote >strategically, 
>candidate B is the Condorcet winner of the reported
>vNM utilities.

No. No one said anything about sincere vNM utilities. You said that
the ratings reported by the voters may or may not be their vNM
utilities. Their reported ratings is what you said to use in order
to determine the pairwise defeats, who beats whom, for the purpose of
determining who should win if the method meets Condorcet's Criterion,
or Beatpath GMC, etc.

I didn't say that B wins by reported utilities. I said that, by
the reported ratings, C is the candidate that should win if the method
meets Condorcet's Criterion or Beatpath GMC.

What does B win by? B wins by the rankings that we derive from the
voted ratings. You never said how to derive rankings from the
voted utilities. You never gave a uniform rule for that. So I
assumed that maybe you meant that, for any method, we should make out
that method's ballot so as to maximize the voter's 0-info utility
expectation. With Schulze's method, that gives us rankings that
elect B.

Again, if you have another uniform rule for deriving, from the
voted ratings, the way to mark a method's method-specific ballot,
for determining the winner by that method, then you should tell us.

Mike Ossipoff







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