[Election-Methods] When Voters Strategize, Approval Voting Elects Condorcet Winners but Condorcet Methods can Elect Condorcet Losers

[Peter Barath]

>>Would it be possible either in Range or in Approval to
>>gain this pairwise comparison information from the
>>already cast votes? Maybe by Condorcet-style votes
>>or something? (People don't like to vote twice.)

>Of course they don't. However, if you choose the pairwise winner,
>you might as well use a Condorcet method, but you'll lose the
>optimization of overall satisfaction.

Well, if you remind me to Condorcet, I have to admit having
a bit of doubt about this loss. I don't remember seeing the
result of this particular simulation. (I mean Condorc-Appr.)

I remember a simulation with full strategic voters but without
make-a-cutoff-and-if-no-condorcet-winner-then-approval method,
and another one which maybe included it but it came with an
arbitrarily chosen 50 percent honest voter, which is unrealistic
by my guess.

(Warren D. Smith gives somewhere an example of distorted
- probably unintentionally - poll answers. In a place where
Nader was not allowed to vote for, people were asked would they
if possible. They gave an unrealisticly high proportion of "yes".
So I don't think polls are good for estimating honesty.)

My guess is Condorcet is a super method as long as we stay
in situations where a Condorcet winner exists.

Theorem (Barath's first and last theorem): It's not possible
by changing honest votes into dishonest ones to change from
a Condorcet-winner to a better Condorcet-winner.

(In other words: Condorcet-strategizing can be based on the
fact that there is not always Condorcet-winner, so by
changing from C-exist to no-C or from no-C to C-exist
or from no-C to another no-C situation.)

Proof sketch: If such move exists, it means there are
ballots dishonestly changed and made Bea win instead of Al.
If Bea is better for these voters then on their sincere
votes Bea must have been in higher position than Al. If with
these honest votes Al beat Bea (like every others a Cond-w must),
then Al still must beat Bea with the dishonest ones, because on
these ballots Bea's position compared to Al cannot be improved.
And if Bea doesn't beat Al, C-winning is out of question.

Maybe by mixing Condorcet and Approval - a highly "honest"
method - we can get a method which gives more than sincere
approval sortings: sincere preference orders!

Before Warren D. Smith or anybody else would make a simulation
for this - with supposedly "strategizing" voters - could
somebody give an example of order-reversal in this
Condorcet-cutoff-Approval method?

Peter Barath

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