[EM] Majority winner set

MIKE OSSIPOFF nkklrp at hotmail.com
Sat Nov 25 16:36:37 PST 2000

 > I agree that BeatpathWinner
 > meets BPGMC. And so does Plurality. I'm not just picking on
 > BPGMC. The usual definitions of the Condorcet Criterion have the
 > same problem. When CC is defined in terms of sincere preferences,
 > as it often is, then no method meets it. When it's defined in
 > terms of voted preferences, then Plurality meets it.

You (Markus) reply:

FPP violates Condorcet and beat path GMC.


    40 voters vote A > B > C.

I reply:

No they don't. Plurality doesn't have rank balloting. Plurality
isn't just a count rule to be applied to rank-ballots. Plurality,
like any voting system, is a combination of a balloting system
and a count rule. If your example uses rank balloting, then it is
not a Plurality example.

In Plurality, you vote A over B if you vote for A. If A wins,
that means that, when compared separately to every one of the other
candidates, A is voted over that other candidate by more voters than
vice-versa. The person who, when compared separately to each of the
others, is voted over him by more voters than vice-versa always wins
in Plurality.

But now I understand why they say that Plurality doesn't meet
CC. But it isn't valid.

By the way, I'm curious whether you'd say that Approval meets CC,
according to your approach.

    In the example above, I didn't make any presumptions
    about whether the voters vote sincerely or strategically.
    In the example above, I didn't make any presumptions
    about the sincere opinions of the voters. Did I?

I reply:

You made an incorrect presumption about Plurality's balloting.
The fact that you can't say whether or not Approval passes CC,
by your way of looking at it, shows that there's something wrong with
that way of looking at it.

If we go by actual voted preferences, then Approval passes CC. If
we go by felt preferences, then Approval, like every method, fails
CC. Using my wording of CC, Approval doesn't pass. (But I want to
add that Approval passes defensive strategy criteria that are of
much more practical importance than CC. Probably nothing else meets
FBC, and the non-Condorcet pairwise-count methods fail WDSC).

This isn't controversial: A voting system isn't a way of counting
rank ballots. A voting system is a balloting system and a count rule
for counting the ballots.

Mike Ossipoff

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