A Manipulable Voting Example

[Mike Ossipoff]

Bruce--

You ask what your example means. I was about to ask you the same question.

I'll answer the question though: It means that in that situation where
some of the voters know for sure how all of the others have voted,
those who have that perfect information can use it to get a result
different from what sincere voting would do, in Condorcet's method,
as defined by its advocates here. It means that in that community where
2 people who haven't voted yet, and know how everyone else has voted,
in that particular situation, it's possible to make Regular-Champion
look better than Condorcet.

Regular-Champion, of course reduces to Plurality in any circular
tie in a 3-alternative election. Plurality by itself would have
elected C also.

Though I haven't yet done the Condorcet count, the fact that
truncation succeeds means that there isn't a Condorcet winner.
Truncation can't succeed in Condorcet's method when there's
a Condorcet winner. In fact, transparently, it can never elect
an alternative with a majority against it if there's any alternative
that doesn't have another alternative preferred to it by full
majority.

So the example proves nothing. It has nothing in common wilth the
public political elections that we want to find the best method for.
And the truncationcouldn't have worked under the conditions
where it's important, in Condorcet's method.

***

But you've shown why I don't recommend Condorcet's method for
meetings using show-of-hands voting. For such meetings I
prefer the methods that I've called BeatsAll//Approval, &
Condorcet//Approval.

***

By the way, notice that Bruce has unilaterally changed the meaning
of "order-reversal". I've been using the term to mean reversal of
1 or more preference orderings. Bruce wants to limite its meaning
to reversal of _all_ of one's preference orderings. I suggest that
if Bruce wants to talk about reversal of all of one's preference
orderings, he call it "comprehensive order-reversal". There's nothing
in the term "order-reversal" that requires reversing more than 1
pairwise preference ordering.

***

Another thing, if the would-be cheaters' candidate happened to have
a Plurality, or if, in a bigger election, happend to be a winner
by Copeland's count rule, either of which could easily happen, then
obviously Regular-Champion would also be "manipulable" in that
situation.

***

But here's something else: I've been repeatedly saying that 
"manipulability" is a term with questionable meaning. Plurality
is "manipulable", because Nader voters, knowing that Nader
hasn't got a chance, can at least help Clinton beat Dole, by
voting for Clinton. They're maniplulating the outcome by voting
other than sincerely. Is that a bad outcome? Are they cheating?
The answer to both questions is no. 

What's bad about Plurality, the strategy problem that it has, is
not that someone can "manipulate"--what's bad about Plurality is
that voters commonly have to use defensive strategy. Drastic
defensive strategy.

Bruce, do you belive that "manipulability", as you mean it, is
a more important consideration than the _need_ for defensive
strategy, and the need for drastic defensive strategy, by
a majority group that wants a particular result?

The academic voting theorists have been barking up all sorts of
wrong trees, studiously avoiding the considerations that are
important to voters & electoral reformers. Even when it's held
right under their nose.


Mike





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