[EM] Demorep's new method

Anthony Simmons bbadonov at yahoo.com
Wed Aug 15 23:20:42 PDT 2001

>> From: Rob LeGrand <honky1998 at yahoo.com>
>> Subject: Re: [EM] Demorep's new method

I don't think going to a nondeterministic method will
eliminate whatever strategy might persist in the
deterministic version.  It just becomes a matter of
probabilities.  And I do find something off-putting about
involving dice in the vote counting.

What I would expect is that whatever strategies applied to
the individual component methods would be diluted by the
combination.  You know, like the usual on-the-order-of-the-
square-root-of-N rule, where things average out enough so the
variation in the combination is smaller than the variations
in the individual components.  What I was thinking is that
that could be bested by deliberately choosing methods that
have conflicting strategies.

Seems like proving any kind of properties would be more
difficult.  Well, not all.  If all methods were to put the
Smith set at the top of the lists, then the total Borda
scores should put them at the top of the composite.  (Since
for every candidate in the Smith set, each score is higher
than for every nonmember, totals should also be higher.  Same
for CW.)

>> Anthony Simmons wrote:
>> > For example, use ranked ballots.  Count them
>> > using three different methods, chosen so that
>> > their strategies conflict, and any strategy that
>> > works for one method would be counterproductive
>> > for the others.  Then take the social rankings
>> > produced by counting the votes using those three
>> > different methods, and use those a ballots in a
>> > Borda count.
>> . . .
>> > At first blush, it looks like Borda could be
>> > used as the metamethod because nobody would be in
>> > a position to use strategy to manipulate it.

>> This is a cool idea.  But the resulting metamethod
>> is still just a (more complex) deterministic
>> ranked-ballot method and is thus vulnerable to
>> strategy.  That strategy might not be as obvious,
>> but it seems to me that, given enough analysis,
>> the metamethod won't be any harder to manipulate
>> than the best Condorcet methods like beatpath or
>> Ranked Pairs.  Another problem is that proving
>> Condorcet or Smith compliance would likely be
>> difficult if you choose methods whose strategies
>> tend to conflict.  Proving monotonicity or clone-
>> independence might be hard too.

>> If rolling a die is allowed, choosing an election
>> method randomly after all ballots are in seems
>> like a great idea to me.  It would have limited
>> randomness if the methods are similar enough.
>> How hard would it be to choose Condorcet methods
>> so that their strategies conflict enough to make
>> it worthwhile?  (Using Borda as one of the
>> methods *might* not be too bad, but using
>> something like IRV or Coombs would be less
>> acceptable.)  I doubt you'd be able to produce
>> a completely non-manipulable scheme using this
>> idea, though.

>> --
>> Rob LeGrand
>> honky98 at aggies.org
>> http://www.aggies.org/honky98/

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