So do you think it still won't find a condorcet winner if it is modified as I suggested:
1) start with a much lower cutoff. Say 10 or 20. Or, if the ballots are simply ranked, start by giving a "yes" to all but the bottom-most candidates.
2) use an average of all previous totals to determine strategy each round.
I guess it won't, because lots of the voters gave that candidate a 0. I'm still thinking the results will converge, if not on a true equilibrium. Unfortunately this stuff is too tedious to work out by hand, so I'd have to write something to test it. But maybe you have a better idea than my own "gut feel".
Just a thought, what if you do this: first time, first round, approve all but the lowest rated candidates on each ballot. If no equilibrium is found, run it again, approving only the highest ranked candidates on the first round. Obviously that is sloppy, but I'm just curious if it might work. I think in the real world, the chance of that "failsafe" having to kick in would be remote.
I can certainly accept that you could contrive a case where it might never find the equilibrium. However, looking at the case you gave, I almost want to say that D shouldn't win, even though he's the condorcet winner (since he is clearly a very polarizing candidate, with half loving him and half hating him).
-rob
On 12/9/05, Rob LeGrand <[EMAIL PROTECTED]> wrote:
You have rediscovered Lorrie Cranor's Declared-Strategy Voting in
batch
mode using Approval and my "strategy A". Some of my current
doctoral
research is concerned with investigating DSV using different systems
(plurality, Approval, Borda, etc.) and strategies like the above.
Please
see http://lorrie.cranor.org/dsv.html for Cranor's dissertation on
DSV.
Unfortunately, DSV in batch mode using Approval and strategy A won't
always find a Condorcet winner. Consider the following votes:
A B C D
33: 100 70 30 0
16: 10 100 70 0
17: 0 70 30 100
34: 30 0 70 100
Reasonably assuming a 50 cutoff for each voter in the first round, B
will
lead in the first "poll". After cutoffs are adjusted, A will lead,
then
C will lead next. Then B will lead again and the cycle repeats. D,
the
Condorcet winner, will never lead, even though the only potential
equilibrium (still assuming strategy A for all voters) results in a
D
win.
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