Simple Nonmonotonic Example

[Mike Ositoff]

> 
>  Mr. Ossipoff wrote--
> 
> 29  31  40
>   A   B   C
>   B       B
> 
> B wins. Now, 3 of the C voters insincerely downrank C, and
> vote A, their last choice, in 1st place.
> 
> The result is that now C wins. Those voters made C win
> by ranking it lower.
> ---
> For the umpteenth time, I mention again that there will be polls.  If no
> candidate is a clear CW, then there WILL BE strategic voting.  How many of
> such candidates are acceptable to a majority (51) of the voters ?

Strategic voting isn't really my concern in that example. If
nonmonotonicity were just a tricky opportunity to try offensive
strategy, it wouldn't be so bad. But say you're a C voter, 
indifferent between A & B. While driving to the polls to vote
for C, you hear on the radio that C has just been caught
taking bribes, and so you decide to make sure, instead, to
vote someone over C, to defeat him. You, pick A to vote over
C, maybe randomly, maybe because you now feel that the has
the best honesty record. You're one of those 3 C voters who
changed their vote.

But, by voting someone over C, you elected C, helped him win
instead of the CW who'd have won had you not downranked C.

When you change your vote, you have a right to expect that
to not change the result in the opposite direction!

Mike Ossipoff





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