[EM] Winning-votes intuitive?

Blake Cretney bcretney at postmark.net
Sun Mar 10 12:55:42 PST 2002

Adam Tarr wrote:

>> The point is that if my first choice is A, the method penalizes me 
>> for not choosing between B and C, by strengthening one or both 
>> candidates, and therefore weakening A.
> Certainly not both candidates!  In the zero-information election, you 
> don't know which one you should weaken... you may swing the wrong 
> 3-way tie by casting an insincere later vote.  It does not seem 
> intuitively obvious to me that casting random later votes will 
> generally help you more than it hurts you.

If you agree that it generally is more helpful to a candidate to have a 
loss decreased then a victory increased, it follows that random ranking 
is better than leaving candidates unranked at the end of the ballot. 
 Winning-votes ensures that a vote in either direction will either have 
no effect or ratchet up the size of the victory between two candidates. 
 The only exception being the discontinuity at a tie, where the value 
goes back to 0 (except in Markus's system).

But is my premise true?  It certainly is for three candidates.  With 
three candidates, both methods are equivalent to Minmax.  Minmax can be 
phrased as giving the victory to the candidate whose defeat is least 
strong.  Having a stronger victory only helps in so far as it increases 
another candidates defeat.

The situation becomes more complex with additional candidates.  However, 
unless you think examples with 4 or more candidates have the reverse 
tendency, they won't cancel out the tendency for three candidates.

Blake Cretney


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