[EM] Beatpath winner

[Eric Gorr]

At 3:16 PM -0400 10/15/03, Andrew Myers wrote:
>In Condorcet elections with the beatpath winner criterion, the
>computation of the beatpath winner involves finding the strongest
>beatpath connecting two candidates. To compute this one can run the
>Floyd-Warshall algorithm on the vote matrix, but with the matrix
>entries corresponding to a loss zeroed out. This zeroing out seems hard
>to justify in some ways and I'd like to understand why it's really
>necessary.

Do you understand that the Beatpath winner method is attempting to 
find the alternative that will pairwise beat every other alternative?

Do you agree that if an alternative does pairwise beat every other 
alternative that it should win?

>If candidate A directly beats candidate B 101 to 100, then the 100 votes
>are thrown out even though there are 100 people who think that B beats
>A. If candidate A ties with B 100 to 100, then both sets of votes are
>thrown out. If A loses 100 to 101, then A's vote are tossed out.

Right...in each of those cases, we only need to know who won so the 
overall winner (or tie) can be determined.

>This
>computation seems very unstable to me because a small change in how
>voters behave causes a potentially large change in the result.

You are describing a very close contest. I would imagine that under 
every voting system where the result was very close, your statement 
would be true. As such, it does not seem particularly relevant.


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== Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 ===
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