[EM] Re: Beatpath winner

[Rob LeGrand]

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

I agree.  You're describing winning-votes.  I prefer margins, which would
replace the 101 and 100 with 1 and 0 instead of 101 and 0.

> What I'd like to understand is what bad things happen if you compute
> beatpaths adding the links that go in the "losing" direction, with their
> appropriate vote count. Clearly you get different answers for some
> elections, but is there a good example that shows that the answers you
> get are inferior?

You're talking about what's called all-votes, as opposed to margins and
winning-votes.  Try

2:B>C>A
3:A>B=C
3:A=B>C
3:C>A=B

The Condorcet winner is A.  Schulze's beatpath method using all-votes picks
B, while using margins or winning-votes picks A.

=====
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/

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