Who has worked out a regression model to predict the winner of a
multicandidate election? (not vote share, but the winner)

A question arose in a student's research project.  Suppose there are
legislative elections held in may districts and that the winner is the
one with the most votes.  We want to predict which candidate will win in
a race with many candidates, using information about the candidates and
their political party identification.  Not all districts have the same
number of candidates, since some parties don't offer candidates in some
districts, while there are some candidates for whom the party
information is missing because the candidates declare themselves as
"independent."

Sometimes a candidate can win with 20 or 30 percent of the vote,
sometimes more is required.

When I first thought about it, it seemed to me it is like a random
utility model of discrete choice, where candidate 1 wins if the vote
total P1 is bigger than the vote total received for all other
candidates.  In the way they write down random utility, then, if I had a
model for total votes received.  Think of PX as utility, go on autopilot
and write down:

P1 = b0 + b1 *X + e1
P2 = c0 + c1 *X  + e2
P3 ..

Then the probability that 1 wins is

Prob( 1 wins ) = Prob ( P1 > P2 and P1 > P3 and P1> P4 ....)

The errors e1 e2 e3 .. are correlated.

I am stopping to ask you who has done this already?  Because I have
great difficulty believing somebody did not do this before.

pj

--
Paul E. Johnson                       email: [log in to unmask]
Dept. of Political Science            http://lark.cc.ku.edu/~pauljohn
1541 Lilac Lane, Rm 504
University of Kansas                  Office: (785) 864-9086
Lawrence, Kansas 66044-3177           FAX: (785) 864-5700

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