Lorrie Cranor's website about her DSV voting system describes
some ways of estimating the Pij from the vote totals in a poll
(or in a previous election with the same candidates).

Here's the URL for the Pivotal Probabilities article:

http://www.research.att.com/~lorrie/pubs/diss/node13.htm#SECTION00520000000000000000

The overall website is about DSV, which is a system that, based on
each voter's expressed utilities, calculates that voter's best
strategy in a Plurality election, and casts his vote in that election.
Then, using those vote totals, it calculates new Pij, and new
Plurality strategies, till the result doesn't change from one
count to the next. It seems too complicated for public elections,
and too difficult to get accepted. And it might have strategy problems.
But the Pivotal Probabilities article is interesting. Hoffman's method
involves more dimensions of outcome-space as we
add more candidates. That isn't true of Cranor's method.

Mike Ossipoff


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