[EM] Intro to list (etc)

Adam Tarr atarr at purdue.edu
Sun Oct 26 18:35:02 PST 2003


>1)  Determine the winner.
>2)  Order the losing candidates from the one with the strongest beatpath 
>against
>the winner, to the one with the weakest.
>3)  Assign the winning candidate a score equal to its beatpath against the
>strongest losing candidate.
[...]
>49% Bush
>12% Gore>Bush>Nader
>12% Gore>Nader>Bush
>27% Nader>Gore>Bush
>
>The results by my proposal would be displayed:
>
>1) Gore 51%
>2) Bush 49%
>3) Nader 27%

That's not quite right.  What I show there is the pairwise counts of each 
of Gore's contests.  Which is really what I want; that seems like the best 
measure when there is a Condorcet winner.  That said, it would look very 
strange to the casual viewer if a loser had a higher score than a 
winner.  So I would add the following fourth step to my process above:

4)  Replace all non-winning candidates' scores with the number of votes 
they received against the winning candidate, unless this amount is larger 
than the winner's score.

So, my ranking of the example on Rob's site would now become:

1) Abby 511
2) Brad 463
3) Cora 460
4) Dave 436
5) Erin 410

It's a bit more pleasing to the eye, isn't it?

This is admittedly a mishmash of a couple different measures, but I think 
it does a good job of getting a monotone ranking out of pairwise 
ballots.  At least, I'll think that until someone comes up with a good 
counterexample.

-Adam




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