[EM] The "Fresh Egg" winner - beyond Condorcet's pairs

[Adam Tarr]

At 03:45 AM 7/5/2003 -0500, Tom Ruen wrote:

>This also makes me see the idea of a progression of criteria of what a
>majority could mean among more than two candidates:
>1. A Top Majority (TM) - If a candidate exists that is never below first
>place among any subset of competitors.
>2. A Fresh Egg Majority (FEM) - If a candidate exists that is always above
>last place along all subset elections with competitors.
>3. A Condorcet Majority (CM) - If a candidate exists that is always above
>last place among all pairwise subset elections with competitors.

I can't help but think, if you've found an approach that only applies when 
the winner is both the IRV winner and the Condorcet winner, then that 
approach won't be very applicable.

>One way of counting a winner in Condorcet might be:
>1. For every pair election, give a point to the candidate in last place. (If
>there are more than one candidate in last place, divide that point equally
>among them all.)
>2. Give victory to the candidate with the least points. (If one candidate
>has zero points, there is a unique winner. Otherwise there may be a tie and
>a winner remains undefined among the tie.)

This is essentially what Copeland does, and Copeland is not only frequently 
ambiguous, but it is easily manipulated by clone candidates.

>One last note - this last-place count doesn't help choose a winner with the
>nasty Condorcet case: (AC=49, BC=48, CB=3)
>a1) A=49, B=51 - A last-place
>a2) A=49, C=51 - A last-place
>a3) B=48, C=52 - B last-place
>b1) A=49, B=48, C=3 - C last-place
>
>My last-place count gives a tie between B and C with one loss each. I
>somewhat like it that my count can't choose between them since each have
>some virtue for different voters, although a true method would need to be
>willing to be more decisive. (Perhaps looking at loss-margins from each
>subset? I'll leave this open.)

Or votes against in defeats.  Either would probably be more illustrative 
than simply counting defeats.

If you want to convince people that this is a useful method, you should 
probably try to find a case where the FE winner clearly differs from the 
winner of the equivalent Condorcet method.

-Ada,