[EM] More surprising summability results
Kristofer Munsterhjelm
km_elmet at t-online.de
Fri Jan 26 05:19:34 PST 2024
A few days ago, I wrote a program that was intended to determine the
minimum number of values requires to tell disjoint winner sets apart,
and I decided to test it with the Condorcet winner sets - i.e. determine
how many values would be required for a summary that tells apart
elections where X is the CW and Y is the CW, for every pair X and Y.
And I couldn't get it to work because it was returning results
suggesting that the number of dimensions required is much lower than the
n^2 I was expecting.
But then I thought a bit about it and I realized there does exist an
O(n) summary that can be used to create a method that passes the
Condorcet criterion... *as long as you give up neutrality*.
It's so obvious in retrospect, but it was very surprising to me before
the fact. Can you see how it would be done?
-km
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