[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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