[EM] Finding "defining" scenario results for a given method

Kristofer Munsterhjelm km_elmet at t-online.de
Tue Feb 15 03:53:56 PST 2022


On 14.02.2022 02:55, Kevin Venzke wrote:

> A slightly different approach could be to focus on finding a few scenarios that
> each independently differentiate as many methods as possible, while also
> correlating as little as possible with the other scenarios' differentiations.
> Then these several scenarios could be used as a litmus test to gauge what a
> proposed rank method is similar to, without having to implement it.

For my minimal strategy simulations, something with very few candidates
would be nice... but I suspect that the three-candidate minimal strategy
method would be very close to fpA-fpC anyway.

I also tried to do something like this in quadelect, by using the mean
Kendall-tau distances between voting methods' results to give the
distance between voting methods, and then constructing a dendrogram from
it with hierarchical clustering.

I got some strange results, so perhaps the "winner agreement distance"
would be better, i.e. the distance between methods is the chance that
they disagree for a randomly chosen ballot. And then use a more
plausible model than impartial culture - say IAC or a spatial model -
for the ballot randomness.

In any case, if you do that, you could try to find an election set that
distinguishes between the left branch and right branch at every level of
the tree. This could possibly work as a more principled way to group
methods together. On the other hand, there's no guarantee that there
exist a single election that will divide the sets in the same way that
the clustering method does (unless that's made a constraint on the
clustering process itself).

With only a few methods (say 9 or 16), it should be feasible to brute
force such an assignment: separate methods into two (or three) equally
sized clusters and check if there's a single election that tells them
apart. You could do that by random checking or by integer programming.
The former is (much) easier to program; the latter either definitely
returns a no (no such election exists) or a yes (here's the separating
election you want).

-km


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