I've added support for Yee diagrams to my election program. Because I've
already implemented a number of multiwinner methods, this let me render
multiwinner Yee diagrams for them.
If you want to browse, just go here:
http://munsterhjelm.no/km/elections/multiwinner_yee/
The elections are (2,5) - that is, council size of 2 and 5 candidates.
Some observations based on this:
- Systems that work based on quota seem to return simple polygonal win
regions for the various councils that can win - or, at least, that's
what they would do if they were monotone.
- Systems that are based on divisor methods return curved regions.
Again, most of them have monotonicity problems.
- Setwise Highest Average, which I thought would be monotone (since it's
based on a monotone method - the highest average party list PR method),
is not so at all. Look at configuration 3, for instance. I suspect the
reason is that the exclusion of prior candidates (in rounds after the
first) can lead to a situation similar to classic IRV nonmonotonicity
examples.
- For Gaussian voter distributions on a 2D map, there's no difference
between Warren and Meek as far as STV goes.
- I was wrong when I said the proportional diagrams would (sans
distortions) be like majoritarian Condorcet. The results for
"Majoritarian Condorcet" at the bottom shows this: with large sigma
values, some regions become larger than would be the case if the
election was done by majoritarian Condorcet. This is one of those things
that's obvious in hindsight: if, in the 1D case, the distribution is
nearly flat, Condorcet would elect a bunch of centrists whereas the
proportionally right thing to do would be to elect the candidates at
uniform intervals of the distribution.
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