[EM] New VSE & nonmanipulability numbers

Jameson Quinn jameson.quinn at gmail.com
Sun May 11 21:03:08 PDT 2014

As I've mentioned several times, I've been working on some new voting
system simulations, akin to Warren Smith's Bayesian Regret work. I have
some new and, I think, interesting results now. I'll explain my full
methodology later, but first, here's an old graph I had which I've updated
using my results:

[image: Imágenes integradas 1]
* These systems (Borda and IRV) have flaws which do not show up in the
graph. Also, Random Ballot should be more than twice as far to the left of
the Y axis as I have put it.
** These systems (SODA, Approval w/Runoff, and Plurality w/Runoff) are in
principle possible to simulate, but I haven't finished doing so yet, so the
numbers used here are educated guesses using my work so far.

The circle size is based on my own subjective evaluation of how "simple"
systems are — dark circles for the simplicity of explanation, and lighter
circles for the simplicity for voters of finding a "good enough" strategy.

Note that MAV is a median system, like MJ, GMJ, or ER-Bucklin; and for
"Condorcet", I used minimax (easiest to program). For "Approval", I did two
separate simulations — one in which all voters put their cutoff at the
average candidate, and another in which they put their cutoffs at a random
point in between their favorite and least favorite. The numbers used here
are an average of those two.

"VSE" (Voter Satisfaction Efficiency) is akin to Bayesian Regret; the
quality of the average result, normalized so that a system which always
chose the highest utility result would get 100% and Random Ballot would get
0%. The VSEs in this chart (aside from RB) run from 95% down to 76% (for
honest voters; with strategic scenarios, they can go as low as 59%).
"Nonmanipulability" is how often there is an effective one-sided strategy
in favor of the honest second place finisher (or in the case of IRV, in
favor of some other candidate). In this chart, the nonmanipulability runs
from 95% (MAV) to 52% (Approval).

The voter utility model is based in a 3 dimensional candidate space with a
2-dimensional voter space (thus, nearness to the plane of voters means
candidate quality). Voters are added to weakly-correlated "clusters"
in a chinese-restaurant-like
process <https://en.wikipedia.org/wiki/Chinese_restaurant_process>.

While I expected a fair amount of what you can see here, there are
certainly plenty of things which surprised me.

I'll be sending more graphs, numbers, and explanations in the coming days.
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