[EM] MMPO(IA>MPO) simulations wrt method similarity

[Kevin Venzke]

I ran some quick simulations on the IAMPO method. They don't incorporate strategy but are encouraging anyway, I think, and kind of surprising.

I also came up with another version that should be even slightly closer to MinMax(WV) without losing the four properties I'm focused on. I've been calling it TPPM for "tied-at-the-top Pairwise Plurality completed by MMPO." Instead of MMPO(IA>MPO) I'd say it's MMPO(tMVF>MPO) where tMVF means "most votes for, but using the tied-at-the-top rule," meaning that on a ballot which ranks A=B at the top, both A and B are counted as having a "vote for" them over the other. I'm pretty sure this works, but no promises yet.

Assuming it does work, the trade-off (which certainly may not be worth it) is that you can avoid the inelegance of requiring the implicit approval concept, in exchange for the inelegance of having to explain the tied-at-the-top rule.

I haven't had a chance to consider the most recent method you described, Forest.

For the simulations I allowed all 9 factions possible (given 3 candidates, no equal-ranking, but truncation allowed) but zeroing out a random number of them. Majority Favorite scenarios were thrown out. The idea was to compare methods' results to the MM(WV) and Approval (or Bucklin) results. As MPO-based methods are prone to being indecisive, I should note that I considered tied results to be distinct outcomes.

The columns are: Method name; rate of agreement with WV result; rate of agreement with Approval/Bucklin result; and rate of picking some third outcome matching neither.

For all scenarios (including those where WV agreed with Approval/Bucklin):
TPPM:  .976  .684  .015
IAMP:  .971  .682  .020
MAMP:  .891  .767  .018
MDDA:  .829  .852  .004
C//A:  .907  .778  .000
MMPO:  .933  .647  .058
IRV :  .681  .513  .262

For only those scenarios where WV disagreed with Approval/Bucklin:
TPPM:  .956  .026  .017
IAMP:  .945  .027  .026
MAMP:  .673  .293  .033
MDDA:  .453  .531  .014
C//A:  .708  .291  .000
MMPO:  .940  .027  .032
IRV :  .711  .182  .105

IAMP means MMPO(IA>MPO). This and TPPM are closer to WV than even MMPO. MDDA is the most approval-ish.

IRV is only here in order to have a comparison with an irrelevant method: You can see in the top table it is doing its own thing a quarter of the time.

There's some chance of implementation error on my part, but at a glance I don't know that anything looks too strange.

I expected to see a compromise between MAMPO and MMPO (which is certainly the case if I use MMPO as a base comparison instead of WV)but I did not expect that we could out-WV MMPO.

Kevin Venzke