[EM] Detailed stats for the ordinal methods

[Kristofer Munsterhjelm]

On 2024-05-09 18:08, Richard, the VoteFair guy wrote:
> Bravo Kristofer!  Thank you for doing these valuable calculations!!
> 
> IMO it reveals two important points:
> 
> * The methods that get the highest resistance to strategic/tactical 
> voting are methods that combine pairwise vote counting with IRV-style 
> counting.  Specifically the lowest failure rates are for:
> 
> ** RCIPE (IRV with pairwise eliminations)
> ** Benham (IRV except stop when pairwise winner)
> ** Smith-IRV (Woodall)
> ** Schwartz-IRV (Schwartz-Woodall)
> ** IRV.

In particular, strategy resistance seems to be linked to the resistant 
set I defined last year. https://electowiki.org/wiki/Resistant_set

Here's a rough example showing just that, with Resistant,Borda. 5k 
elections so it won't take so long to calculate, but the other details 
are as in my previous simulations: 99 voters, 4 dimensions, and 4 
candidates:

    Ties: 0.001 (5)
    Of the non-ties:

    Burial, no compromise:        123     0.0246246
    Compromise, no burial:        72      0.0144144
    Burial and compromise:        147     0.0294294
    Two-sided:                    48      0.00960961
    Other coalition strats:       1       0.0002002
    ================================================
    Manipulable elections:        391     0.0782783

    Worked in 391 (0.0752, 0.0828) out of 4995 for [Inner burial 
set],[ER-Borda] ties: 5

Going from 0.70 to 0.08 by restricting to a particular set is pretty 
respectable.

The IRV hybrids you listed elect from the resistant set because they 
pass a "proper order criterion": if X disqualifies Y, then X is never 
eliminated before Y.

I don't quite know *why* electing from the resistant set seems to grant 
general strategy resistance. I've only been able to prove burial 
resistance, though in practice it limits other strategies too.

-km