[EM] Quick and Clean Burial Resistant Smith, compromise

[Daniel Carrera]

On Fri, Jan 14, 2022 at 6:33 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> Nice! I agree, that is interesting. Benham is known for being pretty
> resistant to strategy in general, so I'm wondering if that strategy
> resistance forces the remaining weakness to be concentrated around easy
> strategies.
>
> Could you try a method from each of the two other categories, and see if
> the trivial strategy is so overwhelmingly succcessful on these too?
>
> E.g. Smith//Plurality (Or Smith,Plurality) from the extremely easy to
> manipulate category, and Minmax from the intermediate-to-high one.
>


That was a good hunch. That seems to be the case for Minimax at least. For
Minimax the successful strategies are less skewed toward the easiest ones,
but for Plurality and Hare they seem to be *more* skewed. I ran a test with
N=4, V=99, C=5, and 20,000 elections.

Method   , 95% c.i.     , trivial, reverse, moderate, majority
Plurality, 0.5807-0.5945, 1.000  , 0.0000 , 0.00000 , 0.318
MiniMax, 0.4032-0.4157, 0.900  , 0.0768 , 0.02284 , 0.210
Benham, 0.0449-0.0505, 0.979  , 0.0188 , 0.00209 , 0.133
Hare     , 0.0660-0.0727, 1.000  , 0.0000 , 0.00000 , 0.137

Incidentally, all the 95% intervals agree with Table 1 of JGA so this makes
me feel more confident that my program is working correctly. In any case,
for Hare and Plurality 100% of the successful strategies were the "trivial"
case. For Benham there are 20 non-trivial strategy successes (18
"reverse" + 2 "JGA"). If Hare had the same trivial/non-trivial ratio as
Benham, you'd expect to see 30 non-trivial successes for Hare. That's large
enough that I should have seen it if it was there. So I feel fairly
confident in saying that Hare and Plurality are both even more heavily
skewed toward the trivial strategy than Benham is.

Lastly, there is Minimax. That one was less heavily skewed toward easy
strategies. Of the successful strategies, 90% were trivial (vs 98% for
Benham) and out of the non-trivial ones, 77% were "reverse" (vs 90% for
Benham). So there seems to be a signal here, but even Minimax seems to be
very heavily skewed toward very easy strategies.

So... in other words... how often is the strategy easy? (i.e. trivial or
"reverse")

Plurality --> 100%
Minimax --> 97.7%
Benham --> 99.8%
Hare --> 100%

Wow.

Cheers,
--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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