[EM] Quick and Clean Burial Resistant Smith, compromise

[Daniel Carrera]

On Thu, Jan 13, 2022 at 8:05 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> Maybe you could get a (very slight?) improvement by ranking the
> candidates in reverse social order, e.g. if A is the winner and the
> social order is A>B>C>D>E>F, then the B>A faction votes B>F>E>D>C>A.
>
> Could be worth a try, at least; but 92% of the time for a 6-candidate
> election is already pretty good!
>

So... I've been experimenting with this idea and I have an interesting
report. Now... the strategy you suggested is quite sophisticated for a real
election. I'm more interested in a strategy that a regular group of voters
could implement if it was explained to them. So let me offer a variation:

1. Let 'A' be the winner
2. Make an educated guess as to how 'A' would cast his own ballot, and
reverse that (and put your preferred candidate on top).

So in your example, if you estimate that 'A' will probably vote A>B>C>D>E>F,
then the B>A faction votes B>F>E>D>C>A.

My reasoning is that this should be a reasonable poor man's approximation
of reverse social order. If 'A' is the presumed winner in a sincere
election, then maybe 'A' is close to the center of mass of the issue space,
and his ballot might approximate social order. If you have an election
between Joe Biden, Bernie Sanders, and Donald Trump, and I ask you to guess
which way each candidate would cast his ballot, you'd have little trouble
coming up with the answers. So I ran my program again. I removed the
"simple" strategy that I had before and inserted the "reverse" strategy
above. I removed the "advanced" strategy because it was getting really
expensive and after many tests it never once succeeded. So the new
simulations only have three strategies:

1) Trivial:  Rank c_k on top, w_A at the bottom, and the other candidates
are ranked according to each voter's preference.

2) Reverse: Compute w_A's ballot, reverse it, and move c_k to the top.
Everyone in the c_k > w_A coalition casts that ballot.

3) Moderate / JGA: Iterate through every single possible ballot that the
c_k > w_A coalition might cast.

I increased the number of elections to 100,000 to get more resolution. Here
are the results:

N, V , C, 95% c.i.     , trivial, reverse, moderate, majority
1, 99, 5, 0.4849-0.4913, 0.884  , 0.1158 , 0.0000  , 0.314
2, 99, 5, 0.1783-0.1832, 0.953  , 0.0452 , 0.0022  , 0.121
3, 99, 5, 0.0797-0.0830, 0.971  , 0.0272 , 0.0021  , 0.119
4, 99, 5, 0.0481-0.0507, 0.978  , 0.0201 , 0.0022  , 0.134

As in my last email, the "trivial", "reverse", and "moderate" columns are
the fraction of strategy successes that were attributed to each strategy. I
think the result is really interesting:

1) If an election is susceptible to strategy, 88-98% of the time the
trivial strategy will work.

2) Out of the remaining strategy successes, 90-95% are attributed to the
"reverse" / "poor man's social order" strategy.

So... your reverse social order strategy works pretty well. It seems to
grab all the low hanging fruit, and it's very hard for a ballot search to
do better than that. For completeness, here's how often the JGA / moderate
strategy produced a result:

* For N=1 --> JGA helped 0 out of SS = 48,804 times
* For N=2 --> JGA helped 39 out of SS = 18,072 times
* For N=3 --> JGA helped 17 out of SS = 8,131 times
* For N=4 --> JGA helped 11 out of SS = 4,936 times

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