[EM] Correlation methods (was Correlated Instant Borda Runoff)

[Simmons, Forest]

Paul Kislanko wrote ...

Awhile back Dave Gamble and I speculated off-list that the "best" election
method would have each candidate fill out an extensive questionaire, and
have each voter fill out the same questionaire. Then a computer program
would find the best correlation between voters' answers and candidates'
answers.

This has the distinct advantage that there would be no advertising,
campaigning, or opportunities for special interests to try to sway the
election. It has the obvious difficulty of defining and calculating the
"best correlation", which is probably impossible except in science fiction.
(It was Isaac Asimov's short story "Franchise" that led us down that path).
 
Forest replies ...
 
Something along this line might be ideal for small groups with whose members have lots of patience for filling out questionaires.

For large scale public elections my suggestion (of just having the candidates fill out the questionaires and publishing the results, including the correlations, before the voters fill out their ballots) might be more practical.
 
In particular, some voters might like to have the option of just indicating their favorite on the ballot, and allowing the computer to rank the other candidates for them from most correlated (with favorite) to least.  These voters would choose the "short form" ballot.
 
Voters who felt that these correlations did not accurately reflect their preference order would choose the long form and rank as many candidates as desired.
 
Among these picky voters there might be some that would like the computer to rank their truncated candidates according to their correlation with their favorite.  There could be a check box on the long form that would allow this.

Again, I emphasize that if a pairwise elimination method is used, then there can be no favorite betrayal incentive except in cases where Favorite and Compromise are pitted against each other at some stage of the elimination before the final pairwise comparison.  
 
This is unlikely to happen if pairwise elimination proceeds from the outside in, i.e. always pitting the two least correlated remaining candidates against each other.
 
But even if it does happen that Favorite and Compromise are both more correlated with X than with each other, then how bad can it be?
 
Only if Favorite beats Compromise beats X beats Favorite is there any justification for betraying Favorite, and then only if there is a chance that your order reversal will make Compromise beat Favorite.
 
And all of this to help Compromise beat a candidate X that has better correlation with Favorite than Compromise does?
 
I don't think that any other Condorcet method can get us better immunity from favorite betrayal than this.
 
Forest
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