[EM] Random Ballot Favorite Chain Climbing

[Forest Simmons]

First a preliminary procedure to make sure no single candidate defeats
every member of the support of the random ballot favorite:
As long as there is such a candidate, retain only candidates of this
índole, recalibrating between elimination steps.


Next: a non-deterministic lottery method ... Random Ballot Favorite Chain
Climbing (RBFCC):

Shuffle the ballots into some random order B1, B2, B3, ... and let ListF be
a list of the candidates in the order induced by the first choices of the
respective ballots in their order ... i.e. according to the order of their
first appearance as a first choice on a ballot in the sequence B1, B2, B3,
...

Now, Chain climb the list ListF by initializing the set variable CHAIN as
the empty set, and then ....
While some member of ListF defeats every member of CHAIN, add the first
such candidate into CHAIN. EndWhile

The head of the completed chain is the RBFCC (random trial) winner.

Next, for each candidate X, let RBFCC(X) be the winning probability for X
under this lottery.

Finally, elect argmax RBFCC(X).

Note that this method is Banks efficient, and obviously reduces to
"fpA-SumfpC" in the eponymous three candidate case.

On a practical note, should the computation of the RBFCC probabilities be
intractable for some ballot set, then repeated trials in a MonteCarlo
simulation of the lottery can be used to determine argmax RBFCC(X) with
arbitrarily low error probability epsilon.

Is this the simplest formulation of what we've been looking for?

It doesn't seem like an easy method to "game".

Other comments? Questions?

Who can write this up in a way that Joe Q Public can easily relate to?

-Forest
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