[EM] Forest's Random Ballot among the candidates not strongly beaten (was: How to describe RAV/ARC)

[Jobst Heitzig]

Dear Forest!

I consider your post, in which you argue in favour of using Random
Ballot among the set P of candidates which are not strongly beaten by
any other, to be perhaps the most valuable post in the last weeks!

I like that method VERY much: It is quite easily described and
motivated, does not require the understanding of any complicated concept
like Smith set or defeat strength or cycle or covering, is monotonic,
clone-proof, Pareto-efficient, IPDA, gives both the approval winner and
the CW a positive probability of winning (at least when they possess
some direct support), and introduces just about the right amount of
randomness.

Here's some further observations I made:

When some individuals raise a possible winner, the set P of possible
winners can only become smaller and the remaining P-members'
probabilities can only increase.

When the number n of candidates increases, I conjecture that (i) the
expected number of candidates which are more approved than the winner is
 of the order log(b) asymptotically, and (ii) also the number of
possible winners is of the order log(b) asymptotically. In other words,
the result is almost approval-optimal and depends only slightly on
randomness. (The only doubt I have is that this could be too few
randomization since it is still possible that some losing candidate
beats all possible winners...)

The Condorcet Loser can only win when s/he is the approval winner.

Although not independent from 2nd place complaints in Steve's sense, the
method fulfils a weaker version of that criterion: When removing a
possible winner X, the other possible winners don't turn into losers,
and only those losers which were strongly beaten by X can turn into
possible winners.

A nice example how the method succeeds in finding a comprimise has the
following sincere prefs and cutoffs:
  51 A>C>>B
  49 B>C>>A
No Condorcet method will elect the obvious compromise C but instead the
CW A. Approval would elect the compromise C but then the A voters would
have strong incentive to vote only A in order to elect A. Your method
will elect A with 51% probability and C with 49%.

What name do you suggest for this excellent method?

Yours, Jobst