[EM] A Proportionally Fair Consensus Lottery for which Sincere Range Ballots are Optimal

[Raph Frank]

On Thu, Nov 19, 2009 at 8:08 PM,  <fsimmons at pcc.edu> wrote:
> If the circled name on the randomly drawn ballot has a rating above the "random
> favorite rating expectation," on any ballot (including the one in play), then
> another ballot is drawn, and the indicated favorite of the second ballot is elected.
>
> Otherwise, the proposed consensus candidate whose name was circled on the first
> drawn ballot is elected.

Effectively, a random voter proposes a consensus candidate.

The random ballot probabilities are determined and each voter is given
the option to vote Yes/No to the consensus candidate.

Unless all prefer the consensus candidate to the expected utility of
the random ballot, the random ballot method is used.

It is clear that honest range is the best plan as it doesn't affect
anything else.

Likewise, you might as well pick your favourite as favourite.

The consensus candidate is different.  It is inherently strategic.

There is the possibility for group "chicken" effects.  For example, a
party could say that all of their supporters are going to rate
candidate X at minimum, so there is no point in nominating that
candidate.  This could cause the other partys' supporters to disregard
that candidate as a potential consensus candidate.

Also, I wonder if it might be worth having a rule that allows
additional consensus attempts.

For example, if 10% refuse, then the other 90% would be given the
option of choosing the consensus candidate.  The 2 choices in that
case would be

Option 1)
Full random ballot

Option 2)
90% chance of consensus candidate
10% chance of random ballot (only the ballots outside the 90% are considered)

This would probably break the strategic "purity" of the single stage method.