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

[Jobst Heitzig]

Dear Raph,

you wrote:
> Likewise, you might as well pick your favourite as favourite.

This is, unfortunately, not true: The labelled favourite influences the
expected ratings against which possible consensus options are compared
on each ballot, so you can have the incentive to exaggerate by labelling
a more extreme candidate than your true favourite in order to lower
those ratings and make your preferred consensus more likely! But this, I
guess, will not decrease but rather increase the method's efficiency in
realistic examples.

> 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.

I guess so, too, but I think we can overcome the unanimity requirement
in a different way. Let me think about it...

Yours, Jobst