[EM] Re: Strong Favourite Betrayal Criterion at last!

[Alex Small]

On Thu, 3 Apr 2003, Chris Benham wrote:
> Forest,
> My answer to your question "Is there a simpler method that factors
> allof the strategy away from the rankings or ratings of the
> candidates?" is yes. Voters can rank  and also Approve whichever
> candidates they please, not even neccessarily Approving the candidate
> they rank as number1. The method  is to have an IRV-like count, except
> that the candidates who are in turn eliminated are those who are the
> least Approved.
> For example, in a 3 candidate race in which you doubt that  Favourite
> can beat Worst  in a runoff, you might number the candidates  1.
> Favourite  2. Middle  3. Worst  , but  only  Approve Middle .

Is this any different from Approval Runoff, where you eliminate all but
the two most approved candidates in the first round, and the second round
is a single pairwise contest?  I ask because you say "the candidates who
are eliminated in turn...", which (to me) implies a sequential process. 
I'm trying to see how you can get a sequential process only using approval
information.

It seems like the key insight needed for Strong FBC is that Strong FBC can
only be satisfied when rankings are only used to resolve a single
2-candidate contest.

So, if we use a rated method to eliminate all but 2 candidates, we can
then use the rankings without any incentive to rank insincerely.

One interesting thing about Approval Runoff is that strategically it
satisfies the Majority Criterion:  When there is a candidate whom a
majority of the voters consider their first choice then he should win. 
With adequate polling data, the majority will be aware of one another, and
they'll approve only their favorite.  He's guaranteed to be one of the top
2, and he'll also automatically win the pairwise contest.

One possible downside:  The largest single organized group of voters (not
necessarily a majority, nor a group that has a common favorite) can
guarantee a candidate's victory by only approving him and a freak.  If
their favorite is a serious candidate he'll automatically beat the freak
in a pairwise contest.



Alex