[EM] Single Contest Method

[fsimmons at pcc.edu]

Andy's chiastic method is a way of utilizing range ballots that has a much more mild incentive than 
Range itself to inflate ratings.  He locates the method in a class of methods each of which is based on a 
different increasing function f from the interval [0,1 ] into the same interval:

Elect the candidate with the highest fraction q such that at least the fraction f(q) of the ballots rate the 
candidate at fraction q of the maxRange value (assuming that minRange is zero).

Just as the median is more stable than the mean, so also these methods are more resistant to rating 
inflation.  In any case there is no incentive for strategically rating X above Y unless sincere ratings also 
put X above Y.

It seems to me that the incentive for rating inflation is so mild in these methods, that if the rankings 
induced by the ratings are later used to decide between two finalists, that fact by itself is enough to 
strongly discourage the extreme inflation or "collapsing to the top" that optimal range strategy requires.

With that in mind, here is my proposal for a "Single Contest" method:

Elect the pairwise winner of the contest between the chiastic winners for the cases where 

   f(q)=q/2, and f(q)=(q+1)/2,

respectively.

If two candidates have range scores symmetrically distributed about the mean range value, the second 
winner will be the one with the smaller standard deviation of ratings, i.e. less controversial, while the first 
one could have about half of its ratings at maxRange and the other half at minRange.  In general, if both 
graphs have approximate symmetry centered at the point (1/2, 1/2) it's about even odds as to which one 
would win the pairwise contest.

I hope that Kevin will put this one in the mix as  "Chiastic Single Contest."