[EM] Single Contest Method

[Kevin Venzke]

Hi Forest,

--- En date de : Mer 27.7.11, fsimmons at pcc.edu <fsimmons at pcc.edu> a écrit :
> 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).

Hmmm. So, noting that I cannot test more than 4 slots due to the design
of the simulation, I want to take each candidate and ask:
Did 100% of the voters rate him 3/3?
Or else did 67+% of the voters rate him 2/3 or higher?
Or else did 33+% of the voters rate him 1/3 or higher?
And then the last possible question is trivial.

That I believe is if f(q)=q. So what I want is this:

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

So the first one asks:
50% rated 3? 33.3% rated a 2+? 16.7% rated a 1+?

It is curious to me that the 50% figure should decrease.

I'm not really sure how to interpret the second one. I was interpreting
the range of q to be 0-100%. I guess I will interpret (q+1) for a
four-slot ballot to mean 133.3%. So then I get:
66.7% rated 3? 50% rated 2? 33.3% rated 1+?

I must not have this correct, because isn't the first test strictly
harder than the second? What is an example where you win on the first
method but not the second?

Thanks.

Kevin Venzke