[EM] Single Contest Method

[Andy Jennings]

On Wed, Jul 27, 2011 at 4:32 PM, Kevin Venzke <stepjak at yahoo.fr> wrote:

> 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+?
>

This is correct.


> 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+?
>

It would be 100% rated 3?  83.3% rated a 2+?  66.7% rated a 1+?

But you are right that it would probably work better with more grade levels.

- Andy
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