[EM] Ways to Evaluate Multiwinner Contests (Greg Nisbet)

[Greg Nisbet]

small correction:
On Sat, Oct 11, 2008 at 6:37 PM, Greg Nisbet <gregory.nisbet at gmail.com>wrote:

>  So far some nice ideas have been proposed for measuring how effective a
> multiwinner method is.
> All of the ones proposed are based on n, let n be a list of utility scores
> for the candidates.
> 1. ln(2*sum(n)+a) we don't know what a is. It's probably pretty close to a
> constant, let's just call it 1.
>
> Note:
> values for the ln(2*sum(n)+a) can be computed exactly if you have time on
> your hands
> f(1) = 1
> f(2) = 1 + 1/2 => 1.5
> f(3) = 1 + 1/2 + 1/3 => 1.83
>
> 2. this iterative procedure:
> def sortpav(n):
>     n.sort()
>     n.reverse()
>     ret = 0
>     for y,x in enumerate(n):
>         ret += x/float(y+1)
>     return ret
> Of course these three procedures can be used for Range Voting, but it is
> not necessary to accept the validity and perfection of Range Voting to use
> these as metrics.
>
> Range Voting resembles utility summation with two fundamental differences
> 1) people vote strategically and 2) a ceiling
>
> So, now we move onto the multiwinner bayesian versions.
> Unlike single winner, the methods for measuring regret so far proposed have
> a floor, specifically 0. See, the ln of negative numbers includes pi*i. I do
> not know how to handle imaginary numbers with regard to voting methods, so I
> am going to outlaw negative numbers as the lazy solution to the problem.
>
> If anyone has a multiwinner method to suggest, a criticism to the metric or
> anything else before I run the simulation please let me know. I know better
> than to call a vote on which metric to use, so if you have an opinion on one
> of them please tell me.
>
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