[EM] Proportional Representation from Ratings Ballots

[Raph Frank]

On Thu, Nov 19, 2009 at 12:49 PM, Raph Frank <raphfrk at gmail.com> wrote:
> If no candidate is elected, a different rule is used, each ballot is
> scaled so that
>
> [w(a)*r(a)]^2 + [w(b)*r(b)]^2 + ... = 1
>
> The running candidate the the lowest score is then eliminated.

Stage 1, (Election stage) select k1 so that

k1*[ w(a)*r(a) + w(b)*r(b) + ..... ] = 1

Each candidate gets

k1*w(x)*r(x)

Stage 2, (Elimination stage) select k2 so that

k2*(w(c)*r(c)^2 + w(d)*r(d)^2 + ... ) = 1 - k1*[w(a)*r(a) + w(b)*r(b)]

Each candidate gets

k2*w(x)*r(x)^2

Eliminate the remaining candidate who scores the lowest.