[EM] Fast algorithms for Yee/Bolson pictures

[Ka-Ping Yee]

On Tue, 19 Dec 2006 raphfrk at netscape.net wrote:
>  So the steps would be:
>
>  a) work out the ballot for a voter at each pixel
>  b) convert result into 2-d frequency domain
>  c) work out the density function (Gaussian)
>  d) convert density function to the frequency domain
>  e) multiply d) by b)
>  f) apply reverse 2-d FFT
>
>  Each pixel now contains the result for the vote centred on that pixel.
>  Repeat for each candidate.
>  This above works for methods which just total the votes.

Yes, this is a good suggestion.  I looked at something like this in
the hope of creating a simulation fast enough that you could move
around the candidates interactively, but got stuck trying to figure
out how to do this for Hare (IRV) elections.  I have a Flash animation
of the same concept on a 1-D political spectrum, and it's fast enough
to be interactive, but 2-D would be really nice.

The technique you propose should work fine for Plurality.  For
Condorcet and Approval, it's straightforward to show that the result
is just a Voronoi diagram, so you can skip all this.


-- ?!ng