[EM] RE : Comments on the Yee/Bolson/et.al. pictures

[Kevin Venzke]

Hi,

--- Warren Smith <wds at math.temple.edu> a écrit :
> The (now with random tiebreaking) Bolson pictures pretty interesting.
> Approval with mean-as-threshold (at least with Bolson's utility function)
> is doing some pretty weird stuff!

I agree... Particularly in graph 3C, I haven't seen anything like that,
and I think it must be an effect of the utility function. The effect of
the reciprocal is that voters lose sensitivity to distance beyond a
point, I think.

Suppose from me there are candidates 10, 20, 100, and 10,000 units
away. By negative distance the average utility is -2532.5. By reciprocal,
the average utility is (.1 + .05 + .01 + .0001)/4 or 0.1601/4 or .040025.
This makes a difference as to whether the third candidate is approved.

I have to think the green win bubble in 3C is where blue is perceived
to be worse than average. That this region even exists in the zoomed-in
graph seems like an issue to me, as it doesn't match my perception of
what "average" is.


In other news, I implemented Warren's suggestion of rerunning each pixel
until there's a sequence of wins by the same candidate, starting with
fast inaccurate elections and increasing the accuracy when the win isn't
consistent.

When I set this up right, it works incredibly well, zipping through
regions of solid color, deliberating on boundaries and leaving them very
sharp.

The main problem is that it chokes on tie regions, ratcheting up the
accuracy in vain as it can't find a decisive winner.

I'm not sure when I'll have time to make an interesting series of graphs
to post...

Kevin Venzke


	

	
		
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