[EM] Re Yee/Bolson pictures

[Warren Smith]

1. About approval-with-mean-as-threshold voting strategy:
the random-spotted regions are due to multitudes of exact ties caused by
everybody approving, e.g, the top two, leading to a 2-way tie.
(Actually such ties can be broken by voters extremely far away, but those 
votes are very rare in the Gaussian distribution, leading effectively
to random tie-breaking.)

This is bad both in the sense that it makes simulations run slowly (with the 
"deliberate only on hard elections" ploy), and in the sense it is socially bad,
and in the sense it is unrealistic.

All 3 of these problems would be fixed by making only, say 75% of the voters use the mean-as-threshold strategy, and the others use oblivious-random thresholds
like Yee was using, or honest range voting.  I.e. make a mix of honest 
and strategic-zero-info range voters. I conjecture that even a quite-small
admixture of honest range voters into this mix (25%, 10% - whatever) will
yield DRAMATIC improvements in social quality and in picture-niceness. 
And it'll definitely break the ties in those random regions so the sims
will run a lot faster. This is an interesting question because I've often said
(and I've been disputed) that range voting is better than approval voting because 
it allows SOME honesty into the mix, even if a great majority of range voters are strategic - which could result in a big social utility win.
It'd be interesting to see a pictorial study of that question.

2. About utility functions & their effect on approval-with-mean-as-threshold:
The funny appearance of some of those pictures may be in part caused by Bolson's use of
1/distance as his utility function.
I consider 1/distance to be unrealistic because it goes infinite at distance=0.
In reality as you (a voter) get closer to your candidate and move through his location,
utlity rises to a peak and then declines, all smoothly.  Infinite utility is nonsense 
and sharp discontinuties are nonsense.
The fact that Bolson's utility aproaches 0 at larges distances is debatable.
Personally it does not bother me, but some might argue that it should keep 
decreasing the further away you walk, and get unboundedly negative, for 
example like -sqrt(distance).
Anyhow, here two some utility formulas I consider more realistic:
  util = 1/(c^2 + distance^2)
  util = 1/sqrt(c^2 + distance^2)
where c=constant chosen to make things interesting  (c is a characteric distance scale) 
and distance=sqrt(xdiff^2 + ydiff^2).

Warren D Smith

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