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

[Warren Smith]

1. I think these pictures have a bright future as both explanatory and
investigative tools.

2. For chrissake, could you all please STANDARDIZE on 200x200 pixel images (Yee's original size)?
That'll make it easier to combine different people's pictures into a unified document at some
point.

3. Random tie-breaking is essential so all candiate winnign chances are always 100%
independent of the candidate-ordering.  Without it your pictures can easily have no meaning
and be indefensible.  All my sims have had random tie-breaking as I realized
its importance many years ago.  I'm just saying this to save you all a lot of
pointlessly wasted time spending hours and hours computing meaningless garbage you'll
just have to redo.

4. I find Venzke's discovery with a 10-candidate set that "IRV tends to favor outsiders"
whereas "Approval(mean-based cutoff) tends to favor centrists" very interesting.
But it needs more investigation with (a) more random 10-point sets - not just one,
and (b) is this merely an artifact of the particular utility function you used?
For example,  1/(c^2+distance^2)  is one utility function (in my opinion a fairly
realistic one since smooth).  Another is  -distance.  Another is  -distance^2. 
Another is -sqrt(distance).  Another is  1/sqrt(c^2+distance^2).
Perhaps with these other choices, the whole
"favors centrists" etc claims might no longer be true.  Who knows?

5. Approval(mean based cutoff)  looks pretty bad in these sims, although so far the
sims have not employed correct random tiebreaking so I don't know how much of
them to believe.   But anyway, it would be interesting when that issue is 
repaired.   This seems to be the possible basis for a good attack against Approval Voting.

6. However, I have proved the following theorems in the large#voters limit:
(a) approval with randomized-oblivious thresholds chosen by voters yields Voronoi diagram.
(b) approval with the following kind of strategic voters, also yield Voronoi diagrams:
       1. run approval election.  (Say X wins.)
       2. cast votes using X's utility as cutoff where
              Y>X  ==>  approve Y.
              Y<X  ==>  disapprove Y.
              Y=X  ==>  toss a fair coin to decide to approve or disapprove Y.
       3. go back to (1) until stabilizes on a single winner who keeps winning.
which two theorems, I suppose, form some sort of defense for approval voting.

7. Why the heck are you simulators not trying RANGE VOTING?  (With voters
who "normalize" their range scores x  via   x -->  (x-worstScore)/(bestScore-worstScore)
so that the best candidate gets range vote 1, the worst 0, and the rest are reals
somewhere in between?  [Bolson actually had "range voting" = "social utility winner"
computing twice the same thing with different names, which was both false and silly.]

Warren D Smith
htp://rangevoting.org