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

Kevin Venzke stepjak at yahoo.fr
Fri Dec 22 00:47:43 PST 2006

```Warren,

--- Warren Smith <wds at math.temple.edu> a écrit :
> 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,

I've looked into a fair number of examples. I just haven't posted them
all, since my graphs don't usually get to a very satisfying resolution
before I interrupt them.

It makes sense that Approval would favor inner candidates. (I wouldn't
call these candidates "centrists," as the median voter is not necessarily
nearby.) Voters located outside the candidates approve maybe the nearest
half of the candidates. But the voters inside the candidates are only
approving the nearest ones.

Diagram:
..X.....................A...B..,.......C..
aaaaaaaaaaaaaaaaaaaaaaaaaaaa
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
ccccccccccc

Say ABC are candidates and X is the median voter. If you extend left
and right indefinitely, you'll elect B or C. If the median voter is X,
though, you know it's going to be B who wins.

> 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?

I'm using negative distance (sqrt of sum of squares of distance on each
axis). I believe Brian Olson's simulation uses the reciprocal of the
distance. I am not sure what you mean by "c" above.

> 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.

My results use random tiebreaking.

I don't agree that Approval looks bad. Yes, a candidate is rewarded for
being on the inside. But to win you have to be the one such candidate
who is nearest the median. So if lots of candidates crop up, planning
to benefit from being inner candidates, where do you think they'll try
to appear? I think it's obvious they will want to crop up near the
median voter, and not some arbitrary location in the issue space.

When you look at it from the standpoint of nomination (dis)incentive,
I think it is IRV that looks quite poor here. You usually have a better
shot at winning if you stand somewhat outside the other candidates, even
if they are nearer to the median than you are.

> 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?

Why implement normalized range voting? That would just be somewhat off
from the SU graph. I'm not even sure you would see the difference.

By the way, is there a fast way to estimate the size of Voronoi cells
inside a rectangle given several points defining their centers? I have
implemented generation of a smaller number of voters who are each capable
of wielding the voting power of a much larger number of voters. This
makes it faster to calculate the winner of a method. But I need a fast
way to distribute the large number of voters among the smaller number
of voters. To be valuable I think it only needs to be somewhat more
accurate than a random allocation.

Kevin Venzke

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