[EM] Problems with finding the probable best governor
MIKE OSSIPOFF
nkklrp at hotmail.com
Wed Jul 19 22:35:35 PDT 2000
EM list--
Since the probable-best-government argument is probably used
as an arguement for Tideman(m), I want to point out that
all that Blake claims for that method is that the margin
of A's defeat of B is a good measure of the probability that
A would be a better President than B would--the probability that
that defeat is "right". As I understand it, then, there's no claim
that Tideman(w) chooses the candidate who in some way is the
one who is most likely to be the best President.
The first thing to point out about that is that Blake is
apparently assuming that everyone is ranking sincerely.
But Blake himself has recommended the "general pairwise-count
defensive strategy" for voters in a Tideman(m) election.
Tideman(m), like any margins method, and like any rank-count
other than Schulze & Condorcet, places on voters a serious need
for strategic voting. And, without sincere voting, the margins of
defeat in Tideman(m) aren't going to say anything about the
likelyhood that the defeats are "right", in terms of how likely
candidate A is to be better than candidate B.
Even if Blake isn't concerned about need for strategy, it
still spoils Tideman(w)'s ability to accomplish what Blake would
like it to accomplish.
Another thing. The goal that Blake discusses is the goal of
finding the candidate who is the most likely to be the best
President. But, as I was saying earlier, Tideman(m), even if
people voted sincerely, and even if probabilities could be
measured as Blake specifies, wouldn't choose the candidate most
likely to govern best. The margins of defeat only tell how likely
each defeat is to be "right". If we want to find out which
candidate is the most likely to govern best, then we don't want
to just make pairwise comparisons; we want to add, for each
candidate, those probabilities, to give each candidate an
absolute election-wide score. For instance, if the number of
people ranking A over B measures the probability that A is better
than B, as is assumed in Blake's justification of Tideman(m), and
if the number of people ranking B over A similarly counts against
A's probability of being the best, which is how Vab-Vba is
justified as the measure of A's probability of being better than B,
then, if we want to find out A's probability of being the best
candidate, we need to add up all the individual pair-orderings
that have A over another candidate, and subtract from that all
the individual pair-orderings that have another candidate over A.
In other words, we should count the rankings by Borda's method.
Of course Borda has even more problems than Tideman(m), but,
if we assume sincere voting, and if we want to pick the candidate
most likely to be the best, based on rankings, then Borda seems
to be the way to do it, based on the assumptions by which Blake
justifies margins as a measure of whether a defeat is "right".
But, if we can count on voters to be sincere, then need we use
rankings? Wouldn't it be even better to use a points-assignment
method? Say people sincerely rate the candidates, and the candidate
getting the overall most rating points wins.
Obviously that would be no good in public elections if everyone
isn't voting sincerely. And people won't vote sincerely in
point-assignment, or Borda, or Tideman(m).
***
Average social utility is a measure of something similar to
Blake's goal.
Under sincere voting,
all the pairwise-count methods that Norm & Steve
tested seem to do about equal in that regard, and better than
other methods, except maybe for Borda. It seems to me that Merrill
got a similar result, though he may have only tested Copeland.
That's with sincere ranking. Since the pairwise-count methods seem
to do about equally in terms of social utility under sincere voting,
then it makes sense to use some other standard to choose between
them. Most of us who participate here feel that the methods'
strategic demands on voters is the standard by which to compare the
methods, and that's why we use the criteria that we use.
It seems to me that Norm said that Borda does noticibly better than
the pairwise-count methods, for social utililty, when everyone
ranks sincerely. It would be interesting to test Points-Assignment
with sincere rating. For instance, say each voter gives a candidate
a negative point assignment equal to the distance between
that candidate & that voter in issue-space. The winner is the
candidate whose combined negative score has the lowest magnitude.
Though Points-Assignment, like Borda, and Tideman(m), isn't
practical for public elections, it would be interesting to find
out how Points-Assignment does, in average social utility, in
comparison to the other methods that were tested.
How much better did Borda do, in comparison to the pairwise-count
methods that were tested?
Mike Ossipoff
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