On Sun, 22 Jul 2001, Rob LeGrand wrote:
> Forest wrote:
> > Personally, I have little sympathy with these kinds of regrets.
> > The kind of regret Mr. LeGrand has been talking about (in the context of
> > CW versus Approval winner) is more or less similar to the kind of regret
> > illustrated by these examples (regretting one's inability to extract
> > strategic advantage due to lack of information about others preferences).
>
> I'm not interested in regret for its own sake. I only want to encourage
> sincere voting as much as possible. Voters who regret that they didn't vote
> insincerely will probably remember and vote differently in the next election.
> I believe I read that public use of Bucklin failed because of regretful voters
> who learned their lesson.
But if the regrets lead to increased support for the CW in the next
election, what harm is there (in a monotonic method)?
>
> > Putting aside regrets and other emotions, let's think of results:
> > Approval does as well or better than Condorcet in zero information cases.
>
> I disagree. According to my simulations, which were designed to measure how
> well methods pick winners when voters are sincere (a rather modest goal, but
> useful in this case), Approval does worse than the worst Condorcet method.
The results of these simulations would depend on what strategy you used
for zero info Approval. Did you use above mean, not below median, above
midrange, above largest gap, some combination of these, or Richard's
optimal method?
> The only methods worse for SU ...
I believe your simulations measured SU by averaging utilities. On that
basis, I would agree that Approval is surpassed by other methods,
especially Cardinal Ratings (the average utility king in the sincere
category).
But as I have argued before, I am not convinced that the most democratic
way to aggregate individual utilities into social utility is through
simple sums or averages.
A crude aggregation method that is more democratic in spirit than
averaging is subtracting all of the utilities from one (assuming
normalized utilities), followed by taking the products of these numbers
within each ballot, subtracting from one again, and averaging all of the
results.
I won't repeat all of my arguments here, but they are related to the fact
that a candidate with greatest average utility can beat out a candidate
with a two thirds majority when traditional averaging is used.
In general, I prefer the candidate with the greatest median utility to the
candidate with greatest mean utility.
> than Approval that I've tested, from best to worst,
> are Coombs, IRV, plurality and bullet (anti-plurality). Approval does about as
> well as Bucklin. Approval's SU performance only gets worse when voters use it
> strategically.
Are you talking zero info strategy?
When voters have significant information, Approval will tend to yield the
CW if there is one. If this decreases Approval's SU performance, that
should give one pause!
Forest
