robert bristow-johnson wrote:
On Jun 9, 2010, at 12:42 AM, Warren Smith wrote:
1. I think using utility=-distance
is not as realistic as something like
utility=1/sqrt(1+distance^2)
I claim the latter is more realistic both near 0 distance
and near
infinite distance.
Why would that be? Do you mean it's more intuitive?
--because utility is not unboundedly large. If a candidate gets
further from you, utility does not get worse and worse dropping to
-infinity.
No. Eventually the candidate as he moves away approaches the worst
he can be for you, which is, say, advocating your death,
:-)
and then
moving the candidate twice as far away doesn't make him twice as bad
from your perspective, and 10X as far doesn't make him 10X worse. It
only makes him a little worse.
i dunno, Warren. maybe if the candidate advocates for starving,
torturing, and then killing your kids and other descendants, relatives.
a holocaust for your ethnic group. then fouls the entire environment of
your homeland to extract resources for he and his unworthy buddies. but
i agree, there might be a limit.
i'll have to confess, that i have trouble with the presumptions of these
simulations in the first place. i have done simulations of physical
processes and communications systems (and have used all three L^1, L^2,
and L^inf norms) but i just am not confident of the assumptions of
social behavior (without first getting some empirical results from
actual social sampling - like getting a handle on how many voters would
change their vote from their favorite candidate if he/she changed her
position on just 1 particular issue, or 2 issues).
To some extent, I think we're going on that the artificial situations
will be "close enough" to real ones that the results are useful, and
thus, more generally, that election methods are robust: if they do badly
in a constructed somewhat-real scenario, they will do badly in a real
scenario.
This is the reasoning when I use Bayesian regret for my simulations, at
least. Optimizing blindly for Bayesian regret would imply choosing a
method that (among other things) may fail to pick a winner preferred by
a majority, and it doesn't take strategy into account either
(Range->Approval->needs strategy, and also show by that Borda, which is
very vulnerable to strategic nomination and burial, gets a better BR
than does Condorcet methods that resist that). However, it seems to be
reasonably good at discriminating between good methods (Condorcet) and
bad (IRV, Plurality, etc).
Your idea about social sampling is a good one, though. Some of this can
be done by analyzing ballot data (e.g. how often does a Condorcet cycle
appear in real life; but beware that strategy may be different for
different methods), while other aspects would have to be done in real
life, so to speak.
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