[EM] response to David Cary re Bayesian Regret
Warren Smith
wds at math.temple.edu
Tue Mar 13 19:15:25 PDT 2007
>David Cary:
What is the justification for Bayesian Regret, as used in IEVS and
described at http://rangevoting.org/BayRegDum.html, being the
"uniquely right" metric, the "gold standard", for comparing different
election methods or varying election scenarios?
Why is the societal utility for a candidate the sum of the voters'
individual utilities for that candidate?
--WDS: it's a standard assumption, indeed the most common way to go, but nevertheless
perhaps cannot truly be justified from lesser axioms.
Some partially-successful attempts to do so are discussed in puzzles #36,37,38 at
http://rangevoting.org/PuzzlePage.html .
>How does that avoid the
problems of being arbitrary or not well-defined, when making
interpersonal comparisons or summations of von Neumann-Morgenstern
utilities?
--WDS: this "problem," on the other hand, really is not a problem. Because when doing
computer simulations, we *can* magically "read the minds" of the simulated voters
and know their exact utilities on a common scale. Even though for real humans,
we have no mindreading device and no obvious way to make everybody adopt common units -
and real human voters may not even know their utilities. (We also can make the simulated
ones have ignorance about their utilties if the simulator so desires.) OK?
This is an important point. These "obstacles" are in fact not obstacles at all to
a computer simulator trying to compare voting methods. It is very important to see that.
>What is Bayesian about the resulting value, which is just
a difference in utility values?
--WDS: "Bayesianism" is about expected utility. I have preferred to focus on "regret"
(which is optimum utility minus actual utility) rather than "utility" but that is
a change that makes no real difference. The whole idea that we want to pick the "best"
voting system to be the one that maximizes expected utility, would be something
Bayes would have fully agreed with, albeit the idea of "social utility" (= sum of
individual utilities) is something perhaps Bayes would have had doubts on (I do not
actually know if Bayes ever thought about multiperson issues).
Warren D Smith
http://rangevoting.org
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