On 02/04/2012 06:47 AM, robert bristow-johnson wrote:
On 2/3/12 11:06 PM, Jameson Quinn wrote:
No, he's saying that when the CW and the true, honest utility winner
differ, the latter is better. I agree, but it's not an argument worth
making, because most people who don't already agree will think it's a
stupid one.
as do i. it's like saying that the Pope ain't sufficiently Catholic or
something like that. or that someone is better at being Woody Allen than
Woody Allen.
but for the moment, would you (Jameson, Clay, whoever) tell me, in as
clear (without unnecessary nor undefined jargon) and technical language
as possible, what/who the "true, honest utility winner" is? how is this
candidate defined, in terms the preference of the voters?
Utilitarianism is a form of ethics that proposes that the actions to be
taken are the ones that produces the greatest good for the greatest number.
To calculate with utilitarianism, you need two things: first, that each
person can put a number on how good they think each decision will be to
them*; and second, that you have a way of combining these numbers to
find the societal good that comes from each choice.
Usually, the combining function is the mean. You could also have a
"makes the worst off best off" (minimax) function, but that's less common.
The socially optimum candidate is the one that, if chosen, would
maximize the combined utility as defined above. By the logic of the
combination function, that candidate "produces the greatest good for the
greatest number".
The true utility winner is the one that would appear to produce the
greatest good for the greatest number when you go by the utilities as
the voters believe them to be, rather than the actual utilities. In a
sense, you can't do better than this: if they got their own utility
wrong, then no method relying only on the reported utilities can
perfectly divine the real ones.
The true honest utility winner (I think) is the one that is chosen by
the method that most often picks the true utility winner when people
vote honestly. For the sort of utilitarianism that uses mean utility,
that's the Range winner when every voter gives unnormalized ratings.
If you're a mean-utilitarian, then it's easy to make examples where
Condorcet - or for that matter, any method that passes Majority - does
the wrong thing. Abd likes to refer to a pizza example like this, where
one person absolutely can't have pepperoni:
2: Pepperoni (0.61), Cheese (0.5), Mushroom (0.4)
1: Cheese (0.8), Mushroom (0.7), Pepperoni (0)
Then any method that passes Majority will pick Pepperoni by 2/3
majority, but the total ratings are 1.22 for pepperoni, 1.8 for cheese,
and 1.5 for mushroom, so Range picks cheese.
Incidentally, so would a minimax operator, too: its score would be 0 for
pepperoni, 0.5 for cheese, and 0.4 for mushroom.
-
* That is, that when comparing choices, people know not just whether one
is better than another to them, but *how much* better, and that the
standard is the same for each such comparison. The latter requirement is
called commensurability.
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