[EM] [CES #4445] Re: Looking at Condorcet

[Kristofer Munsterhjelm]

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.