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

[Juho Laatu]

On 4.2.2012, at 11.12, Kristofer Munsterhjelm wrote:

> 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.

Yes, there are many ways to make decisions. Different elections may have different targets. Sometimes one maybe wants the median to win. And sometimes the Condorcet criterion is exactly what one wants, and some particular Condorcet method may be the ideal and accurate "utility function". Condorcet may be ideal when we e.g. have an unstable society and we want to minimize the level of opposition, maybe the size of majority that supports some of the opposition leaders in his plans to overthrow the elected leader. Condorcet criterion is thus qute well suited for environmments where one tends to think in terms "one person one vote" and "majority".

> 
> 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.

Yes, true utilities are very difficult to measure, even if people woud try to express them as honestly as they can.

> 
> 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.

If one adds few more pepperoni supporters, also Range picks pepperoni. I agree that a typical target when selecting pizza is to make sure that noboby will be too unhallyi. Minimax operator is thus a good approach.

In summary, there sure are elections/selections where one doesn't want to elect the Condorcet winner. That logic however applies to all criteria since different situations have different needs.

When people discuss about weak Condorcet winners, that is often in association with a two-party system where one assumes that the winner has >50% support, and the whole system is built around this fact. That is a valid requirement, if one so wants. But in most single-winner elections that may not be the case.

Juho


> 
> 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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