[Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions

[Howard Swerdfeger]

Jobst Heitzig wrote:
> Dear Abd ul-Rahman,
> 
>>>> In a Range poll, social utility is maximized if everyone votes
>>>> *absolute* utilities, accurately.
>>> Only if "social utility" is defined so that your statement becomes
>>> true by definition (and becomes a triviality thus).
>> "Absolute utilities" means that the utilities are commensurable. Yes,
>> it is a tautology. But it still should be said, because a great deal
>> is written that ignores this.
> 
> You mean, many people "ignore" that you choose to define "social 
> utility" as the sum of individual utilities, while others define it 
> otherwise?
> 
>>>  Welfare economics, however, does not define "social utility" as
>>> the sum of individual utility, it rather defines "social welfare"
>>> in some more sophisticated ways which we already discussed earlier
>>> several times.
>> That is also true. There can be utilities that combine in a nonlinear
>> way. But how complicated do you want to make it? We have enough
>> trouble getting a method in place that will optimize, to the degree
>> that Range does, linear utilities, and many forms of utility *are*
>> commensurable linearly.
> 
> What do you mean by "commensurable linearly"? The question is simple, is 
> it better for society when one has 100 and the other 0 or when both 
> have 50. If the latter is considered better for society, then "social 
> utility" is obviously not the sum of individual utilities. That's what 
> welfare economics is about.
> 

Not to insert myself in a private conversation. But, I was under the 
impression that that an individual utility (Ui) function was usually 
defined as the log of some trade-able commodity.
example Ui = Log($)

So by extension welfare economics would still have reason to exist if 
the "social utility" (SU)was defined as
SU = Sum(Ui)

The trick is in my opinion identifying the trade-able commodity, in 
relation to elections.

My guess at place to start would be something like a Gaussian of the 
distance between a candidate and each voter...or something like that