[Election-Methods] Non-optimal satisfaction measure with average rating

[Stéphane Rouillon]

Counter-example:
Lets assume ballots represent sincere ratings.
50%: A-100 B-70 C-0
30%: B-100  C- 90 A-0
20%: C-100 A-10 B-0
Average ratings: A-52 B-65 C-47
Outcome: B wins
Satisfaction: 30%
A method delivering A as a winner would produce a 50% satisfaction measure.

I do not maximize social utility. But rather individual approbation.
I compare the global result with the optimal result according to the voter.
The optimal result is defined as the  elected representatives that would 
be obtained if every other
voters with the same opportunity than the reference voter had voted like 
the reference voter.
Maybe satisfaction is not the proper terminology.

Stéphane

Stéphane Rouillon a écrit :
> Hi Kevin,
>
> the satisfaction criteria I proposed to evaluate multi-winner methods 
> is independant of PR measurement.
> It is a parallel criteria. For example two different electoral methods 
> could elect the same
> proportion of the political parties candidates (30 Cons and 70 Lib for 
> example),
> but not the same persons. Thus proportional analysis would produce the 
> same
> PR measure but satisfaction analysis could differ in result.
>
> I do not need to know the method. The goal is even to be able to
> evaluate a method without knowing wich one it is.
> All I need is a sincere set of the electorate will (it covers either 
> preference or approbation
> using this word) and the outcome. To be precise I need to know the 
> candidate set
> among which each elector can choose one or several representative (it 
> can be applied to single-winner method too).
>
> No I don't think average rating will always be optimal. I'll try to 
> build a counter-example.
>
> Yes I can build cases where pushing PR to optimality would decrease 
> satisfaction measurement.
>
> SPPA optimizes PR, and after, using this optimal seat distribution as 
> a constraint, optimizes
> satisfaction by choosing which candidate receives seats for each 
> political party.
> At the time, I was calling this maximizing individual approbation.
>
> Stéphane
>
> Kevin Venzke a écrit :
>> Hi Stéphane,
>>
>> --- Stéphane Rouillon <stephane.rouillon at sympatico.ca> a écrit :
>>   
>>> Hello Kevin,
>>>
>>> these ratios are guesses I have for real elections.
>>> But I am fed up with guesses so the goal is to build an objective method 
>>> able to
>>> determine for a perticular set (method, ballots expressing sincere 
>>> preferences, outcome)
>>> of one electoral data, the most satisfying method in the eye of all
>>> voters.
>>>     
>>
>> But if you assume sincerity, won't you end up finding "average rating" to
>> be the best method? Or are you mainly concerned with PR here?
>>
>> If the latter, it seems interesting to me to ask whether "the most
>> satisfying method in the eye of all voters" might actually be incompatible
>> with proportionality?
>>
>> Kevin Venzke
>>
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