[EM] Voter satisfaction measure in a general case?

[Juho Laatu]

> On 15 Oct 2017, at 22:23, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
> 
> On 10/15/2017 07:23 PM, Juho Laatu wrote:
>> I think you can't really have any good rating style satisfaction
>> measures in methods that measure rankings only.
> 
> The only thing I can think of, statistically speaking, is to set up some kind of utility generator that produces ratings style votes, and then randomly sample elections from this utility generator. Throw away every sample that doesn't have the same ranked reduction as the actual data you have, and then calculate the mean utility for each candidate across the samples that remain.

Makes sense. That way you can get a guesstimate on what the rated opinions might have been. In this method you probably assume some level of even distribution of candidates in the sense that if votes are 50:A>B>C, 50:C>B>A, the algorithm assumes that B has equal distance to both A and C. Also vote normalisation will be assumed.

> 
> In other words, if you have an election that is
> 
> 3: A>B>C
> 2: B>C>A
> 1: C>A>B
> 
> (say)
> 
> then you run your utility generator and save every generated scenario where:
> 
> 3 voters rate A higher than B and both higher than C
> 2 other voters rate B higher than C and both of those above A
> 1 other voter rate C higher than A and both of those above B
> there are no other voters
> 
> and then you take the mean utility for A, B, and C across all those generated scenarios.
> 
> In practice, this method becomes completely impractical whenever the number of voters is greater than say, 10 or so. It might be possible to use statistical cleverness to speed up the sampling, but it would probably take a long time to find out just how to be clever in such a way.

Maybe you could use also samples that are close enough to the actual vote set (with some weight that decreases when the distance to actual votes grows).

> 
> It would not be an established method. The utility generator would also have tunable parameters (spatial model? how many dimensions? degree of correlation, etc), and those would have to be set depending on the political context. Introducing noise (n voters vote however they want) would also make it significantly harder.

Old rating based polls could be used as a base. The rankings of this election could be compared to the rankings of those old polls where we have both rating and (derived) ranking information available. Then we would tweak the old ratings a bit into the apparent direction to get our current estimate.

> 
> Apart from that, the only way I think you can do it is to dissolve the problem by asking for ratings information.

Ratings would be more accurate. But also they would have some problems, like interest to push the worst opponents down in ratings in order to give an impression that nobody likes them.

Vote normalisation is also an interesting problem. Maybe the ratings would not be just on a numeric scale, but on a scale that has some named points like "unacceptable", "neutral", "very good".

Juho