[EM] Voter satisfaction measure in a general case?

[Kristofer Munsterhjelm]

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.

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.

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.

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