[EM] Voter satisfaction measure in a general case?
Kristofer Munsterhjelm
km_elmet at t-online.de
Sun Oct 15 12:23:11 PDT 2017
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.
More information about the Election-Methods
mailing list