[EM] Voter satisfaction measure in a general case?

Tue Oct 17 18:41:22 PDT 2017

Different elections could need different kind of ballots. For example, if the number of candidates is high, it could be easier to rate the candidates than rank them all. The ballot could e.g. have one row for each candidate, and twenty boxes to the right of the name of each candidate. The voter would tick one box for each candidate, or not tick any boxes, which would indicate the lowest possible value. This could be a practical approach in some elections, and it would give you also some sort of rating values. Collecting ratings this way (as a by-product) could be a viable approach if you want to keep it simple.

If you have those boxes in the ballot, or some other kind of scale, there are two options. The scale can be either abstract numbers / positions only, or it could contain some guidance, like three lowest boxes having different colour and a descriptive word "not acceptable", etc. Such descriptions would give you some guidance on how strong the feelings of the voters are, and it would make all the voters use the scale in the same way.

One question about voter satisfaction. My ratings are A=40, B=30, C=10. B wins the election. What is the level of my satisfaction? Is it 30 (that's how much I like B)? Or is it 75 (based on normalising my vote to range 0..100)? Or is the level of my dissatisfaction 10 (40-30, that's how much I would have been happier if A had won)? If there is also candidate D that I didn't rate at all (maybe 0 by default), that might or might not change the (above mentioned) normalised value.

The results of Condorcet methods can be quite difficult to interpret to normal voters if the outcome of the election appears to be a pairwise matrix or a complex graph that points out the results of each pairwise comparison. It would be simpler if one could give just one number that indicates how strong the victory was (one way to measure the overall stability of the election, and thereby also some form of satisfiability of the result). Most notably minmax(margins) decides the winner and measures the strength of the victory by counting the number of required extra votes (that would be needed) to win the election (instead of the current winner). This measure is based on number of voters only, not on ratings. All candidates will get a number that tells how far they were from winning the election. That distance could tell something also on the satisfaction level of the supporters of the competing candidates. This was just a side note, but maybe interesting when trying to find numerical measures describing the outcome of the election.

Juho

> On 16 Oct 2017, at 14:44, Magosányi Árpád <m4gw4s at gmail.com> wrote:
> 
> Thanks for the good inputs.I try to summarize here
> 
> proposed methods:
> 
> - set up some kind of utility generator that produces ratings style votes, and then randomly sample elections from this utility generator. 
> - use previous rated votes similarly to the utility generator above
> - ask for ratings
> 
> I also thought about asking about perceived closeness of alternatives
> 
> The reason for asking was to figure out a way to show voter satisfaction measure with vote results, in a general voting application.
> Directions towards solutions I see:
> - utility generators and previous similar votes seems to be too complex for the task
> - optionally asking rates from voters (maybe asking them to put the choices on a two-dimensional field, along with their own position) and use that as the basis of the utility function is an interesting idea maybe worth exploring
> - leaving the choice of an appropriate utility function form to the user when voter satisfaction is measured is the easiest
> 
> 
> 2017-10-16 12:47 GMT+02:00 Juho Laatu <juho.laatu at gmail.com <mailto:juho.laatu at gmail.com>>:
> > On 15 Oct 2017, at 22:23, Kristofer Munsterhjelm <km_elmet at t-online.de <mailto: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
> 
> 
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