[EM] basic fairness question

[Kristofer Munsterhjelm]

Owen Dalby wrote:
> Set a threshold for election on this scale
> (say, 3.5 on a 5-point scale), and the candidates whose average
> scores fall above that threshold are given a seat. In this case the
> candidates with lesser name recognition, and therefore probably fewer
> "votes," would have an average score that is less precise than those
> with greater name recognition, but it would still be a snapshot of
> how some number of voters feel about them. Obviously there would have
> to be some minimum number of votes (or maybe evaluations is a better
> term) on a candidate for it be considered a valid portrait of their
> fitness for election.
> 
> My question is, is this inherently unfair towards anyone from a
> statistical/electoral point of view? In this particular situation,
> picking the number of seats beforehand is somewhat arbitrary--it is
> not a given that it would have to be 15, though that is the number of
> candidates that would fall above an "electable" threshold in my
> estimation.
> 
> Any advice, or fundamental concepts misunderstood by me?

The problem with using straight averaging, at least if you want 
proportionality, is that it's very majoritarian. If 50%+1 vote top marks 
for a set of candidates, and you simply take the candidates with the 
greatest average, then the 50%+1 dictate the composition of the entire 
group.

Unfortunately, I don't know of any really good non-experimental rated 
vote systems that maintain proportionality. You could use reweighted 
Range, but it's not set-proportional. STV has the property that it is, 
which means that if 80% vote for a given set above the rest, 80% of that 
set will be in the outcome (roughly - see Droop proportionality for the 
details).

You could also use your averaging idea, but with a cumulative vote 
rather than a rated vote. This means that you normalize everybody's vote 
so that the ratings sum to the same value.
That would be a continuous version of SNTV; to the degree that it's not 
proportional, it errs in the other direction than Range, namely in being 
too Plurality-like.

(Or perhaps you could use one of the methods above to narrow down the 
field, say to 20, and then ask the voters to check the candidates that 
remain more closely. Maybe that will offset the "unknown name" problem.)

I hope the suggestions have been useful, even if I don't know of any 
concrete method you can use :)

-KM