[EM] Discounted Redundant Layers

[Bart Ingles]

Joe Weinstein wrote:

> What happens when K=1 - a single-winner election - and a nontrivial f
> is used?  Nothing different at all, if our 1-winner grading method is
> pass-fail ('approval'), but something quite interesting and useful if
> we use a higher-resolution method such as centile grading.  A
> candidate will then be rewarded not only for attaining a high average
> grade but also for this average being the result of a broad base of
> consistent support (rather than strong support from some segments of
> the electorate and weak support from others).  In short, depending on
> the particular convex function f used, we can craft a victory
> criterion which may be an attractive compromise between the extremes
> of high average (but possibly badly distributed) support and majority
> preference (which may be tepid and be more than averaged out by strong
> minority disapproval).


One question: why would any voter want to vote anything other than 0.0
or 1.0 for any individual candidate?  I understand that a voter may be
truly undecided about a candidate, but in that case why wouldn't a
coin-toss serve just as well?

Bart