In many settings people must give numerical scores to entities from a small
discrete set. For instance, rating physical attractiveness from 1--5 on dating
sites, or papers from 1--10 for conference reviewing. We study the problem of
understanding when using a different number of options is optimal. We consider
the case when scores are uniform random and Gaussian. We study computationally
when using 2, 3, 4, 5, and 10 options out of a total of 100 is optimal in these
models (though our theoretical analysis is for a more general setting with k
choices from n total options as well as a continuous underlying space). One
may expect that using more options would always improve performance in this
model, but we show that this is not necessarily the case, and that using fewer
choices---even just two---can surprisingly be optimal in certain situations.
While in theory for this setting it would be optimal to use all 100 options, in
practice this is prohibitive, and it is preferable to utilize a smaller number
of options due to humans' limited computational resources. Our results could
have many potential applications, as settings requiring entities to be ranked
by humans are ubiquitous. There could also be applications to other fields such
as signal or image processing where input values from a large set must be
mapped to output values in a smaller set
