@cfrank said in Ordinal Score "(S,P)"-systems:

For an example of an (S,P)-efficient election strategy, consider the voting system that chooses a candidate with a maximal area bounded in (S,P)-space by their production-possibilities frontier. This precludes (S,P)-dominated candidates from winning the election.

Isn't this just score voting? Since for random variable X >= 0 with probability 1, EX = integral{0 to inf}[P(X>t)dt]

@cfrank said in Ordinal Score "(S,P)"-systems:

Unfortunately, while the arbitrary nature of the scores has been eliminated, we have not been able to eliminate the arbitrary nature of the production of frontiers.

So the method you proposed could be considered part of a general class of methods of the following form:

Suppose X_1, X_2 ..., X_N are random variables between 0 and 1, where X_1 >= X_2 >= ... >= X_N with probability 1.

Then {(1,X_1), (2,X_2), ..., (N, X_N)} defines a random frontier.

For candidate C, let p(s) be the proportion of ballots such that candidate C is scored at least s.

Then the expected proportion of vertices on which p(s) >= X_s is (1/N)*sum{k=1 to N}[X_s <= p(s)]

(Note that if X_1 = ... = X_N ~ Unif(0,1), we get score voting.)

Anyway, a criticism I have with the system that you have proposed in which the X_i are products of uniform distributions is that as i becomes larger, the distribution of the X_i become very left-skewed (edit: this should say right-skewed). For a 5 point scale, a candidate who receives a score of 5 on 1% of ballots, and 0 on all others will score about 34%.

Basically, it will be absolutely essential for a candidate to attain a (fairly small) critical mass of max-value scores, since that will gain them almost all of the points available on the higher-valued scores. Among candidates who reach the critical mass, the winner will probably be whoever gets the most 1s (*de facto* turning into approval voting where anything greater than a 0 is full approval).