@cfrank said in Ordinal Score "(S,P)"-systems:
My guess is that if past electoral data were used to produce or to inform the distributions, they would become centered at lower fractions as the ordinal score is increased, and would actually skew to the right. I believe this eliminates the problem you suggested.
I made a mistake, I should have said right-skewed.
In the past, various people have proposed using nonlinear levels for score voting. I have generally criticized this on the basis that it will seem arbitrary to voters. This method is not exactly one of those, but it is similar. Increasing a candidate's score from a 0 to a 1, a 1 to a 2, and so on, on a ballot, will all be worth different amounts (probably), but what amount it is worth depends on the distributions and the amount of support each candidate gets.
You have said that you are concerned that the values of score levels are arbitrary, so you might not be concerned that the amount that an additional point is worth under the proposed system is dependent on these factors; perhaps the approach you have proposed to assigning values to score levels gives them meaning. However, I am a bit skeptical of this.
First, the system might not pass Independence of Irrelevant Ballots. If several max-value ballots are added, then it will tend to reduce the value of higher-value scores relative to lower-value ones on the rest of the ballots.
Second, I can think of cases where basing the distributions on past empirical data leads to points being devalued that clearly should not be devalued. Suppose that the first time a system like this is used, there are two polarizing candidates, and each candidate gets about half of the vote, with each ballot giving one candidate a 5 and the other a 0. The next election is similar, but this time, there is a compromise candidate who gets about a 3 from everybody. The compromise candidate will get a score of 60%, but if slightly less than half of voters gave this compromise candidate no points, then they will still score 60%, because no candidate in the first election got more than, say, 51% of scores above 0. While calibrating the distributions on the performances of two candidates is clearly insufficient and this example is probably unfair, I think it does highlight a general problem that a compromise candidate who gets an unprecedented amount of midrange support will stop receiving credit for additional midrange support beyond what has previously occurred.