Primaries (ideal system for them and philosophy)

[Abel]

This year I posted this idea on the EM mailing list but got no response, in case it interests any of you here:

I was wondering whether under idealized circumstances, assumptions primary elections are philosophically different from social welfare functions (are they "social truth functions"?). With these assumptions I think the most important is who takes part in a primary (and why?). Let's assume a two party or two political block setup to make it easy and that the other side has an incumbent, a presumptive nominee or voters on the side of the primary otherwise have a static enough opinion of whoever will be the nominee on the other side. At first let's also assume no tactical voting or raiding the primary.

If the primary voters are representative of the group who's probably going to show up in the election (except for committed voters of the side), the I propose that the ideal system for electing the nominee is equivalent to Approval:
The philosophical goal of the primary is not to find the biggest faction within the primary voters (plurality) or to find a majority/compromise candidate (Condorcet). The goal is to find the best candidate to beat the opposing party's candidates. If the primary is semi-open, this probably means the opinions of all potential voters of the block/party can be considered, which in theory could make the choice more representative.

In the ordinal sense, the ideal primary system considering all of the above would be this: Rank all candidates, including the nominee of the other party (this is a placeholder candidate in the sense they cannot win the primary). Elect the candidate with the largest pairwise victory (or smallst loss, if no candidate beats) against the opposing party candidate. But this is essentially approval voting, where the placeholder candidate is the threshold, and similar tactical considerations seem the same: At least the ballots should be normalized by voters who prefer all candidates to the other side, but as soon as we loosen some of the assumptions I can see more tactics being available than under normal approval, precisely because there are more variable (e.g. do I as a primary voter assume the set of primary voters misrepresents our potential electoral coalition, and therefore I wish to correct for that?)

Philosophically, this I think a primary election is not the same as a social welfare function, it does not specifically for aggregating preferences, trying to find the best candidate for that group but to try to find the best candidate of that group to beat another grouo. The question is not really who would you like to see elected, but who would you be willing to vote for? One level down, who do you think is most electable, who do you think people are willing to show up for?

Now approval may turn out not to be the best method when considering strategie voters and different scenarios. But would you agree that there is a fundamental difference in the question being asked (compared to a regular election), or is that just an illusion? Or is this in general an ordinal/cardinal voting difference (cardinal using an absolute scale for "truth", while ordinal is options relative to each other)?