Is there any value to averaging in cardinal PR?

In single-winner Score, some contend that a great candidate might lose because of having less name recognition i.e. someone scored 10/10 by 40% of voters and left blank by 60% could lose to someone with a 5/10 from all 100% of voters. To solve this, they use averaging that comes in various forms, so that basically candidates who were scored on less ballots get a boost relative to their actual scores and candidates scored on more ballots.

In PR, there are likely to be a lot of candidates running, so voters will probably prefer to leave blank candidates they dislike, rather than give all of them 0s. This means that any form of averaging will probably need to be very nonaggressive or it would artificially inflate bad candidates’ scores. So is there any form of averaging worth using for cardinal PR?

PR is already complicated enough without no opinion scores.

Unreasonably computation heavy systems for this you can use for optimal methods are systems that assigns your ballot scores of blank candidates based off of how like-minded voters score that candidate.

Here is one example of such a system:

  1. Each voter marks each candidate as approve, disapprove, or no opinion.

  2. There are two groups of ballots, raw ballots and tabulated ballots. These ballots will go into the raw ballots group.

  3. For each possible set of candidates considered:

    1. Remove all ballots from tabulation ballots.

    2. Suppose that (don’t actually do this step):

      1. You added all ballots from raw ballots that didn’t give any ‘no opinion’ scores to any of the candidates to tabulation ballots.

      2. For each ballot s from raw ballots that gave a ‘no opinion’ score to only one candidate in the considered set:

        1. You picked a random ballot r from tabulation ballots that did not disagree with s when scoring the candidates in the considered set (for each candidate in the set that s gives an approval or disapproval towards, the randomly chosen ballot must also give that candidate the same score).

        2. You then added a copy of r to tabulation

      3. For each ballot s from raw ballots that gave a no opinion score to two candidates in the considered set:

        1. You picked a random ballot r from tabulation ballots that did not disagree with s when scoring the candidates in the considered set (for each candidate in the set that s gives an approval or disapproval towards, the randomly chosen ballot must also give that candidate the same score).

        2. You then added a copy of r to tabulation

      4. You repeated this process until you get to ballots that give ‘no opinion’ scores to all candidates in the considered set.

    3. For each possible way to score the candidates in the considered set such that no candidates are given no opinion scores:

      1. Add a ballot to tabulation that scores the candidates that way

      2. Give the ballot a weight equal to the expected number of ballots that scored that candidate that way that would of existed after step 3.2 if you would of preformed that step.

    4. Calculate and record the quality of that set of candidates using the tabulation ballots.

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Is there a way to do averaging that only affects candidates scored on a miniscule portion of ballots? So, say, candidates scored on 1% of ballots get an increase in score, but not candidates scored on 2% of ballots. And is there any way to make that actually change a result, or at least positively impact newcomer candidates’ perception? Is there maybe some way the averaging could be useful in other contexts i.e. making a STAR runoff work in PR?