Please allow me to correct my errors with the form of argumentation I should have presented from the beginning:
Which of the following voters contributes the most to A being seated?
- A5, B5, C5, D5
- A4, B3, C3, D3
- A3, B0, C0, D0
Voter #1 clearly contributes the most to A getting a high grade
…but they do the same for B, C, and D, too. As such, I assert that Voter #1 does not actually contribute to A winning in any meaningful way (outside of a “minimum score to be seated” scenario). As such, it is down to Voter #2 or Voter #3.
To ease the decision, let us add in a 4th voter:
- A3, B4, C5, D4
Any subset of those voters including Voter #3 results in a guaranteed victory for A. In order for A to win without Voter #3, however, you need both to include Voter #2 and to exclude Voter #4.
So what happens if we run a 2 Seat party list election using “Highest Score for Winner” as our metric for “Contributes most”?
Seat 1: A:3.75 > C:3.25, remove Voter 1 (5) and 2 (4)
Seat 2: A:3 > C:2.5
Compare that to what we get with “Difference from Average”:
Seat 1: A:3.75 > C:3.25. Remove Voter 3 (3-0.75 = 2.25) and 2 (4 - 3.25 = 0.75), the totals for voters 1 and 4 being 0 and -1, respectively.
Seat 2: C:5 > B=D:4.5
While it feels right to declare that the ballots with the highest score for a given candidate contribute most to them winning, because (again, outside of victory threshold scenarios) the only real question is the relative contributions the ballot made to the various candidates.
If you have a superior answer as to how to determine that question, I would be very glad to hear it, but the gut reaction that everyone (including myself, mind!) seems to have of “highest score obviously contributes most” seems pretty clearly wrong when you start approaching it critically.
After all, isn’t that the reason that people assume that Min/Max, Approval Style Score voting is “obviously” the most effective method? Because it maximizes the relative contribution between candidates you like and dislike?