Voting on Single-Winner Voting Methods and Smith//STAR
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I wanted to bring up something from the past that never came to fruition, which was the idea to vote on voting systems. The idea was to have users include a ranked score-carrying ballot in their forum signature (you can see mine below as an example), and to intermittently compare them to see what users thought. All that was ~discussed here:
Anyway, after digging through the old forum threads, I tried to reconstruct a “metaelection” from the score ballots that various users have put in their signatures or explicitly posted.
So far I’ve recovered commensurate ballots from only a small collection of users:
- cfrank (myself)
- Jack Waugh
- multi_system_fan
- Marylander
- Andy Dienes (former user)
- Keith Edmonds
(I also found evidence that rob had a ballot in his signature, but I haven’t yet recovered the actual scores.)
While this is not necessarily representative of all users or even voting theory enthusiasts in general, and does not include all voting methods one might in principle prefer, I wanted to see what the results were from the limited scope and “turnout.”
To make the ballots comparable, I grouped together the various rated/cardinal Condorcet methods (e.g. Score Sorted Margins, generic cardinal Condorcet, rated Condorcet), rescaled Marylander’s 0–100 ballot to 0–10, and then compared the common methods.
The aggregate score totals are:
- Cardinal Condorcet: 55.0
- STAR: 48.0
- Approval: 42.9
- Score: 39.1
- IRV: 12.8
- Choose-one/FPTP: 4.0
Pairwise, cardinal Condorcet defeated STAR, Approval, and Score by 4–2, making it the Condorcet winner of the metaelection as well.
It also won under Score, STAR, Borda, Plurality, and IRV. Under Approval, the outcome depended on the approval threshold: using the suggested threshold of 5 gave a three-way tie between cardinal Condorcet, Approval, and STAR, while a stricter threshold (>5) elected cardinal Condorcet outright.
At least from the ballots I could recover, the collective ordering was:
- Cardinal/rated Condorcet
- STAR
- Approval
- Score
- IRV
- Choose-one/FPTP
If anyone knows of additional signature ballots (or can recover rob’s old ballot), it would be interesting to incorporate them.
We can compare with an external poll on Reddit (this poll is not a vote, but asks which single-winner system among alternatives is most preferred):
https://www.reddit.com/r/EndFPTP/comments/1cukxrz/what_singlewinner_method_do_you_support_the_most/
Interestingly (or perhaps uninterestingly?), if we pool together all Condorcet methods, our small toy election matches quite well with the top preferences in the Reddit poll.
I would also like to hold that kind of election not in terms of the most preferred voting method outright, but in terms of what the most feasible reform target to implement would be. That’s a bit vague—for example, would that mean implement state-based/federal approval voting? Or to push for proportional representation in districts?
Based on this preliminary outcome, a cardinal-Smith method with a STAR-style fallback or completion rule might be worth considering, although that specific composite was not itself included uniformly on the ballots. I was also surprised to find that, unless I overlooked something, this specific hybrid had not been proposed before now on this forum. It has been proposed elsewhere, including within various Reddit threads.
Finally, on the subject of voting for voting methods, I wonder if it would make sense to have the electorate vote on their preferred method along with their ballots, or to vote for their preferred method in advance. That’s probably a different topic.