I dreamt up the following single-winner voting system in the car while driving to Eugene, Oregon on vacation. I make no representation that it is any good, nor that it’s better than anything currently known or in use, nor that’s it’s worth your time to read this.
Commentary and rationale will be explained at the bottom of this post
The system is a 2-round system. The first round uses an approval ballot, and the second round asks voters to choose between two candidates.
([•] indicates a constant that can be changed during implementation)
Round One:
Tally all approvals for each candidate
If there are two or more candidates with at least a 50% [•] approval rating, remove all candidates with less than [50%] approval. Otherwise, return the highest-approved candidate as the winner of the election
If there are only two candidates remaining, proceed to Round Two with the two remaining candidates. If there are more than four candidates, remove all but the four [• ; shouldn’t be higher than 6 or 7] highest rated candidates.
Consider all pairs of candidates that includes at least one of the top two candidates. For each pair, a candidate’s Opposing-Approval is that candidate’s approval rating among the 10% [•] that least approve of the other candidate. (That is to say, if the other candidate has less than [90%] approval, it is the first candidate’s approval among those who oppose the other candidate. The quantity approaches the candidate’s overall approval as the approval of the other candidate approaches 100%)
Each’s pair’s Score is the sum of the two candidates’ Opposing-Approval. A higher score means that voters who don’t approve of candidate A tend to approve of candidate B, and vice-versa. If the supporters of A and B tend to overlap, the pair’s score will be low.
Send the pair (among those considered in step 4) with the highest score to Round Two
Round Two
Ask voters which candidate they prefer. The more preferred candidate is the winner. Voters may, of course, express no preference, but that will not affect the outcome.
Commentary and Rationale
I’ve been considering the hypothesis that the polarizing nature of plurality vote (FPTP) may actually be a feature, not a bug. While I suspect this hypothesis is likely (at least mostly) wrong, and that the center-seeking / consensus-building nature of Approval voting is one of its most valuable features, the described system was created to combine the consensus-seeking nature of AV with the contest between two opposing viewpoints provided by FPTP.
Below a certain approval rating, the system behaves like AV as a failsafe against the failure mode present in FPTP where a very unpopular candidate can win as long as their opponent is just as bad (IIRC, Instant Runoff doesn’t completely address this). Likewise, the winning candidate will always be one of the most approved, even if they’re not the highest-approved candidate.
But above a certain level of approval, the system intentionally introduces a degree of polarization, seeking out a pair of candidates with some disagreement between their bases, and choosing one or the other. This increases the “temperature” of the system, allowing potentially controversial but high-value strategies to be tried, encouraging candidates to not just play things safe. This could potentially lead to a bolder style of leadership than pure approval voting (though note that it is a misconception that AV will produce milquetoast, boring, spineless appointees; AV searches for a candidate who is exciting and compelling to all voters, not just to a particular fraction of voters). While some countries may be content with a middle-of-the-road style of leadership like AV provides, perhaps some countries may desire the dynamic quality this system intends to share with FPTP.
Again, I make no representation that this system is actually any good.
Alternative: Something like condorcet voting, where voters receive a random subset of pairs to compare. For a simple analysis, the number of pairs could be 1. (Or instead of pairs, a voter could asked to choose ‘the best’.)
I dreamt up the following single-winner voting system in the car while driving to Eugene, Oregon on vacation. I make no representation that it is any good, nor that it’s better than anything currently known or in use, nor that’s it’s worth your time to read this.
Commentary and rationale will be explained at the bottom of this post
The system is a 2-round system. The first round uses an approval ballot, and the second round asks voters to choose between two candidates.
([•] indicates a constant that can be changed during implementation)
Round One:
Tally all approvals for each candidate
If there are two or more candidates with at least a 50% [•] approval rating, remove all candidates with less than [50%] approval. Otherwise, return the highest-approved candidate as the winner of the election
If there are only two candidates remaining, proceed to Round Two with the two remaining candidates. If there are more than four candidates, remove all but the four [• ; shouldn’t be higher than 6 or 7] highest rated candidates.
Consider all pairs of candidates that includes at least one of the top two candidates. For each pair, a candidate’s Opposing-Approval is that candidate’s approval rating among the 10% [•] that least approve of the other candidate. (That is to say, if the other candidate has less than [90%] approval, it is the first candidate’s approval among those who oppose the other candidate. The quantity approaches the candidate’s overall approval as the approval of the other candidate approaches 100%)
Each’s pair’s Score is the sum of the two candidates’ Opposing-Approval. A higher score means that voters who don’t approve of candidate A tend to approve of candidate B, and vice-versa. If the supporters of A and B tend to overlap, the pair’s score will be low.
Send the pair (among those considered in step 4) with the highest score to Round Two
Round Two
Ask voters which candidate they prefer. The more preferred candidate is the winner. Voters may, of course, express no preference, but that will not affect the outcome.
Commentary and Rationale
I’ve been considering the hypothesis that the polarizing nature of plurality vote (FPTP) may actually be a feature, not a bug. While I suspect this hypothesis is likely (at least mostly) wrong, and that the center-seeking / consensus-building nature of Approval voting is one of its most valuable features, the described system was created to combine the consensus-seeking nature of AV with the contest between two opposing viewpoints provided by FPTP.
Below a certain approval rating, the system behaves like AV as a failsafe against the failure mode present in FPTP where a very unpopular candidate can win as long as their opponent is just as bad (IIRC, Instant Runoff doesn’t completely address this). Likewise, the winning candidate will always be one of the most approved, even if they’re not the highest-approved candidate.
But above a certain level of approval, the system intentionally introduces a degree of polarization, seeking out a pair of candidates with some disagreement between their bases, and choosing one or the other. This increases the “temperature” of the system, allowing potentially controversial but high-value strategies to be tried, encouraging candidates to not just play things safe. This could potentially lead to a bolder style of leadership than pure approval voting (though note that it is a misconception that AV will produce milquetoast, boring, spineless appointees; AV searches for a candidate who is exciting and compelling to all voters, not just to a particular fraction of voters). While some countries may be content with a middle-of-the-road style of leadership like AV provides, perhaps some countries may desire the dynamic quality this system intends to share with FPTP.
Again, I make no representation that this system is actually any good.
Alternative: Something like condorcet voting, where voters receive a random subset of pairs to compare. For a simple analysis, the number of pairs could be 1. (Or instead of pairs, a voter could asked to choose ‘the best’.)