If there are exactly two candidates tied after your convoluted calculations, just elect the one who beats the other head to head.

This seems stupendously obvious to an almost condescending degree, but I feel like this concept is often ignored when getting into the weeds with crazy Condorcet methods.

"If the they tie for the least greatest margin of loss, then elect the tied candidate with the least greatest number of winning votes from their pairwise oppositions." - a Minmax variation

It feels excessive at a certain point. Sometimes, the math for some methods creates more ties rather than fewer (see Schulze). I can't imagine being a voter knowing that a tie between my favorite and another candidate my favorite beat was broken in favor of the other candidate because of some crazy math algorithm I don't understand. I know most of these methods are more theoretical than practical, but to me, any tie-breaking method that doesn't naturally comply with this concept every time is fundamentally broken.

@jack-waugh Almost. Yes, under IRV, your first choice is always counted in the first round, but who cares about the first round? The final tally is the most important one that will get reported, and the final tally is the round that throws out the most ballots. As an example, in the 2021 New York City Democratic Mayoral Primary, Eric Adams was reported to have received 50.5% of the vote to Kathryn Garcia's 49.5%, but that's only because that tally ignored over 140,000 ballots. In reality, Adams only received 43% and Garcia 42%. That matters. Electability is rooted in perception. The voters of NYC were tricked into believing that Eric Adams had majority support when actually there's a clear majority that didn't vote for him. Under Choose-one Voting, that would have been much clearer. Under Choose-one Voting, I know that my vote will always send a message, even if it doesn't affect the outcome of the election.

@rob I'm down to keep working on ballot language. I think we need to come up with several different versions and do real field testing because every voting enthusiast seems to have a different idea about how to shift it. The shortest explanation of the tally is actually a single sentence with two clauses:

Among the candidates who tie for winning the most head-to-head matchups, elect the candidate with the best average rank.

There's some ambiguity in there in my opinion because the word "among" is being leaned on heavily, and I don't like using the mathematically equivalent "best average rank" explanation because I think it's misleading to voters despite the line saying that skipped ranks are ignored. The point is there's definitely a range of how descriptive we can be with it.

@andy-dienes I agree that it's mostly speculation at this point, though I have seen other papers and reports suggesting it's not that I need to find again.

I think the point about voters feeling like they have a fair choice needs to be qualified: it's important that we use systems that won't cause that feeling to backfire down the road. If voters like it at first, great. But if we're lying to them to make it that way, then when they inevitably discover the truth, we may end up in a worse place than where we started. It's important that we set ourselves and society up for success the first time, otherwise morale for voting method reform could be destroyed for a generation or more.

@jack-waugh It fails Independence of Irrelevant Alternatives. Unlike Ranked STAR, Ranked Robin (the official name of this method) is not a score method disguised as a ranked method -- that's what Ranked STAR is for. Ranked Robin fills a different need.

@andy-dienes Do you believe those gains are sustainable?

"In the 2014 survey, the gaps between resident perceptions of three indicators of campaign negativity in RCV and non-RCV cities were narrower than they were in the 2013 version..."

I believe that when voters and candidates are honest and excited, such as the first few cycles after IRV is implemented and FairVote convinces everyone they can finally be positive and honest, then IRV does perform better than Choose-one Voting and exhibits some of the positive effects that are often sold. However, as time goes on and the voters and candidates experience that their shiny new method keeps electing the same politicians as their old one, things will revert. That seems to show up in analyses of voter turnout in IRV jurisdictions after enough time.

https://www.rangevoting.org/IRVturnoutSF.html

@jack-waugh It's really weird reading a Score advocate claim that voting behavior should be based on hatred and fear. Score is all about consensus.

Also, "Tongue Kiss" is super f****** gross. I'm genuinely repulsed and knowing that it's from the person who manages this site makes me want leave the entire forum.

Anyway, 3-2-1 was really designed with with the delegation case in mind, not the undelegated case. Quinn is expecting many voters to rate a single candidate "Good" and then let most of their ballot be filled out by that favorite. You seem to argue in favor of favorites anyway, so I'm not sure what you issue with it is.

Voters tend to use the scores 100, 99, 50, 1, and 0. That corresponds to favorite, backup, meh, lesser evil, greater evil. Your scale is super lopsided. Really, you should just use those 5 terms and then find the two semi-finalists with the fewest "evil" ratings, regardless of whether they're lesser or greater.

@rob We talked in my open democracy discussion last Tuesday, but just so it's down in text, I'll reiterate a few points I made for anyone reading.

In elections with only two competitive factions, any voting method would elect the Condorcet winner basically every time. Even with the hundreds of Ranked Choice (Instant Runoff) Voting elections in modern US history, only a tiny number of them have had 3+ competitive factions, and most of those did not elect the Condorcet winner.

Electing the Condorcet winner is irrelevant when the elections aren't competitive. Ranked Choice (Instant Runoff) Voting clearly doesn't promote competitive elections if for no other reason than its hyperfocus on (false) majority. If a candidate only needs to get half of the electorate to support them in order to win, then they have every incentive to polarize every issue, locking down half of the electorate while ignoring the other half. What makes Score elections competitive is that there is no minimum threshold candidates need to get over to guarantee a win -- they actually have to beat every other candidate, even if another candidate has support from 70% of the electorate; it's a race to the top, not a race to 50%+1.

@jack-waugh The biggest organization that advocates for Ranked Choice (Instant Runoff) Voting says that it doesn’t help to elect third-party candidates.

https://www.fairvote.org/third_party_and_independent_representation

Ranked Choice (Instant Runoff) Voting only eliminates spoilers in favor of electing the correct duopoly candidate. When a voting method has high voting splitting, being a spoiler is about all of the power minor parties have over major parties to keep them accountable. It’s not much, but it’s something. Ranked Choice (Instant Runoff) Voting takes away what little power minor parties currently have over major parties, leaving the duopoly entirely unchecked rather than mostly unchecked.

To demonstrate, think about it from the perspective of a Republican candidate in a close race against a Democrat under Choose-one Voting. Some savvy Libertarian starts drawing away your voters. In order to ensure you can beat the Democrat, you have to concede something to the Libertarians instead of sticking with your party line. Under Ranked Choice (Instant Runoff) Voting, you don’t have to worry about that because the Libertarian votes will just transfer to you after the Libertarian candidate is eliminated. The same dynamic happens between the Democrats and the Green Party. In fact, half of what the Green Party talks about is how to get the Democrats to shift, not how to win elections.

When vote splitting remains in a duopoly, the spoiler effect is arguably a necessary evil. The solution is not to mitigate the spoiler effect — the solution is to eliminate vote splitting, which Ranked Choice (Instant Runoff) Voting doesn’t do because it’s really just iterated Choose-one Voting. Ultimately, the problems of Choose-one Voting can’t be solved by iterating it over and over again.

I could keep going, but whatever their goals are, demonstrate clearly that Ranked Choice (Instant Runoff) Voting doesn’t address them.

@andy-dienes Yes, I'll add clarification to my statement.

I don't think IRV inherently elects more polarizing candidates than Choose-one Voting because of its mechanics. What I've seen is that in the US right now, because of the way IRV is sold, after it's implemented somewhere, candidate (exit) strategy and voter strategy decreases (at least initially). That would cause either method to elect more polarizing candidates, and I'm pointing in particular to (rare) IRV elections like Burlington, VT 2009 and this ongoing Alaska Special General Election with 3 distinct front-runners. As voters and candidates better figure out IRV, I would expect it to "reduce" mostly back to Choose-one Voting with similar candidate and voter strategy. The transparency and familiarity of Choose-one Voting helps it to "stabilize".

@marcus-ogren Good point. The idea behind the Critical Score is to boost candidates with isolated support. It's possible that it goes too far, as you've highlighted. I just found that to sort of achieve the effect I was looking for, I would need a really big exponent for the Power Score.

I wonder how it all washes out in more realistic scenarios, but it's valid to consider someone putting themselves on the ballot and literally not telling anyone just to then score themselves 5 stars. Perhaps there's some kind of balancing that can be built in, but I suspect, on the general advice of James Quinn, that that would likely cause new problems.

Also, for reweighing, I think I used P instead of U because I originally intended to perform the calculation using Power Scores instead of Unity Scores. I just realized that I think I switched in part because I was doing the math wrong in the first place. If we just use the S^2 and the original Power Scores instead of S and the Original Unity Scores, it should still work, and maybe even better. Otherwise, differentiating the Power Scores as their own set of total scores for each candidate is effectively useless.

Looking back at my (limited) testing, I actually tried this and it seemed to work just fine, so the new reweighing formula for each ballot would be 1-(Qx(S1)^2/P1)-(Qx(S2)^2/P2)-... where Q is the number of ballots in a Hare Quota, S1 is the original score given to the first winner on that ballot, P1 is the original Power Score of the first winner, S2 is the original score given to the second winner on that ballot, P2 is the original Power Score of the second winner, and so on.

After a candidate is elected in a given round, we give some influence to them from that winner's supporters before the next round because those voters now have some (more) representation. How much influence do we give? The more stars you originally gave a winning candidate, the more of your influence we give to them, and it's exactly proportional to how much of that candidate's total support you contributed to and the number of voters needed to support that candidate so they can win a seat in the first place. For example, in an election with 150 voters and 5 winners, each winner needs the equivalent of full support from 30 voters to be given a seat because 150 divided by 5 is 30. This quota of 30 voters stays the same throughout the entire tally.

Now, if you gave the first winner 4 stars, which translates to 16 stars, and that winner's original Power Score was 800 stars, then you contributed 2% to their success. Go you! So our 30-voter quota times your 2% means that we give 60% of your original influence to that first winner before the next round, which is not too bad of a loss for a candidate you gave 4 out of 5 stars to! You'd think it would be more like 80%, but this first winner was so popular that they gained more than a quota's worth of support across the electorate. We only give each winner what they need so you don't get punished for supporting a popular candidate.

I feel the point of clarification isn't even needed when I phrase influence in terms of giving yours to winners you supported.

What about STAR-POWER Voting?
Score Then Assign Representatives - Proportional Option With Exponential Ratings

@jack-waugh For actual implementation, you would never bother squaring scores. You would always do Sx|S|.

Mathematically, cubing would be more elegant, and I considered it -- the results would just be a little more biased toward "polarizing" candidates. If a particular jurisdiction preferred that, that would be fine.

The problem is that the masses don't have their cubes memorized and the general explanation would require more syllables:

one hundred twenty-five, sixty-four, twenty-seven, eight, one, zero = 17 syllables

twenty-five, sixteen, nine, four, one, zero = 9 syllables

It's much easier for a person to "feel" the difference between 25 and 4 than 125 and 16.

@andy-dienes Yes, I'll add clarification to my statement.

I don't think IRV inherently elects more polarizing candidates than Choose-one Voting because of its mechanics. What I've seen is that in the US right now, because of the way IRV is sold, after it's implemented somewhere, candidate (exit) strategy and voter strategy decreases (at least initially). That would cause either method to elect more polarizing candidates, and I'm pointing in particular to (rare) IRV elections like Burlington, VT 2009 and this ongoing Alaska Special General Election with 3 distinct front-runners. As voters and candidates better figure out IRV, I would expect it to "reduce" mostly back to Choose-one Voting with similar candidate and voter strategy. The transparency and familiarity of Choose-one Voting helps it to "stabilize".

@andy-dienes I agree that it's mostly speculation at this point, though I have seen other papers and reports suggesting it's not that I need to find again.

I think the point about voters feeling like they have a fair choice needs to be qualified: it's important that we use systems that won't cause that feeling to backfire down the road. If voters like it at first, great. But if we're lying to them to make it that way, then when they inevitably discover the truth, we may end up in a worse place than where we started. It's important that we set ourselves and society up for success the first time, otherwise morale for voting method reform could be destroyed for a generation or more.

@rob I want competitive elections. That's why I'm qualifying your statement -- because it matters. I would agree that Condorcet methods encourage people to run who have wide appeal even in competitive races because the candidates actually need to beat each other. IRV is not a Condorcet method and only appears to tend to elect Condorcet winners because it is so often used in elections that are not competitive. Part of the reason that IRV isn't used in competitive elections is because it doesn't create them, which we need voting method reform to achieve in the US right now. Under IRV, candidates only need to get a majority (really a plurality) of support and then the minimum number of votes they need will naturally flow to them. What you're describing sounds more to me like competition has decreased in favor of one ruling faction, which sounds like the trend across most of California. It doesn't appear to me based on your recounting that IRV has done anything to prevent monopoly rule in San Fransisco.

This new voting method is so fresh that I haven't even named it yet! And I haven't even run it through more than one election, so I'm excited to hear from you all the ways in which it is terrible!

Okay, so the the question is how do we use score voting, which is inherently biased to elect candidates with broad appeal, to elect candidates with more isolated support? My answer: amplify voters' support for candidates at the top end of their ballot. How? The simplest way is to square their scores!

• Voters score candidates from 0 up to 5 stars.
• Add up these scores for each candidate to get their Unity Score.
• Add up the squares of these scores for each candidate to get their Power Score.
• Divide each candidate's Power Score by their Unity Score to get their Critical Score.
• Elect the first winner based on who has the greatest Critical Score.
• Calculate the new weight of each ballot using the formula 1-(QxS1/P1) where Q is the number of ballots in a Hare Quota, S1 is the original score given to the first winner on that ballot, and P1 is the original Unity Score of the first winner.
• Recalculate the Critical Score for each remaining candidate using the new ballot weights.
• Elect the next winner based on who has the greatest recalculated Critical Score.
• Calculate the new weight of each ballot using the formula 1-(QxS1/P1)-(QxS2/P2) where Q is the number of ballots in a Hare Quota, S1 is the original score given to the first winner on that ballot, P1 is the original Unity Score of the first winner, S2 is the original score given to the second winner on that ballot, and P2 is the original Unity Score of the second winner.
• Recalculate the Critical Score for each remaining candidate using the new ballot weights.
• Repeat, using S3 and P3 for the third winner, and so on.

Important note.
Ballot weights are able to go negative after a few rounds. This is intentional. It means that a voter is overrepresented, so now their ballot starts counting against their interests. On the surface, this appears like a huge spot for tactical voting, but in my (admittedly limited) testing, it's hardly an issue and serves more as an incentive for voters to distinguish among a large group of favorites than plan for a possible tiny bit of influence they might have over candidates they probably don't care much about by the rounds it matters. Instead of squaring scores during the calculation of the Power Scores, be sure to multiply scores by the absolute value of the scores to retain their negative nature.

Optionally, the (recalculated) Power Scores can be used to elect candidates instead if a jurisdiction wants winners who are more unifying. The (recalculated) Unity Scores can also be used instead if the jurisdiction wants candidates who are even more unifying.

Really, any power >1 can be used. I picked 2 because it is the simplest and most familiar for voters.

If you give a candidate 0 stars, it's still like you're giving them 0 stars. If you give them 1 star, it's still like you're giving them 1 star. However, if you give them 2 stars, it's like you're giving them 4 stars. If you give them 3 stars, it's like you're giving them 9 stars. 4 stars is like 16 stars and 5 stars is like 25 stars. So you can see how we're amplifying the support you're giving a candidate. That's the whole point of proportional representation. There will be multiple winners and this helps to ensure at least one strongly represents you.

For ballot reweighing, we need to take away one quota's worth of ballot weight from the entire electorate. Because the sum of all S for all voters in any given round is just P, then (sum of all S)/P=P/P=1, so Qx(sum of all S/P)=Q. Subtract Q from the entire electorate and now you have 1 less quota's worth of ballot weight from the entire electorate.

After a candidate is elected in a given round, we take some influence away from that winner's supporters before the next round because those voters now have some (more) representation. How much influence do we take away? The more stars you originally gave a winning candidate, the more influence we take away from you, and it's exactly proportional to how much of that candidate's total support you contributed to and the number of voters needed to support that candidate so they can win a seat in the first place. For example, if you gave the first winner 2 stars and their original Unity Score was 400 stars, then you contributed one half of one percent to their success. Go you! Now, if there are going to be 5 winners in the election, then each winner needs support from one-fifth of the electorate. Let's say this election had 150 voters. That means each winner needs the equivalent of full support from 30 voters, so 30 voters times your one half of one percent means that we take away 15% of your influence from the next round. Not too bad of a loss for a candidate you bothered to give 2 out of 5 stars to! A point of clarification: let's say you lose an additional 40% of influence based on the original score you gave the second winner. That stacks simply with the previous round, so now you've lost 15% plus 40%, so 55%, of your original influence by the third round.

Let me know what's wrong with my new method!

@andy-dienes Do you believe those gains are sustainable?

"In the 2014 survey, the gaps between resident perceptions of three indicators of campaign negativity in RCV and non-RCV cities were narrower than they were in the 2013 version..."

I believe that when voters and candidates are honest and excited, such as the first few cycles after IRV is implemented and FairVote convinces everyone they can finally be positive and honest, then IRV does perform better than Choose-one Voting and exhibits some of the positive effects that are often sold. However, as time goes on and the voters and candidates experience that their shiny new method keeps electing the same politicians as their old one, things will revert. That seems to show up in analyses of voter turnout in IRV jurisdictions after enough time.

https://www.rangevoting.org/IRVturnoutSF.html

@rob 440 elections? More like 4. Most IRV elections in modern US history have only had 2 competitive factions, which any voting method would elect the Condorcet winner in almost every time. In the tiny number of them with 3+ competitive factions, the Condorcet winner was elected in I believe one.