@rob especially if the state is a swing state, making it more difficult for the large parties to secure voters for their platform I think would be a significant influence forcing large parties and their candidates to more scrutinizingly determine the real interests of voters in those states. It may dilute the interests of less competitive states, but since the competitive states are crucial to obtaining the presidency, the large parties will still have to invest strongly in the interests of voters in those states in order to compete with alternatives (and obviously each other) for the crucial swing points. This may lead to something like an arms race of concessions, which happened in New Zealand in 1996 and led to the national adoption of a PR system, according to Arend Lijphart. Obviously that's quite a leap for the U.S., but maybe a less extreme analogue is not so far-fetched.

Maine is one of the thirteen most competitive states for elections according to a 2016 analysis (Wikipedia: Swing state), so I’m not sure their recent establishment is actually strategically foolish, although it’s possible that it wasn’t fully thought through. I agree it isn't clear.

I think it will definitely be interesting to observe how the current political apparatus responds to Maine--and apparently, more recently, and strangely, Alaska:

https://news.yahoo.com/alaska-is-about-to-try-something-completely-new-in-the-fall-election-193615285.html

Since Alaska is far from competitive, I do think this transition was in fact foolish for the reasoning you stated, but it remains to be seen. If we saw a state like Florida transition to a system like Maine's, it would be very interesting to study the relative differences between federal treatments of Florida, Maine, and Alaska as a case study for how "swingy-ness" might influence the effect of such voting system transitions. If Maine experiences an increase in federal power, it would be a good case for the remaining swing states to make a similar transition. If that occurred, the swing states would become a platform foothold for alternative parties to grow.

This is a minor attempt to modify Condorcet methods in a simple way to become more responsive to broader consensus and supermajority power. It’s sort of like the reverse of STAR and may already be a system that I don’t know the name of. In my opinion, the majority criterion is not necessarily a good thing in itself, since it enables tyrannical majorities to force highly divisive candidates to win elections, which is why I’ve been trying pretty actively to find some way to escape it.

For the moment I will assume that a Condorcet winner exists in every relevant case, and otherwise defer the replacement to another system.

First, find the Condorcet winner, which will be called the “primary” Condorcet winner. Next, find the “secondary” Condorcet winner, which is the Condorcet winner from the same ballots where the primary Condorcet winner is removed everywhere.

Define the Borda difference from B to A on a ballot as the signed difference in their ranks. For example, the Borda difference from B to A on the ballot A>B>C>D is +1, and on C>B>D>A is -2.

If A and B are the primary and secondary Condorcet winners, respectively, then we tally all of the Borda differences from B to A. If the difference is positive (or above some threshold), then A wins, and if it is negative or zero (or not above the threshold), then B wins.

For example, consider the following election:

A>B>C>D [30%]
A>B>D>C [21%]
C>B>D>A [40%]
D>B>C>A [9%]

In this case, A is a highly divisive majoritarian candidate and is the primary Condorcet winner. B is easily seen to be the secondary Condorcet winner. The net Borda difference from B to A is

(0.3+0.21)-2(0.4+0.09)<0

Therefore B would be chosen as the winner in this case.

Some notes about this method:
It certainly does not satisfy the Condorcet criterion, nor does it satisfy the majority criterion. These are both necessarily sacrificed in an attempt to prevent highly divisive candidates from winning the election. It does reduce to majority rule in the case of two candidates, and it does satisfy the Condorcet loser criterion, as well as monotonicity and is clearly polynomial time. It can also be modified to use some other metric in the runoff based on the ballot-wise Borda differences.

Continuing with the above example, suppose that the divisive majority attempts to bury B, which is the top competitor to A.
This will change the ballots to something like

A>C>D>B [30%]
A>D>C>B [21%]
C>B>D>A [40%]
D>B>C>A [9%]

And if the described mechanism is used in this case, we will find instead that C is elected. So burial has backfired if B is "honestly" preferred over C by the divisive majority, and they would have been better off indicating their honest preference and electing B.

And again, suppose that the divisive majority decides to bury the top two competitors to A, namely B and C, below D, keeping the order of honest preference between them. We will find

A>D>B>C [30%]
A>D>B>C [21%]
C>B>D>A [40%]
D>B>C>A [9%]

In this case, the secondary Condorcet winner is D, and the mechanism will in fact elect D, again a worse outcome for the tactical voters.

Finally, suppose that they swap the order of honest preference and vote as

A>D>C>B [30%]
A>D>C>B [21%]
C>B>D>A [40%]
D>B>C>A [9%]

Still this elects D.

As a general description, this method will elect the Condorcet winner unless they are too divisive, in which case it will elect the secondary Condorcet winner, which will necessarily be less divisive. I believe that choosing the runoff to be between the primary and secondary Condorcet winners should maintain much of the stability of Condorcet methods, while the Borda runoff punishes burial and simultaneously addresses highly divisive candidates.

https://www.forbes.com/sites/steveforbes/2022/09/23/weird-undemocratic-voting-system-is-taking-hold-in-us/?sh=3e3faf2b2714

This is a very unfortunate depiction of IRV and rank choice voting in general, it’s the kind of terse and poorly-informed (or simply pernicious) dogmatism that upholds the current status quo.

But who knows, maybe it’ll backfire! Getting people to say, “What? What is this thing?” and to actually investigate may be a good thing in the end. As Condorcet wrote, “truth alone will obtain a lasting victory.”

@jack-waugh yes, sadly pushing to the exterior of the doughnut is the most pertinent prisoner’s dilemma of today. Not an easy problem to solve without cooperation.

@rob I like this concept, I was also trying to consider the prospect of interstate pacts. In the case of less competitive states, an alternative voting system pact might be set to go into effect only once a sufficiently "large" group of states enter into the agreement (maybe measured according to their electoral college points as you suggest), which could easily negate the difficulties of diminishing federal influence when competing with a large FPTP block.

I think electors tend to be mostly faithful to the interests of their states (at least as far as can be determined by the gerrymandered districts), especially I think since they have the pressure of public scrutiny to more-or-less rubber stamp the results as they come in, and hopefully they also have some humility in their own decision-making powers and confidence in the larger process. I do think it gets problematic because entrusting electors to distribute their votes according to a less black-and-white indication of state interests does give them significantly more political power and responsibility that they will also need to be held accountable for. Generally I don't mind the concept of electors/representative arbiters as long as the incentives are sorted out. The way I see it all we can hope for is a system that consistently gives results that are good enough for national success, and if such a system does the job that'd be just fine with me.

I also think it’s a good sign that we’re at the point of discussing potential issues with real large-scale implementation.

@Jack-Waugh you’re right about For-and-Against, the modification I suggested is much less significant because it requires the pairs to match exactly, whereas For-and-Against counts all the positives and all the negatives. Just another example of how arbitrary the concept of “balance” in this formalism is. I liked your strengthening of the argument, you’re absolutely right about that as well, because it virtually eliminates any level of information voters might have about other ballots.

Maybe there is something more tangible that F-balance is trying to point to, but it isn’t clear what it might be. In my opinion, with respect to the concept of balance, the strengthened construction should by all reason send equal.vote back to the drawing board, especially if they can’t even formalize a valid counter-argument.

@rob I tried to send him an email Maybe an open letter is fine

“Hello Mr. Forbes,

My name is Connor Frankston. I recently read this very short article of yours, and I wanted you to know that the sentiments you express there are hindrances to necessary voting reform. While instant runoff voting is not by any means perfect, your article does absolutely nothing to address any of the positive qualities of instant runoff voting, and likewise does nothing at all to address any of the negative qualities of the present plurality voting system.

There are other ranked choice voting systems that many (including myself) consider generally superior to both methods, and to write off ranked choice voting altogether based on this specific, somewhat pathological instance, seems to reflect a pernicious sort of cognitive bias.

Otherwise, I would be interested to hear a less terse rendition of your arguments to the contrary.

Thank you,

Connor”

Since I started learning about voting theory I've struggled with accepting the Condorcet criterion. I think my position on it has been tempered a bit and softened, but I still have some criticisms I wanted to express.

In my opinion one of the strongest argument for the Condorcet criterion is very simple and as follows: It should not be that the winner of an election should have any other candidate preferred over them by a majority in a head-to-head election between the two. This is totally practical, since in reality a large majority could perhaps in principle simply overthrow the election results, for example. Unfortunately this is not possible to satisfy in general, as demonstrated by the Condorcet paradox. Hence, the condition is qualified to be upheld `"whenever possible," and one arrives at the Condorcet criterion. If one applies Condorcet's Jury Theorem, and assumes that in any head-to-head election there is an objectively ``better" choice, and simultaneously that each voter is more likely than not to indicate that choice as their preference in each head-to-head match, then we concoct some level of information-theoretic corroboration for the criterion.

There are issues with this argument, however, and also with the conditions for applying the Jury Theorem. Most substantially, and as recognized by Condorcet himself, the concept of a "better" choice is inherently subjective---that is, each voter has a different conception of what might constitute a good choice, hence the notion of a socially shared objective ideal is questionable at best. Even in that case, it does not seem theoretically appropriate to treat voters simply as independent, identically distributed Bernoulli random variables. More or less, this is equivalent to saying that each voter is already biased to make the ``correct" choice, or that already more voters than not will almost certainly make that choice. By that reasoning the result of the theorem is almost circular. At the same time there is no possible empirical support for the conditions supporting its conclusion in the context where individual preferences rather than the subjective identifications of a single socially shared objective is being indicated.

There are valid applications of the Jury Theorem: for example, in a jury. If one assumes that the jurors are competent, and that each has a higher chance than not of identifying the guilt of a defendant, then majority rule of the jury is likely to produce the correct verdict. The issue with extending the scope of the Jury Theorem is that, at least in theory, the guilt versus innocence of a defendant is an objective circumstance with the potential of being identified, whereas the ``best candidate" in an election simply is not, because it is by nature an opinion.

My second issue with the Condorcet criterion is the rather obvious observation that the majorities that elect the winners of each pairwise face-off can differ from each other substantially. This may not seem important on its face, but in fact, this is the root cause of the Condorcet paradox. A Condorcet cycle must have links that are supported by distinct majorities, one crowd shouting something here and another crowd shouting something else there. The social choice theorist listening to these different voices as though they come from one mouth will naturally be twisted into confused circles. It is true that there is necessarily an overlap between any two majorities, but there needn't be any overlap at all shared by any three of them. As such, while the premise of a Condorcet system seems positively-motivated, a Condorcet winner appears to be a figure that rises from the ashen remains of a chaotic competition, not necessarily a figure that represents a broad consensus of the electorate, although this may be the case.

The third issue I take with the Condorcet criterion is that the pairwise face-offs operate fundamentally within a majoritarian paradigm. May's Theorem only applies to situations where each voter can make only one of three indications---the first candidate, the second candidate, or neutral. This scope does not encompass general range voting systems, for example, so that it is not generally clear that a majority rules principle is the optimal method of social choice even between just two alternatives. The standard thought experiment might be called the ``pizza topping" problem, where three friends wish to contribute equally to purchase a single-topping pizza, but two friends prefer a topping that the third is allergic to. A majority rule decision is simply anti-social in this instance.

My final issue is that rank order systems put a large burden on voters, and it may just be impractical to expect each voter to indicate a full ranking of candidates unless the candidate pool is fairly small.

Anyway, I know that people like the Condorcet criterion, and I see its merits as well. I just wanted to know whether supporters (more or less) of it would be able to address those points in its defense, or raise any other criticisms that might point to better alternatives.

Thank you!

@rob that seems reasonable to me. A long while ago I was trying to consider score distribution metrics of the form

Avg*F(Stdev/Avg)

where F is a decreasing function (probably exponentially) and F(0)=+1. The metric scales directly with the distribution, but it’s only sensible for scores that aren’t negative unless you do a canonical shifting by the minimum score. It might also be considered a bit haphazard and computationally obnoxious, since standard deviations are annoying.

But something like

Avg/2^(Stdev/Avg)

would elect C.

If there was a faster formula to get a decent measure of the spread, that would be nice. Possibly the IQR or some other quantile range could be a substitute, and we would have

Avg/2^(IQR/Avg)

or we could possibly involve the median as well somehow.

The ratio Stdev/Avg is also known as the coefficient of variation. Apparently there is another more robust measure of dispersion that is very easy to compute: https://en.m.wikipedia.org/wiki/Quartile_coefficient_of_dispersion

QCD=(Q3-Q1)/(Q3+Q1)

Something like the metric

Avg/2^(QCD)

could possibly be applicable.

@rob I have already mentioned that the definition of a majority only applies in a constrained paradigm. My answer is that the question preconceives a paradigm that may be inappropriate, and that alternatives may be superior.

For example, let’s say we have two choices for lunch: peanut butter and jelly sandwiches, or fruit cups.

51% of the people at the lunch marginally prefer peanut butter and jelly sandwiches to fruit cups, but 10% of the people are allergic to peanuts. Furthermore, let’s say that 49% even strongly prefer the fruit cups to peanut butter.

Do you really think it’s a better idea to have peanut butter sandwiches than to have fruit cups?

I think it’s clear that empathy is necessary here to come to a sociable solution. A selfish majority rules paradigm doesn’t make any sense here and doesn’t produce a good outcome.

I don’t know of a good system, I have suggested one before involving allowing voters to send in ballots, making the candidates anonymous except for their score distributions, and then having the electorate vote on which candidate to select according to those score distributions only. I actually do think this would be a better system than straight up majoritarianism. Unfortunately it requires more effort on the part of the electorate.

@jack-waugh this I’m not sure about. It seems like a multi-winner system, in fact the proponents don’t seem to be advertising it as a single winner method, probably because it suffers from vote splitting.

It seems more like a polling method to assess the relative importance of issues voters consider, but even then it seems like those issues on the poll need to be mostly mutually exclusive, or else vote splitting will take effect. And once the options are mutually exclusive, it seems to draw focus on hedging bets about what others are likely to agree upon rather than on indicating true individual preferences, although those true individual preferences might show through if the “survey responses” (ballots) rather than the QV results alone are investigated.

I think it’s probably too arbitrary and also almost surely doesn’t make do on its promise.

Hi everybody, I wanted to revisit this topic and open up a discussion about quadratic voting. This recently came up at a meeting I attended, and my initial reaction was that it suffers from vote splitting, and that diminishing returns could be incorporated into a scoring system without introducing vote splitting. What are your thoughts about this method?

@isocratia hmmm I still would like to see an example of the difference. Like I said I think your method is sufficient but I’m not sold yet on the necessary part. It might not matter anyway since sufficiency is by definition good enough! But I’m just curious.

@isocratia yes it is sufficient to serve that function, my question is about whether the second phase is necessary to induce the same functionality. It seems like one could impose an approval threshold to remove undesirable candidates, and then proceed from there with a proportional approval method over the remaining candidates, requiring only a single approval indication. Is there something wrong with this?

@isocratia yes I understand the definition of the method you described. But what I mean is, what does the second phase and the two-phase-approval ballot introduce that could not be encoded with just the one phase and an ordinary approval ballot?

@isocratia does there need to be more than one phase? Why not have a single phase and remove candidates without sufficient support before a restricted proportional approval?

@sarawolk yes more or less a thought experiment, trying to address some dissonance between the possibility of a Condorcet winner having low support and a support (approval) winner being different from the Condorcet winner even when one exists.

In this case, I mean that a candidate is either supported or not supported by a voter according to the support cutoff of their ballot. I’m using the word “support” rather than “approval,” because I don’t think approval is an appropriate word philosophically (or mathematically). The positive emotional connotation of “approve” is all that bothers me. “Support” seems more emotionally neutral and has a mathematical meaning that aligns well with what is happening in the system, for example, “the support of a distribution.”

https://en.m.wikipedia.org/wiki/Support_(mathematics)

The quantity of support of a candidate is simply the number of voters who formally support that candidate on their ballot.

Here is another attempt at a modification. In sequence, if there is a Condorcet loser, they are eliminated. If there is no Condorcet loser, a candidate with the least quantity of support is eliminated, with ties broken by rank runoff if possible. Repeat until one candidate remains.

@sarawolk I do understand what you mean, the issue being that on a ballot, candidates may not be lined up in order. One could indicate the ranking position at which support begins. Rank order ballots in general are another topic.

I’m not pining for this or any related method, I’m just trying to think of possible “reasonable” ways to combine support and ranking that are distinct from existing methods.

The prospect of combining the two though begs the question of how exactly to do so, and the ones I’ve considered introduce several somewhat complicated tactical dilemmas, so I’m not sure it’s any kind of promising direction.

@paretoman I’m actually not sure I understand precisely what you mean. Could you elaborate more with a small example?

@psp_andrew-s said in **INTRODUCING** 2-Choice Voting (2CV) - An Improved Iteration on RCV and STAR:

In fact, any system that forces voters to make any kind of explicit preference decision will incur vote splitting.

Andrew, this doesn't make sense. Ranked pairs operates solely upon explicit preference decisions in the form of a rank ordering of candidates, and it satisfies independence of clones, meaning that there is no vote splitting at all.

We can have a discussion as to what "desirable" means, but for our purposes it means that the winning candidate had a significant amount of 1st choice preference among the voting population, as well as acceptance/preference from among 51% of the entire voting population.

By your criterion of desirability, choose-one is sufficient. You do see that, right?

A better voting method does not need to completely eliminate vote splitting... That's not an issue as long as the systems sufficiently reduces the IMPACT of vote splitting, which 2CV does to negligible levels.

Again, I have given an explicit example where 2CV enables minority rule due to vote splitting. As I repeat, if you instantiate my example as described, including varied preference profiles rather than a monotone one-dimensional spectrum, you will see what is in fact unnecessary to see, since I already proved it mathematically: 2CV enables minority rule due to vote splitting. That certainly is not, as you say, reducing the impact of vote splitting to negligible levels.