Best posts made by cfrank

I think there are many of us here who prefer some voting system or another over approval voting. I also think there is room for improvement. However, approval voting has a huge advantage in its simplicity and potential for integration into existing infrastructure. This is totally besides the comparisons to make in terms of game theoretical stability with Condorcet methods and expressivity with Score or others.

My thought is that, if we are really going to make progress by consolidating our support behind a single voting system, then realistically, Approval voting fits the bill. That isn’t to say that it should be the final destination for voting reform, but it would absolutely be a major step forward. While IRV is something of a tokenism, Approval would be an actual game changer.

Any thoughts about this are welcome.

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.

@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.

@k98kurz I don’t think there should be any uncertainty in the default for a voter’s ballot.

@democrates I meant a Condorcet winner only among the front runners (for example, the candidates with the top K scores, here we are taking K=2). If there is no Condorcet winner among them, then we can choose the top scoring candidate.

In your case, if two candidates have the same second-greatest score, and the three front runners form a Condorcet cycle, then you can use the scores to break the tie. If this was used, then Jill Stein would have won the election.

That isn’t “the correct” solution (there is no such thing), but it is somewhat less arbitrary than flipping a coin or operating by alphabetical order, neither of which has anything to do with relevant information that is readily available on the ballots.

If we were being engineers about choosing a high quality candidate to win the election, we could even compute the distribution of scores, take the candidates whose scores exceed some elbow point, and find the Condorcet winner among those candidates with the top scoring candidate as the backup if no Condorcet winner exists. That’s basically a generalization of STAR with a dynamic front-runner selection method.

There are other ways to proceed. For example, we could remove Condorcet losers, then try to find the Condorcet winner of all remaining candidates, iteratively eliminating the lowest scoring candidate until a Condorcet winner emerges.

@lime the point of this post isn’t to argue that approval voting is superior to other methods or that modifications wouldn’t improve approval voting, it’s to point out that despite other methods being potentially superior, standard approval voting is probably the most realistic target for near future steps toward substantially reformed voting.

Unfortunately, more choices does mean the system is more complicated. You can observe that the addition of even a very simple, marginal modification as you suggest already raises questions. Every question about a method is an opportunity for distrust to be exploited, even if the method is ultimately better. Plurality is terrible, but almost nobody had questions about it, and that’s why it’s stuck around for so long. Do you see what I mean? I may be a bit jaded, but I’m hoping to be realistic.

I don’t mean to be a downer, but my point is a bit sad: in terms of what people would prefer, such as more choices or buttons, what we have to deal with is exactly the fact that people are having a hard time getting what they prefer. The political status quo is strongly opposed to voting reform, it will have to relinquish substantial power and accountability to the people under an effective voting system. There’s a reason only flawed tokenisms like IRV have passed through legislature in recent times. In fact, there is a history of voting reforms being enacted and then reversed.

@toby-pereira yes you’re right, it was just a thought that occurred to me when I was thinking about how to discourage bullet approvals, but it has irreconcilable flaws that are now apparent.

@wolftune this is a well-known Condorcet method due in spirit to Tideman and called “Bottom N Runoff” where N=2 (hence “Bottom Two Runoff,” I.e. BTR or B2R). Generally speaking, these methods use some kind of absolute criterion (like least number of first place votes, lowest score, lowest approval, etc.) to decide which “bottom” candidates to subject to an elimination round, eliminates a Condorcet loser among them, and iterates until the desired number of winners remain. You are right, they’re pretty good methods. I like them.

@k98kurz mirroring @Lime, I think any advantage conferred to one candidate over any other in an election should be granted on an opt in basis. A voter shouldn’t have to opt out from conferring an advantage to a candidate.

@sarawolk you mean for us to use RCV instead of IRV? What do we call non-IRV ranked choice voting methods? I get that the onus is on us to make the alteration, but it’s actually both strange and quite annoying that IRV has presumptuously taken that title, as if other ranked choice voting methods don’t exist.

@toby-pereira yes this place seems to have surges of activity punctuated by somewhat lengthy periods of silence. I actually think that may be indicative that we have generally come to some (not fully comprehensive) tacit agreements—or what Tideman would call a “pseudo-consensus”—through our past more active discussions, which may be a good thing. Or maybe it’s indicative that many of us have gotten even more disillusioned with the abysmal state of public education in the theory and politics of voting. Some of both probably.

I also think that most people who are members here have historically focused on single winner methods, but if my intuition is accurate (and I may be way off and significantly biased by my own trajectory of thought), it seems like we may have converged on a recognition that PR systems are probably just all around a more promising means of achieving a democratic system of adequate quality.

We have had ongoing parallel discussions about PR systems here, but it may not be as active as on other forums. Again, that may not be a bad thing, as often in this area I find that much active discussion is driven by individuals with pet ideas (I am guilty of this). I definitely encourage engagement across a variety of forums, hopefully there is cross-talk between members on this site and other sites like Reddit. But this site I think tends to lean toward the conservative/skeptical side (not as in “right wing” in terms of the politics, but rather moderate, hopefully my meaning is clear) of the voting theory conversation, which—again in my opinion—is probably because most of our community is quite fairly educated in the area.

In my opinion that’s a good thing, because we need both kinds of discussions going on—a combination of constructive skepticism/criticism and supportive engagement/dialogue. You may like to share links to interesting discussions you are having on other forums, that might engage more of our community.

@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.

@democrates what should happen is that a Condorcet winner should be identified among the frontrunners if one exists. If one doesn’t exist, who knows.

@rob you're absolutely right, there needs to be a third dimension which is vertical to indicate distance from all three qualities, which perhaps should be in a cube as you depict or perhaps a tetrahedron with some indication of depth.

@k98kurz the qualitative experience of a voter has only little to do with the tactics they will employ to get what they want most. We also have to consider what can be easily implemented. While I don’t disagree with you about the suggestion that certain improvements could be made, I do believe (in agreement now with @SaraWolk) that this kind of argument is actually counterproductive to getting voting reform off the ground in the current phase. Adjustments can be made later. Right now we need to get something decent through to replace choose one voting, and that should be urgent priority #1. I strongly believe that the best way we can do that is by pushing with a concerted effort for basic, ordinary approval voting. My opinion is that we need to shift away from the “anything other than choose one” attitude and toward a specific replacement, and my estimation is that approval voting—while definitely not perfect—is the least contentiously agreed upon improvement.

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!

@toby-pereira I totally agree with you here. And a point to supplement or maybe just reiterate your stance on “benevolent dictators,” there’s a definite survivorship bias there. The business dictators who fail don’t show up in the news, while the ones who succeed are often lauded as geniuses without due regard for the role of pure luck or factors totally unrelated to their supposed acumen. The same goes for stock market investors—many who come out on top end up believing they have a special intuition to “outsmart” the market, but when compared with randomly generated portfolios, their inclinations usually fare no better, and often do worse (due to their relative lack of diversity, they are not as robust against market volatility).

So basically, when uncertainty is involved, failure doesn’t always indicate a poor strategy, not any more than success indicates a good one. This reduces my confidence that business dictatorships actually tend to promote the success of a company.

@bmjacobs my intuition is that it will take a lot of education to convince the mainstream public that nondeterminism is a viable solution to certain voting theoretical problems. Putting that aside, what would your position be regarding auditing and transparency for a nondeterministic system, and whether this kind of system could be feasibly implemented without worries about rigging?

@robla thank you! I agree that the 3 meta-criteria are too vague, that’s a part of why I’m trying to map out the space of voting systems in a methodical way to see if any patterns emerge that might inform or conform to my vague intuitions. So far it seems like some of the obvious patterns have emerged, such as ballot type (with the possible exception of approval, which has mildly controversial inputs in the chart due to questionable assumptions).

@k98kurz there are a few points to make about the Republic of Venice as it might compare to the situation we face now.

First, based on what I’m reading, it was mostly a hereditary, aristocratic oligarchy without broad-based democratic participation. It did not have a written constitution, or a formal bill of rights. Second, it was not a confederation of sovereign states but a centralized unitary government. Third, it had a much smaller and more homogenous population (in terms of culture) than the United States, which was spread out over far less land and simultaneously had a lower population density.

These things make it much easier for the small elite political class to settle affairs in whatever way they might agree upon amongst themselves, including using a chosen voting system. The political elite class was also much more highly educated than the rest of the population. When it comes to voting systems for us, there are strict laws and regulations that need to be satisfied, in addition to the need for support from a much more numerous and heterogeneous population, many of whom are relatively uneducated or misinformed, compounded with deliberate efforts against technical voting reform by our own political elite (and associated media). This is why I’m advocating for a simple reform, like approval voting. I’m also considering what @SaraWolk suggests, namely that another method like RCV (IRV) might be a more practical conduit for change, even though it is significantly less ideal.