A voting theory primer for rationalists

post by Jameson Quinn (jameson-quinn) · 2018-04-12T15:15:23.823Z · score: 226 (70 votes) · LW · GW · 67 comments

Contents

  What is voting theory?
  Why is voting theory important for rationalists?
  What are the branches of voting theory?
  What are the basics of single-winner voting theory?
    TL; DR?
  What are the basics of multi-winner voting theory?
  Anticlimactic sign-off
None
67 comments

What is voting theory?

Voting theory, also called social choice theory, is the study of the design and evaulation of democratic voting methods (that's the activists' word; game theorists call them "voting mechanisms", engineers call them "electoral algorithms", and political scientists say "electoral formulas"). In other words, for a given list of candidates and voters, a voting method specifies a set of valid ways to fill out a ballot, and, given a valid ballot from each voter, produces an outcome.

(An "electoral system" includes a voting method, but also other implementation details, such as how the candidates and voters are validated, how often elections happen and for what offices, etc. "Voting system" is an ambiguous term that can refer to a full electoral system, just to the voting method, or even to the machinery for counting votes.)

Most voting theory limits itself to studying "democratic" voting methods. That typically has both empirical and normative implications. Empirically, "democratic" means:

In order to be considered "democratic", voting methods generally should meet various normative criteria as well. There are many possible such criteria, and on many of them theorists do not agree; but in general they do agree on this minimal set:

Why is voting theory important for rationalists?

First off, because democratic processes in the real world are important loci of power. That means that it's useful to understand the dynamics of the voting methods used in such real-world elections.

Second, because these real-world democratic processes have all been created and/or evolved in the past, and so there are likely to be opportunities to replace, reform, or add to them in the future. If you want to make political change of any kind over a medium-to-long time horizon, these systemic reforms should probably be part of your agenda. The fact is that FPTP, the voting method we use in most of the English-speaking world, is absolutely horrible, and there is reason to believe that reforming it would substantially (though not of course completely) alleviate much political dysfunction and suffering.

Third, because understanding social choice theory helps clarify ideas about how it's possible and/or desirable to resolve value disputes between multiple agents. For instance, if you believe that superintelligences should perform a "values handshake" when meeting, replacing each of their individual value functions by some common one so as to avoid the dead weight loss of a conflict, then social choice theory suggests both questions and answers about what that might look like. (Note that the ethical and practical importance of such considerations is not at all limited to "post-singularity" examples like that one.)

In fact, on that third point: my own ideas of ethics and of fun theory are deeply informed by my decades of interest in voting theory. To simplify into a few words my complex thoughts on this, I believe that voting theory elucidates "ethical incompleteness" (that is, that it's possible to put world-states into ethical preference order partially but not fully) and that this incompleteness is a good thing because it leaves room for fun even in an ethically unsurpassed world.

What are the branches of voting theory?

Generally, you can divide voting methods up into "single-winner" and "multi-winner". Single-winner methods are useful for electing offices like president, governor, and mayor. Multi-winner methods are useful for dividing up some finite, but to some extent divisible, resource, such as voting power in a legislature, between various options. Multi-winner methods can be further subdivided into seat-based (where a set of similar "seats" are assigned one winner each) or weighted (where each candidate can be given a different fraction of the voting power).

What are the basics of single-winner voting theory?

(Note: Some readers may wish to skip to the summary below, or to read the later section on multi-winner theory and proportional representation first. Either is valid.)

Some of the earliest known work in voting theory was by Ramon Llull before his death in 1315, but most of that was lost until recently. Perhaps a better place to start would be in the French Academy in the late 1700s; this allows us to couch it as a debate (American Chopper meme?) between Jean-Charles de Borda and Nicolas de Condorcet.

Condorcet: "Plurality (or 'FPTP', for First Past the Post) elections, where each voter votes for just one candidate and the candidate with the most votes wins, are often spoiled by vote-splitting."
Borda: "Better to have voters rank candidates, give candidates points for favorable rankings, and choose a winner based on points." (Borda Count)
Condorcet: "Ranking candidates, rather than voting for just one, is good. But your point system is subject to strategy. Everyone will rate some candidate they believe can't win in second place, to avoid giving points to a serious rival to their favorite. So somebody could win precisely because nobody takes them seriously!"
Borda: "My method is made for honest men!"
Condorcet: "Instead, you should use the rankings to see who would have a majority in every possible pairwise contest. If somebody wins all such contests, obviously they should be the overall winner."

In my view, Borda was the clear loser there. And most voting theorists today agree with me. The one exception is the mathematician Donald Saari, enamored with the mathematical symmetry of the Borda count. This is totally worth mentioning because his last name is a great source of puns.

But Condorcet soon realized there was a problem with his proposal too: it's possible for A to beat B pairwise, and B to beat C, while C still beats A. That is, pairwise victories can be cyclical, not transitive. Naturally speaking, this is rare; but if there's a decision between A and B, the voters who favor B might have the power to artificially create a "poison pill" amendment C which can beat A and then lose to B.

How would a Condorcet cycle occur? Imagine the following election:

1: A>B>C

1: B>C>A

1: C>A>B

(This notation means that there's 1 voter of each of three types, and that the first voter prefers A over B over C.) In this election, A beats B by 2 to 1, and similarly B beats C and C beats A.

Fast-forward to 1950, when theorists at the RAND corporation were inventing game theory in order to reason about the possibility of nuclear war. One such scientist, Kenneth Arrow, proved that the problem that Condorcet (and Llull) had seen was in fact a fundamental issue with any ranked voting method. He posed 3 basic "fairness criteria" and showed that no ranked method can meet all of them:

Arrow's result was important in and of itself; intuitively, most people might have guessed that a ranked voting method could be fair in all those ways. But even more important than the specific result was the idea of an impossibility proof for voting.

Using this idea, it wasn't long until Gibbard and Satterthwaite independently came up with a follow-up theorem, showing that no voting system (ranked or otherwise) could possibly avoid creating strategic incentives for some voters in some situations. That is to say, there is no non-dictatorial voting system for more than two possible outcomes and more than two voters in which every voter has a single "honest" ballot that depends only on their own feelings about the candidates, such that they can't sometimes get a better result by casting a ballot that isn't their "honest" one.

There's another way that Arrow's theorem was an important foundation, particularly for rationalists. He was explicitly thinking about voting methods not just as real-world ways of electing politicians, but as theoretical possibilities for reconciling values. In this more philosophical sense, Arrow's theorem says something depressing about morality: if morality is to be based on (potentially revealed) preferences rather than interpersonal comparison of (subjective) utilities, it cannot simply be a democratic matter; "the greatest good for the greatest number" doesn't work without inherently-subjective comparisons of goodness. Amartya Sen continued exploring the philosophical implications of voting theory, showing that the idea of "private autonomy" is incompatible with Pareto efficiency.

Now, in discussing Arrow's theorem, I've said several times that it only applies to "ranked" voting systems. What does that mean? "Ranked" (also sometimes termed "ordinal" or "preferential") systems are those where valid ballots consist of nothing besides a transitive preferential ordering of the candidates (partial or complete). That is, you can say that you prefer A over B or B over A (or in some cases, that you like both of them equally), but you cannot say how strong each preference is, or provide other information that's used to choose a winner. In Arrow's view, the voting method is then responsible for ordering the candidates, picking not just a winner but a second place etc. Since neutrality wasn't one of Arrow's criteria, ties can be broken arbitrarily.

This excludes an important class of voting methods from consideration: those I'd call rated (or graded or evaluational), where you as a voter can give information about strength of preference. Arrow consciously excluded those methods because he believed (as Gibbard and Satterthwaite later confirmed) that they'd inevitably be subject to strategic voting. But since ranked voting systems are also inevitably subject to strategy, that isn't necessarily a good reason. In any case, Arrow's choice to ignore such systems set a trend; it wasn't until approval voting was reinvented around 1980 and score voting around 2000 that rated methods came into their own. Personally, for reasons I'll explain further below, I tend to prefer rated systems over purely ranked ones, so I think that Arrow's initial neglect of ranked methods got the field off on a bit of a wrong foot.

And there's another way I feel that Arrow set us off in the wrong direction. His idea of reasoning axiomatically about voting methods was brilliant, but ultimately, I think the field has been too focused on this axiomatic "Arrovian" paradigm, where the entire goal is to prove certain criteria can be met by some specific voting method, or cannot be met by any method. Since it's impossible to meet all desirable criteria in all cases, I'd rather look at things in a more probabilistic and quantitative way: how often and how badly does a given system fail desirable criteria.

The person I consider to be the founder of this latter, "statistical" paradigm for evaluating voting methods is Warren Smith. Now, where Kenneth Arrow won the Nobel Prize, Warren Smith has to my knowledge never managed to publish a paper in a peer-reviewed journal. He's a smart and creative mathematician, but... let's just say, not exemplary for his social graces. In particular, he's not reluctant to opine in varied fields of politics where he lacks obvious credentials. So there's plenty in the academic world who'd just dismiss him as a crackpot, if they are even aware of his existence. This is unfortunate, because his work on voting theory is groundbreaking.

In his 2000 paper on "Range Voting" (what we'd now call Score Voting), he performed systematic utilitarian Monte-Carlo evaluation of a wide range of voting systems under a wide range of assumptions about how voters vote. In other words, in each of his simulations, he assumed certain numbers of candidates and of voters, as well as a statistical model for voter utilities and a strategy model for voters. Using the statistical model, he assigned each virtual voter a utility for each candidate; using the strategy model, he turned those utilities into a ballot in each voting method; and then he measured the total utility of the winning candidate, as compared to that of the highest-total-utility candidate in the race. Nowadays the name for the difference between these numbers, scaled so that the latter would be 100% and the average randomly-selected candidate would be 0%, is "Voter Satisfaction Efficiency" (VSE).

Smith wasn't the first to do something like this. But he was certainly the first to do it so systematically, across various voting methods, utility models, and strategic models. Because he did such a sensitivity analysis across utility and strategic models, he was able to see which voting methods consistently outperformed others, almost regardless of the specifics of the models he used. In particular, score voting, in which each voter gives each candidate a numerical score from a certain range (say, 0 to 100) and the highest total score wins, was almost always on top, while FPTP was almost always near the bottom.

More recently, I've done further work on VSE, using more-realistic voter and strategy models than what Smith had, and adding a variety of "media" models to allow varying the information on which the virtual voters base their strategizing. While this work confirmed many of Smith's results — for instance, I still consistently find that FPTP is lower than IRV is lower than approval is lower than score — it has unseated score voting as the undisputed highest-VSE method. Other methods with better strategy resistance can end up doing better than score.

Of course, something else happened in the year 2000 that was important to the field of single-winner voting theory: the Bush-Gore election, in which Bush won the state of Florida and thus the presidency of the USA by a microscopic margin of about 500 votes. Along with the many "electoral system" irregularities in the Florida election (a mass purge of the voter rolls of those with the same name as known felons, a confusing ballot design in Palm Beach, antiquated punch-card ballots with difficult-to-interpret "hanging chads", etc.) was one important "voting method" irregularity: the fact that Ralph Nader, a candidate whom most considered to be ideologically closer to Gore than to Bush, got far more votes than the margin between the two, leading many to argue that under almost any alternative voting method, Gore would have won. This, understandably, increased many people's interest in voting theory and voting reform. Like Smith, many other amateurs began to make worthwhile progress in various ways, progress which was often not well covered in the academic literature.

In the years since, substantial progress has been made. But we activists for voting reform still haven't managed to use our common hatred for FPTP to unite behind a common proposal. (The irony that our expertise in methods for reconciling different priorities into a common purpose hasn't let us do so in our own field is not lost on us.)

In my opinion, aside from the utilitarian perspective offered by VSE, the key to evaluating voting methods is an understanding of strategic voting; this is what I'd call the "mechanism design" perspective. I'd say that there are 5 common "anti-patterns" that voting methods can fall into; either where voting strategy can lead to pathological results, or vice versa. I'd pose them as a series of 5 increasingly-difficult hurdles for a voting method to pass. Because the earlier hurdles deal with situations that are more common or more serious, I'd say that if a method trips on an earlier hurdle, it doesn't much matter that it could have passed a later hurdle. Here they are:

(0. Dark Horse. As in Condorcet's takedown of Borda above, this is where a candidate wins precisely because nobody expects them to. Very bad, but not a serious problem in most voting methods, except for the Borda Count.)
1. Vote-splitting / "spoiled" elections. Adding a minor candidate causes a similar major candidate to lose. Very bad because it leads to rampant strategic dishonesty and in extreme cases 2-party dominance, as in Duverger's Law. Problematic in FPTP, resolved by most other voting methods.
2. Center squeeze. A centrist candidate is eliminated because they have lost first-choice support to rivals on both sides, so that one of the rivals wins, even though the centrist could have beaten either one of them in a one-on-one (pairwise) election. Though the direct consequences of this pathology are much less severe than those of vote-splitting, the indirect consequences of voters strategizing to avoid the problem would be exactly the same: self-perpetuating two-party dominance. This problem is related to failures of the "favorite betrayal criterion" (FBC). Problematic in IRV, resolved by most other methods.
3. Chicken dilemma (aka Burr dilemma, for Hamilton fans). Two similar candidates must combine strength in order to beat a third rival. But whichever of the two cooperates less will be the winner, leading to a game of "chicken" where both can end up losing to the rival. This problem is related to failures of the "later-no-harm" (LNH) criterion. Because LNH is incompatible with FBC, it is impossible to completely avoid the chicken dilemma without creating a center squeeze vulnerability, but systems like STAR voting or 3-2-1 minimize it.
4. Condorcet cycle. As above, a situation where, with honest votes, A beats B beats C beats A. There is no "correct" winner in this case, and so no voting method can really do anything to avoid getting a "wrong" winner. Luckily, in natural elections (that is, where bad actors are not able to create artificial Condorcet cycles by strategically engineering "poison pills"), this probably happens less than 5% of the time.

Note that there's a general pattern in the pathologies above: the outcome of honest voting and that of strategic voting are in some sense polar opposites. For instance, under honest voting, vote-splitting destabilizes major parties; but under strategic voting, it makes their status unassailable. This is a common occurrence in voting theory. And it's a reason that naive attempts to "fix" a problem in a voting system by adding rules can actually make the original problem worse.

(I wrote a separate article with further discussion of these pathologies [LW · GW])

Here are a few of the various single-winner voting systems people favor, and a few (biased) words about the groups that favor them:

FPTP (aka plurality voting, or choose-one single-winner): Universally reviled by voting theorists, this is still favored by various groups who like the status quo in countries like the US, Canada, and the UK. In particular, incumbent politicians and lobbyists tend to be at best skeptical and at worst outright reactionary in response to reformers.

IRV (Instant runoff voting), aka Alternative Vote or RCV (Ranked Choice Voting... I hate that name, which deliberately appropriates the entire "ranked" category for this one specific method): This is a ranked system where to start out with, only first-choice votes are tallied. To find the winner, you successively eliminate the last-place candidate, transferring those votes to their next surviving preference (if any), until some candidate has a majority of the votes remaining. It's supported by FairVote, the largest electoral reform nonprofit in the US, which grew out of the movement for STV proportional representation (see the multi-winner section below for more details). IRV supporters tend to think that discussing its theoretical characteristics is a waste of time, since it's so obvious that FPTP is bad and since IRV is the reform proposal with by far the longest track record and most well-developed movement behind it. Insofar as they do consider theory, they favor the "later-no-harm" criterion, and prefer to ignore things like the favorite betrayal criterion, summability, or spoiled ballots. They also don't talk about the failed Alternative Vote referendum in the UK.

Approval voting: This is the system where voters can approve (or not) each candidate, and the candidate approved by the most voters wins. Because of its simplicity, it's something of a "Schelling point" for reformers of various stripes; that is, a natural point of agreement as an initial reform for those who don't agree on which method would be an ideal end state. This method was used in Greek elections from about 1860-1920, but was not "invented" as a subject of voting theory until the late 70s by Brams and Fishburn. It can be seen as a simplistic special case of many other voting methods, in particular score voting, so it does well on Warren Smith's utilitarian measures, and fans of his work tend to support it. This is the system promoted by the Center for Election Science (electology.org), a voting reform nonprofit that was founded in 2012 by people frustrated with FairVote's anti-voting-theory tendencies. (Full disclosure: I'm on the board of the CES, which is growing substantially this year due to a significant grant by the Open Philanthropy Project. Thanks!)

Condorcet methods: These are methods that are guaranteed to elect a pairwise beats-all winner (Condorcet winner) if one exists. Supported by people like Erik Maskin (a Nobel prize winner in economics here at Harvard; brilliant, but seemingly out of touch with the non-academic work on voting methods), and Markus Schulze (a capable self-promoter who invented a specific Condorcet method and has gotten groups like Debian to use it in their internal voting). In my view, these methods give good outcomes, but the complications of resolving spoil their theoretical cleanness, while the difficulty of reading a matrix makes presenting results in an easy-to-grasp form basically impossible. So I personally wouldn't recommend these methods for real-world adoption in most cases. Recent work in "improved" Condorcet methods has showed that these methods can be made good at avoiding the chicken dilemma, but I would hate to try to explain that work to a layperson.

Bucklin methods (aka median-based methods; especially, Majority Judgment): Based on choosing a winner with the highest median rating, just as score voting is based on choosing one with the highest average rating. Because medians are more robust to outliers than averages, median methods are more robust to strategy than score. Supported by French researchers Balinski and Laraki, these methods have an interesting history in the progressive-era USA. Their VSE is not outstanding though; better than IRV, plurality, and Borda, but not as good as most other methods.

Delegation-based methods, especially SODA (simple optionally-delegated approval): It turns out that this kind of method can actually do the impossible and "avoid the Gibbard-Satterthwaite theorem in practice". The key words there are "in practice" — the proof relies on a domain restriction, in which voters honest preferences all agree with their favorite candidate, and these preference orders are non-cyclical, and voters mutually know each other to be rational. Still, this is the only voting system I know of that's 100% strategy free (including chicken dilemma) in even such a limited domain. (The proof of this is based on complicated arguments about convexity in high-dimensional space, so Saari, it doesn't fit here.) Due to its complexity, this is probably not a practical proposal, though.

Rated runoff methods (in particular STAR and 3-2-1): These are methods where rated ballots are used to reduce the field to two candidates, who are then compared pairwise using those same ballots. They combine the VSE advantages of score or approval with extra resistance to the chicken dilemma. These are currently my own favorites as ultimate goals for practical reform, though I still support approval as the first step.

Quadratic voting: Unlike all the methods above, this is based on the universal solvent of mechanism design: money (or other finite transferrable resources). Voters can buy votes, and the cost for n votes is proportional to n². This has some excellent characteristics with honest voters, and so I've seen that various rationalists think it's a good idea; but in my opinion, it's got irresolvable problems with coordinated strategies. I realize that there are responses to these objections, but as far as I can tell every problem you fix with this idea leads to two more.

TL; DR?

What are the basics of multi-winner voting theory?

Multi-winner voting theory originated under parliamentary systems, where theorists wanted a system to guarantee that seats in a legislature would be awarded in proportion to votes. This is known as proportional representation (PR, prop-rep, or #PropRep). Early theorists include Henry Droop and Charles Dodgson (Lewis Carroll). We should also recognize Thomas Jefferson and Daniel Webster's work on the related problem of apportioning congressional seats across states.

Because there are a number of seats to allocate, it's generally easier to get a good answer to this problem than in the case of single-winner voting. It's especially easy in the case where we're allowed to give winners different voting weights; in that case, a simple chain of delegated voting weight guarantees perfect proportionality. (This idea has been known by many names: Dodgson's method, asset voting, delegated proxy, liquid democracy, etc. There are still some details to work out if there is to be a lower bound on final voting weight, but generally it's not hard to find ways to resolve those.)

When seats are constrained to be equally-weighted, there is inevitably an element of rounding error in proportionality. Generally, for each kind of method, there are two main versions: those that tend to round towards smaller parties (Sainte-Laguë, Webster, Hare, etc.) and those that tend to round towards larger ones (D'Hondt, Jefferson, Droop, etc.).

Most abstract proportional voting methods can be considered as greedy methods to optimize some outcome measure. Non-greedy methods exist, but algorithms for finding non-greedy optima are often considered too complex for use in public elections. (I believe that these problems are NP-complete in many cases, but fast algorithms to find provably-optimal outcomes in all practical cases usually exist. But most people don't want to trust voting to algorithms that nobody they know actually understands.)

Basically, the outcome measures being implicitly optimized are either "least remainder" (as in STV, single transferable vote), or "least squares" (not used by any real-world system, but proposed in Sweden in the 1890s by Thiele and Phragmen). STV's greedy algorithm is based on elimination, which can lead to problems, as with IRV's center-squeeze. A better solution, akin to Bucklin/median methods in the single-winner case, is BTV (Bucklin transferable vote). But the difference is probably not a big enough deal to overcome STV's advantage in terms of real-world track record.

Both STV and BTV are methods that rely on reweighting ballots when they help elect a winner. There are various reweighting formulas that each lead to proportionality in the case of pure partisan voting. This leads to an explosion of possible voting methods, all theoretically reasonable.

Because the theoretical pros and cons of various multi-winner methods are much smaller than those of single-winner ones, the debate tends to focus on practical aspects that are important politically but that a mathematician would consider trivial or ad hoc. Among these are:

Prop-rep methods would solve the problem of gerrymandering in the US. I believe that PLACE is the most viable proposal in that regard: maintains the locality and ballot simplicity of the current system, is relatively non-disruptive to incumbents, and maximizes breadth of voter choice to help increase turnout.

Oh, I should also probably mention that I was the main designer, in collaboration with dozens of commenters on the website Making Light, of the proportional voting method E Pluribus Hugo, which is now used by the Hugo Awards to minimize the impact and incentives of bloc voting in the nominations phase.

Anticlimactic sign-off

OK, that's a long article, but it does a better job of brain-dumping my >20 years of interest in this topic than anything I've ever written. On the subject of single-winner methods, I'll be putting out a playable exploration version of all of this sometime this summer, based off the work of the invaluable nicky case (as well as other collaborators).

I've now added a third article on this topic [LW · GW], in which I included a paragraph at the end asking people to contact me if they're interested in activism on this. I believe this is a viable target for effective altruism.

67 comments

Comments sorted by top scores.

comment by Jameson Quinn (jameson-quinn) · 2018-04-12T18:32:06.428Z · score: 37 (11 votes) · LW · GW

I haven't mentioned futarchy ("markets for predictions, votes for values") at all here. Futarchy, of course, would not be classed as a voting method in my typology; it's something bigger than even than my concept of a voting system. I think that the main useful thing I can say about futarch is: if you're going to spend energy on it, you should spend some energy on understanding lower-level voting methods too.

ETA: I guess I think I can expand on that a bit. The issue is that when you embed one system inside another one, there's some inevitable bleed-over in terms of incentives. For this meta-reason, as well as for the simple reason of direct applicability, one lesson from voting theory that I think would apply to futarchy is that "patching a problem can make it worse, because strategic outcomes can be the 'opposite' of unstrategic ones." That's an intuition that for me was hard-won, and I wouldn't expect it to be easy for you to learn it just by hearing it. If that's true and you still want to learn it, spend some time thinking about honest and strategic outcomes in various voting methods in the five levels of pathology I mentioned above. The playable exploration I mention at the end will substantially focus on these ideas, in a way I hope will be visually and interactively easy to digest.

comment by ryan_b · 2018-04-12T16:18:26.168Z · score: 31 (10 votes) · LW · GW

Exciting stuff! It would not shock me in the least for this to be a common point-of-reference for various rationalist experiments (i.e. houses, startups, etc). I have a bunch of questions:

1) Do these voting systems have anything to say about voting for referendums, or is the literature constrained to candidates? Is there any sense in which a batch of competing referendums would not be treated the same as single-winner races?

2) You mention the practical concerns of laypeople being able to grasp the process and counting the votes a few times - is there a body of research that focuses on these elements, or is this work being done by the Center for Election Science?

3) You mention the use of a Condorcet method being used by Debian in internal voting - is there a sense of which methods are suitable for use in organizational voting, as distinct from political voting, ie some of them are unusually sensitive to scale? Further, how is deployment in an organization weighed as evidence regarding deployment in elections?

4) Can you recommend a source which discusses voting theory from the perspective of information aggregation, in the same way as has been done for markets?

comment by Jameson Quinn (jameson-quinn) · 2018-04-12T16:32:50.715Z · score: 11 (4 votes) · LW · GW

1) In most cases, the voting method options when voting on competing (non-sapient) plans are the same as those for candidates. In fact, as I said, Arrow's theorem and Sen's theorem were originally posed as being about voting over world-states rather than candidates. And approval voting, with a 50% threshold, has been used various times in practice for voting on incompatible ballot initiatives.

The exception to this rule is when voting methods use delegation in some way (such as "liquid democracy", SODA, PLACE, and to a much lesser extent 3-2-1). Obviously, these methods require sapient candidates, or at least some kind of impartial divergence measure over candidates.

2) As I hinted, I think that the academic literature on this tends to focus more on the axiomatic/Arrovian paradigm than it should. I suspect that there is some political science research that relates, but aside from a few simple results on spoiled ballots under IRV (they go up) I'm not familiar with it.

3) Organizations are probably more able to tolerate "complicated" voting methods — especially organizations of "nerds", such as Debian or the Hugo awards. But my intuition in this area is based on anecdotes, not solid research.

4) Hmm... I'll have to think about that one, I'll get back to you.

comment by Said Achmiz (SaidAchmiz) · 2018-04-13T19:11:46.386Z · score: 17 (4 votes) · LW · GW

I might’ve missed this, as I didn’t read some of the sections of this post quite as closely as I could have, but here’s a question which, I think, is critical:

Has there been any research aimed at determining which voting method is easiest to understand (for people who aren’t specialists in the field[1], or, in other words, for the general public)? (And, by extension: how hard is each method to understand? How do they compare, in this regard?)

Comprehensibility by the general public seems to me to be a sine qua non of any voting method we’re to consider for adoption into the political process.

[1] Or, as we might say, “voting theory nerds”.

comment by Douglas_Knight · 2018-04-22T17:09:30.946Z · score: 11 (3 votes) · LW · GW

In particular, one could ask: Do people take advantage of the options in the voting systems that they do have? To what extent do Australians make use of ranked choice? I don't know. It appears to me that most British Labour Party members,† faced with a slate of 5 candidates for PM, restrict their consideration to viable candidates and don't take advantage of their opportunity to express their preferences, even though the party goes out of its way to nominate diverse candidates.

† Labour Party members are a small group, more like activists than American primary voters, who are, in turn, more involved than general election voters. The Party is trying to move in the American direction, but hasn't moved far. The Tories don't have primaries at all.

comment by Jameson Quinn (jameson-quinn) · 2018-04-13T20:10:35.204Z · score: 3 (1 votes) · LW · GW

There has definitely been attention to this question. All of the proposals I support in practice (Approval, 3-2-1, or STAR for single-winner; and PLACE for multi-winner) are among the simpler to vote and to explain.

But most of the research is in the form of proprietary focus groups or polling, so unfortunately there's no good source I can point you to. I'm working to change that.

comment by Said Achmiz (SaidAchmiz) · 2018-04-13T20:12:21.033Z · score: 5 (1 votes) · LW · GW

How does the comprehensibility of these methods compare with that of the system we have now?

comment by Jameson Quinn (jameson-quinn) · 2018-04-16T13:50:57.616Z · score: 10 (3 votes) · LW · GW

I'm assuming that "we" is the USA; and "the system" is FPTP (that is, you're ignoring the electoral college and the system of primaries and redistricting).

Approval is just as easy to understand, and in fact easier to avoid ballot spoilage.

3-2-1 and STAR are both a bit more complicated, but not much; either one can still be distilled down to 9 words.

PLACE is significantly more complicated for vote-counting, but to cast a ballot, it's still just about as simple as FPTP. In fact, if you take into account the fact that you are more free to ignore strategic concerns, it's arguably simpler.

comment by Ben Pace (Benito) · 2018-04-21T10:59:39.437Z · score: 16 (4 votes) · LW · GW

I've curated this post for these reasons:

  • This is an opinionated introduction to a piece of math-based social theory.
  • The two followups on Moloch [LW · GW] and Alignment [LW · GW] also helped flesh out the key intuitions.
  • It's written by someone with a lot of expertise in the field.

My biggest hesitation(s) with curating this:

  • I didn't find it practical (yet). In my head voting theory is still its own disconnected thing from the ways I think about solving social or utilitarian problems in my life.
  • It's quite long.

Overall though the opinionated style of the writing made it much more readable, and I expect to come back here when thinking more about preference aggregation in my own work (on LW). I'm a big fan of people writing down their expertise in a digestible way - thanks for writing these up!

comment by Jameson Quinn (jameson-quinn) · 2018-04-21T17:09:42.017Z · score: 4 (1 votes) · LW · GW

What would I have to do to make this a sequence?

comment by Ben Pace (Benito) · 2018-04-21T17:18:21.460Z · score: 10 (2 votes) · LW · GW

Go to the library [LW · GW] page, scroll down to 'community sequences', and hit the button 'new sequence'. You need an image for the header/icon.

comment by ChristianKl · 2018-04-13T18:21:49.130Z · score: 15 (5 votes) · LW · GW

Most elections aren't big. Most elections are about questions like a random group electing their chairman. It's a lot easier to convince a random group to use a different voting system than to change the way voting is done on a national election.

I think the most likely way to create change in the national way of voting is to first change the way smaller groups run their elections.

Your post doesn't really analyses the desirable features of an electoral system and I think that's a common failure mode for people who think theoretically about voting systems without any practical involvement into implementing them.

Running elections costs time and given that most groups need to elect their chairman every year minimizing the amount of time it takes to make that election is desirable.

The role of an election is not just about finding the optimal candidate but about establishing that the candidate was picked in a trustworthy way. This means that "our tech person runs a server and we trust the results of the voting software" is not a satisfactory strategy. Complex counting rules also make fraud easier.

comment by Jameson Quinn (jameson-quinn) · 2018-04-13T18:47:05.552Z · score: 23 (5 votes) · LW · GW

This is a theory post. I post activism stuff elsewhere.

(Anybody reading this in Somerville, MA who's interested in activism on this, get in touch with me via gmail. Obvious address, both names. Also goes for other parts of US, or for BC, less urgently.)

comment by Qiaochu_Yuan · 2018-04-16T23:53:14.457Z · score: 13 (3 votes) · LW · GW

Thanks for writing this! Very informative.

I saw a paper (which I don't remember enough about to find, unfortunately) in which a bunch of voting theorists got together and voted on the best voting method, using approval voting (I think?), and the winner was approval voting. I wonder if anyone also saw this and saved it so they can tell me how to find it?

comment by Jameson Quinn (jameson-quinn) · 2018-04-17T00:01:54.414Z · score: 29 (7 votes) · LW · GW

http://www.lse.ac.uk/website-archive/newsAndMedia/news/archives/2011/04/VotingSystems.aspx

comment by ryan_b · 2018-04-17T15:02:26.519Z · score: 11 (2 votes) · LW · GW

I'm curious about the question of wasted votes. In the link you provide to explain PLACE, it talks about wasted votes a lot. My understanding is this:

1) Under the loose definition, any vote not for the winning candidate is wasted.

2) Under the strict definition, any vote not needed to win is also wasted.

This is deeply unintuitive to me. Just inferring from the above, this suggests that what should be done is to calculate the least-worst smallest-majority candidate, and then everyone else stays home. The direct implication is that votes are intrinsically worthless, which seems weird. As a term-of-art it seems to be so heavily dependent on FPTP as to be inapplicable elsewhere.

Am I reading too much into it, and it just basically means 'the badness of FPTP'? How prevalent is this concept in distinguishing between voting systems, in your view?

Has it undergone any recent changes, for example as a result of the voting utility calculations when comparing different decision theory agents?

comment by Jameson Quinn (jameson-quinn) · 2018-04-17T16:32:29.768Z · score: 15 (3 votes) · LW · GW

This is a very good question. I have a friend who's working on making a rigorous definition for "wasted votes" that squares with your rough understanding, and she's a smart, professional mathematician; if it were trivial, she'd have solved it in 10 minutes.

You are basically right about your understanding and intuition. In particular, under FPTP, "wasted votes" includes anybody who doesn't support a winner, and some of those who do. But note that in a multi-winner voting method, it's possible to ensure that a supermajority of votes have some say in picking the winner. For instance, if all ballots are full strict rankings, under STV only 1 Droop quota are wasted; for 19 winners, that would be just 5%.

This is an active area of research and I hope to be able to come back to your comment a year or so from now and have a better answer.

(ps. It's PLACE, not PACE.)

comment by ryan_b · 2018-04-18T16:51:28.630Z · score: 5 (1 votes) · LW · GW

Oops, typo. Fixed!

comment by Kaj_Sotala · 2018-04-18T20:52:29.070Z · score: 11 (2 votes) · LW · GW

In principle, I agree with your point that the concept of wasted votes seems pretty incoherent.

In practice, I have frequently felt somewhat bad over having voted for someone in a way which feels like it "wasted" my vote. Despite knowing that this makes no sense.

I'm guessing something-something-tribal-instincts-that-want-to-place-you-in-the-same-coalition-as-the-guys-with-the-most-power-something-something.

comment by ryan_b · 2018-04-18T22:11:17.492Z · score: 6 (2 votes) · LW · GW

So I know this is a common feeling, but I have never felt that way. To provide some intuition for the other way, consider the concept of the popular mandate: when a President or Governor in the United States wins by a large margin, they have extra political capital for driving their agenda.

Importantly this political capital is spent among other elites, so at the very least other elected officials are prone to treat it as significant.

It seems obvious to me that voting is an information-bearing signal, but something must be amiss here because I appear to be in a small minority and without agreement from experts.

comment by Jameson Quinn (jameson-quinn) · 2018-04-12T19:29:28.170Z · score: 11 (4 votes) · LW · GW

I've been moderately hard on IRV, and its supporters, in the above. I want to state here for the record that though IRV is my least-favorite serious* reform proposal, I think that it would solve a substantial fraction of the voting-system dysfunction of FPTP; that if IRV were more of a focus of this essay than it is, there are other decent pro-IRV arguments I could include; and that there are IRV supporters whose intellect and judgement I respect even as I disagree with them on this.

*That excludes Borda. #SorryNotSaari

comment by Luke A Somers · 2018-04-12T16:59:30.901Z · score: 9 (3 votes) · LW · GW

What are the improved Condorcet methods you're thinking of? I do recall seeing that Ranked Pairs and Schulze have very favorable strategy-backfire to strategy-works ratios in simulations, but I don't know what you're thinking of for sure. If those are it, then if you approach it right, Schulze isn't that hard to work through and demonstrate an election result (wikipedia now has an example).

comment by Jameson Quinn (jameson-quinn) · 2018-04-12T17:04:04.610Z · score: 11 (4 votes) · LW · GW

Actually, I was talking about the kind of methods discussed here.

As to Schulze and Ranked Pairs, these two are very similar in philosophy. In terms of criteria compliances and VSE, RP is slightly superior; but Schulze has the advantage of Markus Schulze's energetic promotion.

comment by Luke A Somers · 2018-04-12T17:24:01.758Z · score: 5 (2 votes) · LW · GW

In terms of explaining the result, I think Schulze is much better. You can do that very compactly and with only simple, understandable steps. The best I can see doing with RP is more time-consuming and the steps have potential to be more complicated.

As far as promotion is concerned, I haven't run into it; since it's so similar to RP, I think non-algorithmic factors like I mentioned above begin to be more important.

~~~~

The page you linked there has some undefined terms like u/a (it says it's defined in previous articles, but I don't see a link).

>it certainly doesn’t prevent Beatpath (and other TUC methods) from being a strategic mess, without known strategy,

Isn't that a… good thing? With the fog of reality, strategy looking like 60% stabbing yourself, 30% accomplishing nothing, 10% getting what you want… how is that a bad trait for a system to have?

In particular, as far as strategic messes are concerned, I would definitely feel more pressure to use strategy of equivocation in SICT than in beatpath (Schulze), because it would feel a lot less drastic/scary/risky.

comment by Jameson Quinn (jameson-quinn) · 2018-04-12T17:37:34.265Z · score: 6 (2 votes) · LW · GW

Note that I don't endorse that page I linked to, it's just the best source I could find for definitions of "improved Condorcet" methods.

"U/A" is some strange class of voting scenarios where voters have a clear a priori idea about what is "unacceptable" versus "acceptable" and strategize accordingly. I don't think it's analytically very helpful.

comment by Luke A Somers · 2018-04-12T17:55:45.362Z · score: 6 (3 votes) · LW · GW

I see. I figured U/A meant something like that. I think it's potentially useful to consider that case, but I wouldn't design a system entirely around it.

comment by Jameson Quinn (jameson-quinn) · 2018-04-12T15:38:57.021Z · score: 9 (4 votes) · LW · GW

Should this be broken up into sub-posts?

comment by ryan_b · 2018-04-12T16:02:18.681Z · score: 22 (6 votes) · LW · GW

I think this serves as an excellent centralized reference, and so would argue no. However, it might be good to break out new posts if the comments turn into a deep dive on any particular subject, if as a summary if nothing else.

comment by JustinMElms · 2018-05-01T19:24:53.256Z · score: 8 (3 votes) · LW · GW

Not the best place to put this comment, but there's a confusing mistake on the PLACE FAQ where the pie candidate shows a voting option for "Other Ice Cream Candidate" instead of "Other Pie Candidate."

Does anyone have an electorama account to remedy that?

comment by Jameson Quinn (jameson-quinn) · 2018-05-03T17:08:43.311Z · score: 4 (1 votes) · LW · GW

Thanks, fixed.

This is probably the best place to note that Electorama is limping along on a mostly-broken installation of mediawiki that a nice person set up like 15 years ago. Migrating it to, say, a GitHub Pages wiki would be a substantial benefit to the electoral reform community. If anybody wants to do that, I can get you a database dump.

comment by Endolith (endolith) · 2019-07-26T04:43:38.756Z · score: 6 (2 votes) · LW · GW

For the record, it was migrated to https://electowiki.org/wiki/Main_Page

comment by Sniffnoy · 2018-04-27T22:49:49.736Z · score: 8 (2 votes) · LW · GW

There are two things I would add to this:

  1. The other big disadvantage of Borda is teaming, where nominating more candidates makes a party more likely to win (opposite of vote-splitting).

  2. It seems that to me the advantage of party-less systems in multi-winner elections is that, if your voting system succeeds so well that parties are no longer playing such a big role, you don't have to later change it to be party-less to complete the transition. :)

...also I was going to ask a question about rated-runoff methods (i.e., did anyone consider the most obvious form of rated runoff) but in fact you answered it on your VSE page where you explain score-runoff voting. So, thanks for introducing me to that!

Edit: One addiitional note -- it seems to me that the endorsement mechanism you came up with for 3-2-1 voting, where rather than specifying a full ballot of your own you can just cast a single vote for a candidate and thereby copy their ballot -- that's something that could be tacked on to a lot of methods, couldn't it? As a way of simplifying them for people who really can't handle the additional complexity. (Not that still really licenses that much additional complexity, but...) I guess it does have the potential downside that outside the context of something like 3-2-1 voting, where it can be done implicitly rather than explicitly, it might lead people to just short-circuit the process and subvert the point of the new voting system...

comment by MakoYass · 2018-04-26T04:51:09.616Z · score: 8 (3 votes) · LW · GW
Due to its complexity, [SODA] is probably not a practical proposal, though.

I don't follow, how is that complexity a problem? I googled SODA, stumbled onto a sample ballot here: https://wiki.electorama.com/wiki/SODA_voting_(Simple_Optionally-Delegated_Approval)#Sample_Ballot it doesn't seem like it even matters if voters fully understand the (very succinct) instructions, the thickest voters will just treat it like an approval voting system, which is pretty adequate, isn't it?

Having the candidates' delegations be in there wont really impose much cognitive overhead, humans are very sensitive to the alignments of their leaders/factions, that information is largely already in their heads and taken into account.

Have I not understood what you were referring to? Is the voter interface not where it is?

comment by Jameson Quinn (jameson-quinn) · 2018-04-28T20:31:13.769Z · score: 6 (2 votes) · LW · GW

Yes, the voter interface is the main thing, and SODA is quite simple on that. But to get a reform actually enacted, you usually have to explain it more-or-less-fully to at least some nontrivial fraction of people, and SODA is hard to explain.

comment by Chase Roycroft (chase-roycroft) · 2018-04-22T16:21:10.286Z · score: 8 (3 votes) · LW · GW

Many of these methods can (I think) select multiple winners. For large elections, this is usually pretty unlikely, but still possible. What's your preferred method of dealing with that possibility? And have you looked into maximal lotteries? http://dss.in.tum.de/files/brandt-research/fishburn_slides.pdf

comment by Jameson Quinn (jameson-quinn) · 2018-04-22T17:05:32.992Z · score: 7 (2 votes) · LW · GW

You're talking about the possibility of "ties" at various stages in a method's procedure — that is, cases where a difference is being checked for sign but is equal to zero. As you say, this becomes vanishingly unlikely in large elections. In that case, any tiebreaker will do; if nothing else is clearly better, just draw lots.

comment by daozaich · 2018-04-16T11:32:26.306Z · score: 8 (2 votes) · LW · GW

Re SODA: The setup appears to actively encourage candidates to commit to a preference order. Naively, I would prefer a modification along the following lines; could you comment?

(1) Candidates may make promises about their preference order among other candidates; but this is not enforced (just like ordinary pre-election promises). (2) The elimination phase runs over several weeks. In this time, candidates may choose to drop out and redistribute their delegated votes. But mainly, the expected drop-outs will negotiate with expected survivors, in order to get at least some of their policies implemented (with the same kind of enforcement as regular pre-election promises). Hence, this phase is "coalition building".

An interesting final phase (3), in order to encourage compromise / beneficial trade would be something like: Once we are down to candidates with > 25% approval, we randomize the result. The probability of a candidate to win could be something like the square, or third power, of his approval. The threshold of 25% is in order to prevent complete crackpots from winning the election, and might need to be even more brutal. The randomization serves to allow the two remaining highest approval platforms to negotiate a compromise, weighted by their chance of winning the final lottery. In practice, one would hope that the randomization is never applied: That is, the highest candidate makes enough concessions in order to make the second candidate agree to drop out.

This way, we preserve minority rights, and get a pretty good outcome if the candidates are actually reasonable and trustworthy parties (instead of persons) that are capable of committing to modify the values they will espouse once in power.

Obvious disadvantages are (1) negotiation skill and integrity become essential (integrity in the christiano sense: You need to be predictable in which promises you will break under which contingencies), because the winner is decided though coalition building, rather than voting; and (2) some voters might object to shady backroom deals being the explicit procedure, and (3) randomization may make losers very pissed if the dice are ever rolled (which hopefully is never, because of positive-sum trades).

You can obviously combine this with a 3-2-1 system (where only candidates reaching at least 50% "OK" votes are eligible, and otherwise "Good" votes are counted; if no candidate receives 50% OK, then the election is repeated, under the assumption that Belgium is better than Trump, i.e. better a constitutional crisis and government by interim civil servants than government by crazy elected officials).

edit: I forgot to mention the other big advantage of the probabilistic phase (3): Enforcing continuity, i.e. preventing small factions from gaining oversized influence by playing kingmaker.

comment by Jameson Quinn (jameson-quinn) · 2018-04-16T13:41:40.233Z · score: 8 (2 votes) · LW · GW

The point of SODA isn't so much as a serious proposal; I prefer 3-2-1 for that, mostly because it's easier to explain. SODA's advantage is that, under "reasonable" domain restrictions, it is completely strategy-free. (Using my admittedly-idiosyncratic definition of "reasonable", it's actually the only system I know of that is. It's a non-trivial proof, so I don't expect that there are other proposals that I'm unaware of that do this.) Forcing candidates to pre-commit to a preference order is a key part of proving that property.

I do see the point of your proposal of having post-election negotiations — it gives real proportional power to even losing blocs of voters, and unifies that power in a way that helps favor cooperative equilibria. Some of that same kind of thinking is incorporated into PLACE voting, though in that method the negotiations still happen pre-election. Even if post-election negotiations are a good idea, I'm skeptical that a majority of voters would want a system that "forced" them to trust somebody that much, so I think keeping it as a pre-election process helps make a proposal more viable.

comment by TheWakalix · 2018-04-30T01:32:06.536Z · score: 7 (2 votes) · LW · GW
his last name is last name is great source of puns

Typo: his last name is a great source of puns.

comment by MakoYass · 2018-04-22T12:07:18.786Z · score: 7 (2 votes) · LW · GW

It seems that to lift up one candidate to the top of our ballots we are implicitly expressing a judgement that they're better than every other candidate in the contest. Problem is, most of us know nothing about most of the candidates in most contests. We shouldn't be expressing things like "A > B > all others". We should prefer to say "A > B" and leave leave every other comparison grey. Let other voters, who actually know about C and D and E fill in the rest of the picture. There might be candidates who are better than A. We shouldn't pretend to know.

So my question is.. do you know of any systems that incent or at least allow voters to express their uncertainties?

I'm seeing Dark Horses everywhere, when I think about specific ways of implementing that.

[I'm having some thoughts about collaborative filters/content ranking/recommender systems. I'm not sure how relevant they are to voting theory in elections, related, I suppose, so I wont omit them.

Imagine a gang of <bad people who do not represent the demographic of the site> going to every old thread that not many people are paying attention to, posting a comment espousing <bad> views, then casting, say, 10 Comparison Judgements saying "our <bad> comment is better than the incumbent top comment". When you break up the task of ranking the whole set, so that we can each focus on comparing the candidates we know, leaving the rest to others, non-representative sections of the population will dominate some sections of the job, malicious or not. When they can create any number of new sectors at will, at the top of the ranking, in ways people are unlikely to notice quickly enough to fix, that will create many problems. I suppose... the solution to monitor the way the full ranking is being broken up, in some way, and look for skewed samples?

This might be easier to tackle in collaborative filtering if the system had some general way of noticing that the <bad> users are generally, reliably very different from <normal> users, that <bad> users and <normal> users don't generally like the same things, and that the preferences of <bad> users shouldn't be considered in forming content rankings for normal users. I think a lot could be done with that. I know that sounds like it would thicken our tribal filter bubbles a whole lot, but once we can name and characterise the people of each filter bubble it becomes a lot easier to figure out how to bring them back together. They were already apart, you see. Identifying them doesn't make it worse. Once you can identify them, detecting shared ground between hostile tribes becomes trivial. Being able to identify judgements that even very different sorts of people agree on could be generally useful as a heuristic for finding objective truths. I don't know what would happen if you told the system to strongly amplify anything that fits into those hot intersections. It's not inconceivable to me that it'd give rise to some unprecedented sort of harmony.]

comment by Jameson Quinn (jameson-quinn) · 2018-04-22T14:34:21.671Z · score: 7 (2 votes) · LW · GW

There are indeed various methods which allow for expressing uncertaintly, in principle. For instance, in score voting, you can count average instead of total score. Similar adjustments work for Bucklin, Condorcet, 3-2-1, STAR, etc.

The problem is, as you say, the "Dark Horse" one, which in this case can be seen as a form of selection bias: if those who like a candidate are more likely to give them a score than those who hate them, the average is biased, so it becomes advantageous to be unknown.

The best way to deal with this problem is a "soft quota" in the form of N pseudo-votes against every candidate. More-or-less equivalently, you can have every blank ballot count as X% of a vote against.

It's usually my feeling that as a practical matter, these kinds of extra epicycles in a voting method add more complexity than they're worth, but I can imagine situations (such as a highly geeky target population, or conversely one that doesn't care enough about the voting method to notice the complexity) where this might be worth it.

comment by MakoYass · 2018-04-23T07:51:16.092Z · score: 4 (2 votes) · LW · GW
For instance, in score voting, you can count average instead of total score.

I'm not sure I understand how that would do it. I've thought of a way that it could, but I have had to independently generate so much that I'm going to have to ask and make sure this is what you were thinking of. So, the best scheme I can think of for averaged score voting still punishes unknowns by averaging their scores towards zero (or whatever you've stipulated as the default score for unmentioned candidates) every time a ballot doesn't mention them, but if the lowest assignable score was, say, negative ten, a person would not be punished as severely for being unknown, as they would be punished if they were known and hated. Have I got that right? And that's why it's better, not because it's actually fair to unknowns but because it's less unfair?

[Hmm, would it be a good idea to make the range of available scores uneven, for instance [5, -10], so that ignorers and approvers have less of an effect than oppponents (or the other way around, if opponents seem to be less judicious on average than approvers, whichever).]

The best way to deal with this problem is a "soft quota" in the form of N pseudo-votes against every candidate. More-or-less equivalently, you can have every blank ballot count as X% of a vote against.

But that's just artificially amplifying the bias against unknowns, isn't it? Have you had so much trouble with dark horses that you've come to treat obscurity as a heuristic for inferiority? You know what else is obscure? Actual qualifications. Most voters don't have them and don't know how to recognise them. I worry that we will find the best domain experts in economics, civics, and (most importantly for a head of state) social preference aggregation, buried so deeply in the Dark Horse pile that under present systems they are not even bothering to put their names into the hat.

[Hmm, back to recommender systems, because I've noticed a concise way to say this; It's reasonable to be less concerned about Dark Horses in recommender systems, because we will have the opportunity to measure and control how the set {people who know about the candidate} came to be. We know a lot about how people came to know the candidate, because if they are using our platform for its intended purpose, it was probably us who introduced them to it. We will know a lot more- if not everything there is to know- about the forces that bias the voting group, so we can partially correct for them.]

I'm going to keep talking about recommender systems, because it's not obvious to me that election systems and general purpose demography analysis, discovery, and discussion systems should be distinct.

comment by Jan_Kulveit · 2018-04-15T22:47:52.135Z · score: 6 (2 votes) · LW · GW

Thanks for this introduction to voting systems! I always wanted to know more about them, but never actually got to study it more - so usually I just suggested approval voting as a reasonable default. (Hence we use it in CZEA)

Btw what do you think of this voting method? https://web.d21.me/en/ (pushed by somewhat eccentric mathematician-trader-billionaire Janecek)

(Btw I would suggest this post gets to curated)

comment by Jameson Quinn (jameson-quinn) · 2018-04-16T09:20:25.306Z · score: 25 (7 votes) · LW · GW

This is a system where voters can give +1, 0, or -1 points to candidates in two-member districts, and the highest-score candidates win. So far, that sounds like score voting. However, there are also limits on how many candidates a given voter can support (4) and oppose (2), making this method something like single non-transferable voting.

This voting method is not mathematically clean, and is subject to every one of the pathologies I described. It's not particularly hard to describe, but also a bit confusing at first glance. It is probably less likely to be caught in lesser-evil than FPTP, but that's the best thing I can say about it. Verdict: thumbs emphatically down.

comment by ektimo · 2018-04-27T18:41:55.692Z · score: 4 (2 votes) · LW · GW

The greater the number of voters the less time it makes sense as an individual to spend researching the options. It seems a good first step would be to randomly reduce the number of voters to an amount that would maximize the overall quality of the decision. Any thoughts on this?

comment by Jameson Quinn (jameson-quinn) · 2018-04-28T20:29:24.550Z · score: 5 (2 votes) · LW · GW

That's basically a form of multi-stage election with sortition in the first stage. Sortition is a pretty good idea, but unlikely to catch on for public politics, at least not as an every-election thing.

One version of "sortition light" is to have a randomly-selected group of people who are paid and brought together before an election to discuss and vote, with the outcome of that vote not binding, but publicized. Among other things, the sortition outcome could be posted in every voting booth.

comment by ektimo · 2018-04-30T19:57:55.936Z · score: 1 (1 votes) · LW · GW

Interesting and thanks for your response!

I didn't mean there would be multiple stages of voting. I meant the first stage is a random selection and the second stage is the randomly chosen people voting. This puts the full weight of responsibility on the chosen ones and they should take it seriously. Sounds great if they are given money too.

The thing I feel is missing but this community has a sense for is that the bar to improving a decision when people have different opinions is far higher than people treat it. And if that's true then the more concentrated the responsibility the better… like no more than 10 voters for anything?

comment by Jameson Quinn (jameson-quinn) · 2018-04-12T14:42:33.789Z · score: 4 (3 votes) · LW · GW

(I had several hundred karma on the old Less Wrong site under a nym. Is there both a reason to want to reclaim that and a way to do so?)

comment by habryka (habryka4) · 2018-04-12T17:22:54.121Z · score: 16 (5 votes) · LW · GW

We haven't ported the old karma over yet, but are working on it. Sorry for the delay on that, but it should be fixed within the month.

comment by zulupineapple · 2018-04-16T15:15:23.085Z · score: 2 (1 votes) · LW · GW

I see two problems conflated here: (1) how to combine many individual utilities, and (2) how to efficiently extract information about those utilities from each voter.

In this view, a particular voting system is just a way to collect information to build an accurate model of the voter's utility, which would then be used in some simple way. Of course, actually reducing something like ranked voting to utility maximization would be hard. But that's not a point against this perspective.

Problem (1) is presumably solved by simple utilitarianism though there are still some questions, e.g. about how to make utilities of different people comparable. I think we usually say "let all utilities be positive and let them sum to 1", but that's not necessarily correct. E.g. Quadratic voting might be an attempt to solve this problem differently.

Problem (2) is the part where we worry about whether the system invites honest voting, or whether the voters will understand it.

One issue (2) should care a lot about, that you didn't mention, is the amount of information extracted. It doesn't matter how cleanly a system works, if it doesn't extract much information from the voters about their preferences. I.e. a high VSE, presumably achieved by building a good model of the voter's utility, is the only thing that matters, while the 5 problems you listed are of little practical interest.

comment by Jameson Quinn (jameson-quinn) · 2018-04-16T19:41:02.934Z · score: 10 (3 votes) · LW · GW

Certainly, that's a reasonable point of view to take. If you fully embrace utilitarianism, that's a "solution" (at least in a normative sense) for what you call problem (1). In that case, your problem (2) is in fact separate and posterior.

I don't fully embrace utilitarianism. In my view, if you reduce everything to a single dimension, even in theory, you lose all the structure which makes life interesting. I think any purely utilitarian ethics is subject to "utility monsters" of some kind. Even if you carefully build it to rule out the "Felix" monster and the "Soma" monster, Godel's incompleteness applies, and so you can never exclude all possible monsters; and in utilitarianism, even one monster is enough to pull down the whole edifice. So I think that looking seriously at theorems like Arrow's and Sen's is useful from a philosophical, not just a practical, point of view.

Still, I believe that utilitarianism is useful as the best way we have to discuss ethics in practice, so I think VSE is still an important consideration. I just don't think it's the be-all or end-all of voting theory.

Even if you do think that ultimately VSE is all that matters, the strategy models it's built on are very simple. Thinking about the 5 pathologies I've listed is the way towards a more-realistic strategy model, so it's not at all superseded by existing VSE numbers. And if you look seriously at the issue of strategy, there is a tension between getting more information from voters (as you suggest in your discussion of (2), and as would be optimized by something like score voting or graduated majority judgment) and getting more-honest information (as methods like 3-2-1 or SODA lean more towards).

comment by MakoYass · 2018-04-23T11:37:29.557Z · score: 9 (3 votes) · LW · GW

I can't find a definition of Soba?

I think any purely utilitarian ethics is subject to "utility monsters" of some kind

Isn't that fairly easily solved by, as the right honorable Zulu Pineapple says, "let all utilities be positive and let them sum to one"? It would guarantee that no agent can have a preference for any particular outcome that is stronger than one. Nothing can have just generally stronger preferences overall, under that requirement.

It does seem to me that it would require utility functions to be specified over a finite set of worlds (I know you can have a finite integration over an infinite range, but this seems to require clever mathematical tricks that wouldn't really be applicable to a real world utility function?). I'm not sure how this would work.

Do remember, at some point, being pulled in directions you don't particularly want to go in under obligation to optimise for utility functions other than yours is literally what utilitarianism (and social compromise in general) is, and if you don't like pleasing other peoples' strange desires, you might want to consider conquest and hegemony as an alternative to utilitarianism, at least while it's still cheaper.

Hmm what if utility monsters don't exist in nature, and are not permitted to be made, because such a thing would be the equivalent of strategic (non-honest) voting and we have stipulated as a part of the terms of utilitarianism that we have access to the True utility function of our constituents, and that their twisted children Felix and Soba don't count. Of course, you would need an operational procedure for counting individual agents. You would need some way of saying which are valid and which ephemeral replicas of a mind process will not be allowed to multiply their root's will arbitrarily.

Going down this line of thought, I started to wonder whether there have ever or will ever exist any True Utility Functions that are not strategic constructions. I think there would have to be at some point, and that constructed strategic agents are easily distinguishable from agents who have, at least at some point, been honest with themselves about what they want, and the constructions could be trivially excluded from a utilitarian society. Probably.

comment by Jameson Quinn (jameson-quinn) · 2018-04-24T11:17:50.855Z · score: 10 (3 votes) · LW · GW

"Soba" referred to the happy drug from Brave New World; that is, to the possibility of "utility superstimulus" on a collective, not individual, level.

"Sum to one" is a really stupid rule for utilities. As a statistician, I can tell you that finding normalizing constants is hard, even if you have an agreed-upon measure; and agreeing on a measure in a politically-contentious situation is impossible. Bounded utility is a better rule, but there are still cases where it clearly fails, and even when it succeeds in the abstract it does nothing to rein in strategic incentives in practice.

As to questions about True Utility Functions and a utopic utilitarian society... those are very interesting, but not at all practical.

comment by MakoYass · 2018-04-26T04:01:03.728Z · score: 9 (3 votes) · LW · GW

(That's Soma. I don't believe the joy of consuming Soba comes close to the joy of Soma, although I've never eaten Soba a traditional context.)

comment by Jameson Quinn (jameson-quinn) · 2018-04-28T20:31:47.294Z · score: 4 (1 votes) · LW · GW

Oops, fixed.

comment by zulupineapple · 2018-04-24T14:46:54.042Z · score: 4 (1 votes) · LW · GW
those are very interesting, but not at all practical.

In what practical context do we work with utilities as explicit numbers? I don't understand what context you're thinking of. If you have some numbers, then you can normalize them and if you don't have numbers, then how does a utility monster even work?

comment by TheWakalix · 2018-04-30T01:41:52.094Z · score: 3 (1 votes) · LW · GW
Zulu Pineapple

(I read it as Zu Lupine Apple.)

comment by zulupineapple · 2018-04-17T07:57:12.878Z · score: 6 (2 votes) · LW · GW

The point is that whatever solution you propose, you have to justify why it is "good", and you have to use some moral theory to explain what's "good" about it (I feel that democracy is naturally utilitarian, but maybe other theories can be used too).

For example, take your problem 0, Dark Horse. Why is this a problem, why is it "bad"? I can easily imagine an election where this dark horse wins and everyone is ok with that. The dark horse is only a problem if most people are unhappy with the outcome, i.e. if VSE is low. There is nothing inherently bad about a dark horse winning elections. There is no other way to justify that your problem 0 is in fact a problem.

strategy models [VSE] is built on are very simple

Of course, the simulations of what the voters would do, used in computing the VSE, are imperfect. Also, the initial distribution of voter's true utilities might not match reality very well. Both of those points need work. For the former, I feel that the space of possible strategies should be machine-searchable, (although there is no point to account for a strategy if nobody is going to use it). For the latter, I wonder how well polling works, maybe if you just ask the voter about their preferences (in a way different from the election itself), they are more likely to be honest.

comment by Jameson Quinn (jameson-quinn) · 2018-04-17T10:39:38.818Z · score: 6 (2 votes) · LW · GW

I wrote a separate article discussing the pathologies [LW · GW], in which I gave utility-based examples of why they're problematic. This discussion would probably be better there.

comment by Francois Armand (francois-armand) · 2018-07-06T10:58:15.468Z · score: 1 (1 votes) · LW · GW

Hello,

Thank you for that very insightful article.

Sorry to post a question so long after its publication, I hope it will reach you. I'm wondering how all these methods stands for anonimity of voters, I'm explaining: in most election, there is a lot of candidats (at leat, it's the case in France, where for example the last 1st round of Presidential election had 11 voters. That leads to a lot of unique permutation (for example, with Approval, we can encode 2^11 = 2048 states, for a fully sorted algo we get 11!, etc). In France, votes are organized in small polling station of generally less than 2000 people.

So it seems that a bad actor would be able to threat people to vote for someone, forcing them to vote for a special encoding, and that just by comparing the number of total vote for that encoding, the bad actor would get a good guess about the actual vote of the threaten people.

Is there any electoral algorithms robust againts that threat vector?

Thanks,

comment by Jameson Quinn (jameson-quinn) · 2018-07-07T18:55:38.524Z · score: 1 (1 votes) · LW · GW

"Summable" voting methods require only anonymous tallies (totals by candidate or candidate pair) to find a winner. These do not suffer from the problem you suggest.

But for non-summable methods, such as IRV/RCV/STV, you are absolutely correct. These methods must sacrifice either verifiability/auditability or anonymity. This is just one of the reasons such reforms are not ideal (though still better than choose-one voting, aka plurality).

comment by Francois Armand (francois-armand) · 2018-07-13T16:37:11.392Z · score: 2 (2 votes) · LW · GW

By the way, just to be sure I understood correctly: 3-2-1 is a summable voting method and so is not subject to that risk?

If so, it seems to be definitly the best voting method available.

comment by Francois Armand (francois-armand) · 2018-07-09T08:20:54.600Z · score: 2 (2 votes) · LW · GW

Thanks.

As fall of democracies goes, it seems that auditability is a better properties to have than anonymity (because when the totalitariam regime is sufficiently powerful to openly threat people, anonymity most certainly doesn't matter anymore. But on a working democracy, people need to be sure of the transparency of the system to believe and accept it).

Is there a place where all these methods are formally defined in a comparable way?

I'm a little lost with all the acronym, and having all of them in a big table with their algorithm & properties would be extremelly useful.

comment by Francois Armand (francois-armand) · 2018-07-13T16:29:37.636Z · score: 2 (2 votes) · LW · GW

Obviously, you did it somewhere, and now that I navigated a little bit more in the mass of very good documents you produced, I can point towards:

  • http://electology.github.io/vse-sim/VSE/ for the code repository, with a long explanation, of a statistical test of a lot of methods. That implies that we have the actual code to understand:
    • the model used (for voters preferences and strategies - extremely interesting!)
    • the actual algorithmic definition of all the methods
    • nice VSE graph for each method :)
  • http://electology.github.io/vse-sim/VSEbasic/ which is a nice summary of the main methods.

Also, I wanted to point out that there was a big real life test of a variant of score voting (with 6 score from "reject" to "very good") before french presidential election in 2017: https://articles.laprimaire.org/l%C3%A9lection-pr%C3%A9sidentielle-au-jugement-majoritaire-les-r%C3%A9sultats-373e089315a4

(sorry in French).

The scrutin was a little complex, with a first tour with 16 candidates and >10k voters. Each voter was presented a random set of 5 candidates and was asked for evaluation of each candidate project on ~10 aspects (your clusters) (each time with the 6 states scale) (see https://articles.laprimaire.org/r%C3%A9sultats-du-1er-tour-de-laprimaire-org-c8fe612b64cb). Smart contracts on ethereum were used to register votes.

Then a second round took the 5 bests candidates, and more than 30k voters ranked them. (https://articles.laprimaire.org/r%C3%A9sultats-du-2nd-tour-de-laprimaire-org-2d61b2ad1394)

It was a real pleasure to participate to it because you really try to estimate each candidate project, and you don't try to be strategic.

But it does not seems possible in real life major elections (like French or USA presidential), because it requires quite a lot of time and will from voters.

comment by dennisV · 2018-06-26T21:26:57.224Z · score: 1 (1 votes) · LW · GW

Another view of voting is where an objective opinion or belief is being formed about ANYTHING that can be named. It might be a belief about utility where the utility can only be seen subjectively but an objective value would be useful in planning, for instance. Another example is determination of what a given set of users might buy given prior page views, or what the value of a given piece of intelligence is to a given audience at a given time and related to a given topic. Such a voting structure is needed in crowd sourcing and in 'training'/'supervision' in machine learning. It is also necessary for determination of what is or is not fake news, where certain 'voters' might be given a greater weighting to their votes on given topics. As with reducing ranked voting to utility maximization, the problems of using these are complex, even though the intention of statistics in general would seem to be directed to the same facilities. Like machine learning, the issue is the great 'dimensionality' of the problem, and statistical solutions don't work well. In fact, where dichotomies exist (failed praxis), statistics simply fail without the use of probabilistic techniques such as expectation analysis. A system for handling all of this type of consensus mechanisms is on the way. See Patent US20140075004 - System And Method For Fuzzy Concept Mapping, Voting Ontology Crowd Sourcing ... - Google Patents; Patent US20140075004 - System And Method For Fuzzy Concept Mapping, Voting Ontology Crowd Sourcing ... (2nd pointer is to the list of projects that were required to acknowledge the patent as prior art) .

One aspect of interest regarding the edge of statistics mentioned is that in a causality based world (see 'The Book of Why'), the causality must still be addressed even if the statistical approaches don't seem to work. Answers from the two may disagree (where 'common sense' seems to be).

comment by JPW · 2018-04-23T14:08:29.260Z · score: -5 (3 votes) · LW · GW

>>>> Borda: "My method is made for honest men!"

This is why it would miserably fail. We live in a fallen world. We would like to live in a rational one. We do not. We will not until irrational behavior is punished in some horrible fashion. Preferably punished by the Darwin Gods w/o any human intervention that irrational monkeys with car keys can blame.

comment by TheWakalix · 2018-05-03T02:43:18.334Z · score: 3 (1 votes) · LW · GW

Being wrong does not mean that you deserve to suffer. Even beyond the moral disagreement, an environment where disagreement implicitly carries the wish that your opponent suffer horribly is not a good place to find truth. That will, among other things, promote defensiveness, tribalism, and overconfidence.