Thoughts on electoral reform

post by Tobias_Baumann · 2020-02-18T16:23:27.829Z · score: 71 (36 votes) · EA · GW · 27 comments

Contents

  Which voting system should we advocate for?
  How promising is electoral reform?
None
25 comments

Excessive political polarisation, especially party polarisation in the US, makes it harder to reach consensus or a fair compromise, and undermines trust in public institutions. Efforts to avoid harmful long-term dynamics, and to strengthen democratic governance, are therefore of interest to effective altruists.

One concrete lever is electoral reform. By changing to a better voting system, we could (so the argument goes) elect officials that better represent the electorate, resulting in a more functional political process.

Within effective altruism, approval voting is the most prominent proposal for reform (see e.g. this post [EA · GW]). The Center for Election Science, which advocates approval voting, appears to be the only electoral reform organisation with significant ties to the EA community - e.g. in the form of a grant from OpenPhil.

In this post, I will question the focus on approval voting, and argue that it might be better to support other proposed voting systems that have a track record in competitive elections. I’ll also offer some thoughts on how promising electoral reform is.

Which voting system should we advocate for?

There are many possible methods and many different criteria to evaluate a voting method, some of which are provably incompatible. So, like other methods, approval voting satisfies some criteria and fails others. (See here for an overview of single-winner voting methods and satisfied/failed criteria.) Given that no perfect method exists, we should arguably look for a method which works well in practice and has good chances of being adopted.

Would approval voting work well in competitive elections? I think there are good reasons to be sceptical:

Advocates of approval voting have responded to those criticisms. And of course, approval voting does also offer advantages: it avoids the spoiler effect and tends to favour moderate "compromise candidates". The latter is of particular interest if reducing polarisation is one of the main goals of electoral reform. However, the tendency to favour moderate candidates could also be considered a bias and is not universally viewed as a positive feature of a voting system.

All things considered, I’m not convinced that we should advocate for approval voting rather than other methods (e.g. instant runoff voting or Condorcet methods). It seems to me that effective altruism has not examined approval voting (or alternatives) in sufficient detail.

In general, my impression is that discussions of voting reform suffer from the problem that people tend to pick their favourite method and then cherry-pick one-sided arguments in favour of it. In particular, people overemphasise criteria that favour their method does well while ignoring or and downplaying problems. The Center for Election Science often talks about no favourite betrayal (which approval voting satisfies) and not much about later-no-harm (which it fails). FairVote doesn't talk much about no favourite betrayal and talks a lot about later-no-harm - because their favoured method (instant runoff voting) satisfies later-no-harm but fails no favourite betrayal.

Given all this, what kind of voting system should we advocate for (if any)?

Since there is (some degree of) consensus that plurality voting is bad, but no consensus on which alternative is best, we should focus on the reform proposals that are most viable. That’s arguably instant runoff voting (IRV, called ranked choice voting / RCV in the US), which is championed by FairVote. Unlike approval voting, IRV has a track record in competitive elections and is much more in line with conventional notions of “majority”. (My personal favourite voting system would be a Condorcet method such as Ranked Pairs, but there are no large organisations advocating this, and it’s unlikely that Condorcet methods will be adopted.)

IRV isn’t perfect either. It also fails important criteria, and it isn’t clear whether IRV results in less polarisation. Still, IRV seems clearly superior to plurality voting and has stood the test of time, so I think efforts to implement IRV are worth supporting. (Even the very simple step of adding a runoff between the top two candidates would be a significant improvement over plurality voting.)

Note that this discussion is mostly about single-winner elections such as US presidential elections, rather than multi-winner elections, such as electing a parliament (e.g. the House of Representatives). It seems not obvious, overall, whether we should focus on changing single-winner elections or parliamentary elections.

For parliamentary, I think it’s best to use a form of proportional representation rather than (or in addition to) first-past-the-post in single-seat constituencies. Proportional representation tends to lead to multi-party systems that require cross-party collaboration and reduce the team sport mentality that drives US polarisation.

How promising is electoral reform?

Clearly, work on electoral reform is premised on the belief that the status quo of plurality voting (in the US/UK) is a poor voting method. I think this isn’t entirely obvious. A steelman of plurality voting is that it grants power to the largest coherent political coalition (coherent in the sense of being able to coordinate on a single candidate). That may be less than 50% of the voters, but it’s not prima facie unreasonable to put the largest coherent political coalition in charge of things. The fact that plurality voting provides tactical incentives that limit the number of (realistic) options (often leading to a two-party system) can be seen as a feature, not a bug: it channels democratic decision-making and produces clear results.

Still, I think the downsides of plurality voting outweigh its advantages, and there is some degree of consensus among experts that plurality voting is not a good system.

Suppose, then, that we have settled on a voting system that would be a significant improvement over the status quo. That raises the question of how tractable it is to change the voting system for high-stakes elections such as the US president or the House of Representatives. Such efforts face significant vested interests of individuals and parties that benefit from the current system. Also, countries rarely make dramatic changes to their voting procedures once established, though there are exceptions (e.g. New Zealand’s switch to proportional representation).

Electoral reform also doesn’t seem particularly neglected. There are several organisations advocating electoral reform in the US and UK. In terms of funding, the Hewlett Foundation’s Madison Initiative is a major player that’s interested in electoral reform (supporting FairVote’s advocacy for ranked choice voting) and other ways to strengthen US democracy.

All things considered, I think electoral reform, while probably not a “top tier” intervention, should be part of the longtermist EA portfolio.

27 comments

Comments sorted by top scores.

comment by cole_haus · 2020-02-19T01:22:58.672Z · score: 33 (10 votes) · EA(p) · GW(p)

I just finished reading Democracy for Realists recently which argues that:

They demonstrate that voters—even those who are well informed and politically engaged—mostly choose parties and candidates on the basis of social identities and partisan loyalties, not political issues. They also show that voters adjust their policy views and even their perceptions of basic matters of fact to match those loyalties. When parties are roughly evenly matched, elections often turn on irrelevant or misleading considerations such as economic spurts or downturns beyond the incumbents’ control; the outcomes are essentially random. [...]

Achen and Bartels argue that democratic theory needs to be founded on identity groups and political parties, not on the preferences of individual voters.

I'm not fully settled on how much weight to give to this perspective, but I think it's important to remember the empirical facts of voting as it happens in the real world and not just the idealizations of social choice theory. Presumably this leads to a quite different notion of the optimal electoral system and the optimal series of electoral reforms.

(This isn't meant to say that the social choice theory perspective and the points brought up in this post are unimportant. I just thought it was an interesting book and a good reminder to look at this whole other set of criteria.)

comment by Max_Daniel · 2020-02-19T11:17:37.843Z · score: 18 (6 votes) · EA(p) · GW(p)

(The following summary [not by me] might be helpful to some readers not familiar with the book:

https://casparoesterheld.com/2017/06/18/summary-of-achen-and-bartels-democracy-for-realists/ )

comment by aaronhamlin · 2020-02-21T00:55:48.907Z · score: 31 (20 votes) · EA(p) · GW(p)

Disclaimer: I'm the executive director for The Center for Election Science.

There’s some good stuff in this post.

Excessive political polarisation, especially party polarisation in the US, makes it harder to reach consensus or a fair compromise, and undermines trust in public institutions. Efforts to avoid harmful long-term dynamics, and to strengthen democratic governance, are therefore of interest to effective altruists. One concrete lever is electoral reform.

Great stuff.

Still, I think the downsides of plurality voting outweigh its advantages, and there is some degree of consensus among experts that plurality voting is not a good system. … Still, I think the downsides of plurality voting outweigh its advantages, and there is some degree of consensus among experts that plurality voting is not a good system.

Understated, but still good stuff. Also, experts really hate plurality. See one such meeting of experts where not a single person approved of plurality. As an aside, they favored approval voting with IRV following in second.

All things considered, I think electoral reform, while probably not a “top tier” intervention, should be part of the longtermist EA portfolio.

I might disagree on the degree, but my sentiment overlaps with its place in longtermism.

The post gets at the idea that anything is better than plurality and that we shouldn’t feel like we have to pick among systems. But then it ultimately picks among systems. This is the dilemma we find ourselves in. We have to advocate for something, and when we’re presenting an opportunity, it is only reasonable for those exploring to consider the options. If experts don’t then do the correcting, then errors will go ignored, and poor decisions will be made.

My full empathy goes to anyone who does the legwork to create a post here (it’s challenging and it’s putting yourself out there). But practically all the arguments raised in this well-meaning post are addressed in the previous posting [EA · GW], which also links to the approval voting criticisms article and limits of RCV. If after looking, you don’t see it addressed, please reply and I’ll see if I can find an answer. You’ll find answers about later-no-harm and bullet voting, proportional approaches, the reflection of candidate support, practicality, and much more.

I'm noticing that the arguments referenced here come almost exclusively from FairVote. As a caveat, this organization repeatedly argues that approval voting should not be used in virtually any circumstance (despite when experts clearly disagree and even prefer approval voting). They also failed to acknowledge any faults within an RCV election where virtually every RCV mistake occurred. It’s hard to take them seriously after that. This refers to the Burlington election where voters got a worse outcome for ranking their favorite first, candidates could have been harmed by getting more higher-preference rankings, voter segments would have gotten a better outcome staying at home, and the candidate who could beat everyone head to head was eliminated due to RCV’s tendency to vote split along the middle. They also discouraged others from looking at election data from alternative voting methods in a Wall Street Journal article.

FairVote frequently cites Dartmouth while omitting any other reason that might have caused voters to choose fewer candidates (like few candidates being on the ballot and an enormous number of write-ins). As one can also get from the approval voting criticisms article, even when a majority choose only one candidate, the remainder who choose multiple candidates can (1) have a material effect in choosing a different winner and (2) give support to candidates who would otherwise be invisible. These repeals were not “often” the case. This argument also fails to acknowledge all the cities that repealed RCV due to either complaints of complexity or flat-out bad winners being elected. There are also cities that take forever to implement RCV or don’t do it at all due to the cost of software and new machines. This is one big reason why Fargo and St. Louis wanted approval voting instead of RCV.

This isn’t to say that any FairVote reference is bad, just that it potentially warrants more investigation.

When we are looking at voting methods, a good track record isn’t merely recorded uses. We need to see how it performs in competitive elections that have a different plurality winner. And note that practically any alternative voting method will handle spoiler candidates who get little support. Want more data? Funding a research department for CES would go a long way.

It’s also important to remember that no voting method can guarantee a majority and that methods like RCV merely contrive a majority through eliminating candidates via vote splitting—sometimes by eliminating the best candidate. Metrics that you can use to see whether a good winner was elected involve looking at Condorcet matrixes and candidate utilities (note that using explicit Condorcet methods is not practical due to “tie-breakers” from cycles). It’s not enough to say that a method didn’t provide a “majority” and so that method must have chosen the wrong winner.

It’s also important to note that CES was seriously vetted for close to a year before a grant was awarded. This grant from two years ago wasn’t a rash decision. This is a system that has been studied academically since the late ’70s with one of its developers on the CES board of advisers.

Also, CES went into this space agnostic about the voting method. We took the time in our early years (before we had any funds) to really think about the alternatives, including practicality as a concern. This is not the same approach that other organizations have taken either going with a system merely because it either (1) has previous use, or (2) superficially approximates the setup of a separate proportional method (STV).

Ultimately, I think for EA to switch to a voting method that already has funding relative to approval voting (and has serious issues) would be a mistake. This is a space that is overall extremely underfunded relative to other election reform areas given its importance (see earlier analysis [EA · GW]). As an organization, we’ve already demonstrated how cost-effective we can be in a much shorter time frame compared to peers in our space. We hired staff and got approval voting in its first US city all within a year of initial funding.

Failing to provide further support or removing it at this crucial time wouldn’t be the optimal move here. It would just eliminate a promising alternative approach from being tested at all. If this is perceived as too much of a risk, then I would fear how this mentality would keep EA from pursuing other efforts where outcomes are even more unclear.

comment by Pablo_Stafforini · 2020-02-19T02:13:12.351Z · score: 31 (14 votes) · EA(p) · GW(p)

Thanks for writing this—I think electoral reform is an interesting and important cause area.

[Approval voting] fails the later-no-harm criterion

All voting systems violate intuitively desirable conditions, so noting that some system violates some condition is in itself no reason to favor other systems. One needs to look at the full picture, see what conditions are violated by what systems, and pick the system that minimizes weight-adjusted violations. (There is a clear parallel here between voting theory and population ethics: impossibility theorems have demonstrated in both fields that there exists no voting rule or population axiology that satisfies all intuitively plausible desiderata, so violation of a condition can't be adduced as a reason for rejecting the rule or axiology that violates it.)

But there is a much better approach, namely, to assess different systems by their "voter satisfaction efficiency" (VSE). Instead of relying on adequacy conditions, this approach considers the preferences that the electorate has for rival candidates and deals with them using the apparatus of expected utility theory. Each candidate is scored by the degree to which they satisfy the preferences of each voter, and then rival voting systems are scored by their probability of electing different candidates. Monte Carlo simulations independently performed by Warren Smith, Jameson Quinn and others generally find that approval voting has higher VSE than instant-runoff voting, and that both approval voting and instant-runoff voting have much higher VSE than plurality voting.

Given these results, I think the priority for EAs is to support whichever alternatives to plurality voting are most viable in a particular jurisdiction, rather than obsess over which of these alternatives to plurality is the absolute best. Of course, I also think it makes sense to continue to research the field, and especially refine the models used to compute VSE. What EAs definitely shouldn't do, in my opinion, is to spend considerable resources discrediting those alternatives to one's own preferred system, as FairVote has repeatedly done with respect to approval voting. Much more is gained by displacing plurality than is lost by replacing it with a suboptimal alternative (for all reasonable alternatives to plurality).

(In case it isn't obvious, I'm definitely not saying that you have done this in your essay; I'm rather highlighting a serious failure mode I see in the "voting reform" community that I believe we should strive to avoid.)

comment by Mathieu Putz · 2020-02-20T18:53:50.471Z · score: 15 (8 votes) · EA(p) · GW(p)

Hello, I think you make a good point, about the necessity to carefully weigh the up- and downsides of each system.

I do not have a strong view on which alternative voting system is best, since I haven't looked into it deeply enough. Still I want to address this proposition:

Much more is gained by displacing plurality than is lost by replacing it with a suboptimal alternative (for all reasonable alternatives to plurality).

I mostly agree with this position, especially in scenarios where no other option is realistically on the table. However, I do want to point out, that adopting a sub-optimal system can have a considerable cost and that it is not entirely obvious that this cost is irrelevant relative to the gains obtained from switching away from the status quo; in particular, if one believes that the difference in outcomes between two alternative voting systems is big.

For instance, one might assume alternative voting system B to lead to much better results than system A. If this were the case, then switching to A (the weaker system), though (probably) better than the status quo in itself, could still lead to outcomes that are worse than if the switch had not happened. This is for 2 main reasons:

First, as Tobias points out, countries do not change their voting system frequently. Hence this sub-optimal system A might potentially stick around for a century to come, before maybe being changed to the better alternative B. It might be preferable to postpone the switch by a few years, hopefully increasing the odds of switching to B instead of A.

Secondly, this new system A will inevitably be questioned by the electorate and the media. If system A then yields controversial results that are not obviously better than the results one would have got with the status quo system, the whole switch might be viewed as a mistake by the general population. This might even lead to less trust in the political system, though probably only in the short run. Still, a negative experience of this kind, may not only have short-term bad consequences for the country itself in the form of further erosion of trust, but could also discourage other countries from switching away from their respective status quo system for years to come.

Of course, I'm not arguing that switching should be postponed until absolute certainty of one system being better than all others is reached. (That point will probably never come.)

And, of course, I also acknowledge, that the opposite of the described scenario might happen, i.e. that one country switching might encourage others to do so, rather than discourage.

All I'm saying is that there is a case against switching and that therefore, not any system that seems preferable to the status quo ought to automatically be endorsed.

comment by Pablo_Stafforini · 2020-02-20T18:46:10.324Z · score: 5 (3 votes) · EA(p) · GW(p)

Thanks to your comment, I can now endorse what you said as a more accurate and nuanced version of the position my previous comment tried to articulate. Agreed 100%.

comment by Tobias_Baumann · 2020-02-19T10:28:30.224Z · score: 9 (6 votes) · EA(p) · GW(p)

I'm not entirely convinced that VSE is the right approach. It's theoretically appealing, but practical considerations, like perceptions of the voting process and public acceptance / "legitimacy" of the result, might be more important. Voters aren't utilitarian robots.

I was aware of the simulations you mentioned but I didn't check them in detail. I suspect that these results are very sensitive to model assumptions, such as tactical voting behaviour. But it would be interesting to see more work on VSE.

What EAs definitely shouldn't do, in my opinion, is to spend considerable resources discrediting those alternatives to one's own preferred system, as FairVote has repeatedly done with respect to approval voting. Much more is gained by displacing plurality than is lost by replacing it with a suboptimal alternative (for all reasonable alternatives to plurality).

Strongly agree with this!

comment by Pablo_Stafforini · 2020-02-19T13:02:03.734Z · score: 11 (5 votes) · EA(p) · GW(p)
I suspect that these results are very sensitive to model assumptions, such as tactical voting behaviour. But it would be interesting to see more work on VSE.

I agree with this. An approach I find promising is that of Nicolaus Tideman & Florenz Plassmann. In one study, the authors consider several different statistical models, use them to simulate actual elections, and rank the models by how best they approximate actual results. Then, in a subsequent study, the authors use the top-ranking model from their previous study to evaluate a dozen or so alternative voting rules, finding that plurality, anti-plurality, and Bucklin perform worst. As far as I'm aware, this is the only example of an attempt to assess voting rules by conducting simulations with a model that has been pre-fitted to actual election data. I believe that extending this approach may be among the most impactful research within this cause area.

comment by MichaelStJules · 2020-02-19T09:57:38.216Z · score: 8 (3 votes) · EA(p) · GW(p)
Monte Carlo simulations independently performed by Warren Smith and Jameson Quinn generally find that approval voting has higher VSE than instant-runoff voting, and that both approval voting and instant-runoff voting have much higher VSE than plurality voting.

A priori, I think this could end up being quite sensitive to the distributions of votes they used. Did they choose them based on surveys/polls of voter preferences?

comment by ClayShentrup · 2020-02-21T08:23:03.656Z · score: 3 (2 votes) · EA(p) · GW(p)

A variety of utility distribution models were tried, and it turned out not to matter very much.

The simulations by N. Tideman had methodological flaws and didn't measure the right thing, thus being approximately as useful as a random coin flip in this mathematician's view.

comment by Pablo_Stafforini · 2020-02-19T13:03:35.630Z · score: 3 (2 votes) · EA(p) · GW(p)

Yeah, see my reply [EA(p) · GW(p)] to Tobias.

comment by MikkW · 2020-03-18T23:44:31.655Z · score: 3 (2 votes) · EA(p) · GW(p)

I think it's worth being aware of lock-in effects; while I agree that it's unproductive to put down alternative approaches, it's also important to do what we can to avoid locking in a suboptimal choice- if Ranked Choice gets locked in over Approval Voting, and if Approval is actually better, it may be very hard to change it in the future, leading to much long-term disutility, perhaps even more than if the shift away from FPTP takes a little longer in the process of getting it right.

But I do agree that bickering and putting alternatives down probably isn't the best way to mitigate lock-in

comment by David_Moss · 2020-02-18T19:53:52.862Z · score: 19 (11 votes) · EA(p) · GW(p)

It's great to see more reflection about approval voting and possible alternatives. I think the EA community should probably favour a lot more research into these alternatives before it invests resources in promoting any of these options.

Excessive political polarisation, especially party polarisation in the US, makes it harder to reach consensus or a fair compromise, and undermines trust in public institutions. Efforts to avoid harmful long-term dynamics, and to strengthen democratic governance, are therefore of interest to effective altruists.

I will note that many political theorists think that reducing polarisation and increasing consensus should not be our goals in democracy and need not be positive things e.g. agonistic theorists. This is especially so when, increasing consensus and compromise solutions is identified with "moderate" or centrist (which, as you note, could be construed as a bias).

comment by MikkW · 2020-03-18T23:53:03.114Z · score: 1 (1 votes) · EA(p) · GW(p)

Tl;dr: We should argue before the election, and build a consensus when it's time to actually get stuff done

I don't think reducing (tribal) polarization is at odds with agonism. There's plenty of room for healthy debate about what direction we should go in, but when in comes to actually deciding who has power, we want to track the median of what people think, not sway back and forth between two extremes (which is a compromise in and of itself)

comment by G Gordon Worley III (gworley3) · 2020-02-18T19:48:40.447Z · score: 15 (9 votes) · EA(p) · GW(p)

In the US, especially for federal elections and especially especially for election of the president, I expect voting reform to have low tractability because I believe it requires constitutional reform at the national and possibly the state level. Given how hard it is to pass amendments to the federal constitution and given that there are a lot of incentives to maintain the status quo, this seems like an uphill battle that can suck up money and generate no results.

Local election reform is probably much more tractable, especially at the municipal level, since the voting procedures are managed in ways that are more easily changed.

comment by RandomEA · 2020-02-19T06:43:40.120Z · score: 15 (5 votes) · EA(p) · GW(p)

With respect to the necessity of a constitutional amendment, I agree with you on presidential elections but respectfully disagree as to congressional elections.

For presidential elections, the proposal with the most traction is the National Popular Vote Interstate Compact, which requires compacting states to give their electoral votes to the presidential ticket with a plurality of votes nationwide but only takes effect after states collectively possessing a majority of all electoral votes join the compact. Proponents argue that it is constitutional (with many believing it can be done without congressional consent), while opponents say that it is unconstitutional and in any case would require congressional consent. See pages 21-30 of this Congressional Research Service report for a summary of the legal issues. Regardless of which side has the better argument, it's unlikely that an interstate compact would be used to adopt instant runoff voting or approval voting for presidential elections because i) absent a law from Congress, it would be up to non-compacting states whether to switch from plurality voting in their own state (which could mean voters in some states would be limited to choosing one ticket) and ii) it is questionable whether Congress has the power to require non-compacting states to switch (though see pages 16-17 of this article arguing that it does).

As for congressional elections, it's worth noting that the U.S. Constitution does not require plurality voting and does not even require single member districts. Indeed, ranked choice voting was used in Maine for congressional elections in 2018, and a federal judge rejected the argument that it is unconstitutional due to being contrary to historical practice. And while single member districts have been used uniformly for nearly two centuries, it was not the only method in use at the founding and courts tend to give special weight to founding era practice (see e.g. Evenwel v. Abbott for an example related to elections), which makes me think that FairVote's single transferable vote proposal is on solid constitutional footing.

comment by MikkW · 2020-03-18T23:55:50.286Z · score: 1 (1 votes) · EA(p) · GW(p)

In practice, states decide how to vote in both congressional and presidential elections (Maine for example, uses ranked choice for both). It is true that getting rid of the electoral college requires a federal amendment, but the electoral college isn't actually that bad; the big problems can be solved within its framework

comment by ClayShentrup · 2020-02-21T07:35:41.230Z · score: 10 (8 votes) · EA(p) · GW(p)

> All things considered, I think electoral reform, while probably not a “top tier” intervention, should be part of the longtermist EA portfolio.

My view is that electoral reform, specifically alternative voting methods, is by far the biggest “bang for the buck” utility-increasing reform for humanity. I began studying alternative voting methods in 2006, largely focused on the findings of a Princeton math PhD named Warren Smith, who created RangeVoting.org to publicize his research. What was very surprising and counterintuitive were the Bayesian regret calculations he performed via computer simulation, showing that an upgrade from plurality voting to score voting (aka range voting) nearly doubled the human-welfare increasing impact of democracy. Approval voting is just score voting on a 0-1 scale and it performs almost as well as score voting with a range like 0-5; and of course it has the advantage of using ordinary ballots and not requiring voting machine upgrades. As Smith puts it:

there are very few causes out there with this much "bang for the buck." Examine the numbers yourself. I do not believe religious causes can compete. Disaster relief cannot compete (in the long term; for large disasters in the short term, it can). Curing diseases also cannot compete except for the biggest killers. E.g, ending malaria or halving illiteracy each would cause an amount of good comparable to range voting, but would probably be more difficult to accomplish.

More recently, a Harvard stats PhD named Jameson Quinn performed his own computer simulations using slightly different modeling assumptions, and presenting the results inverted and normalized to voter satisfaction efficiency (VSE) rather than Bayesian regret. However he found similar results to Smith's.

That last point about the cost (the second component in "bang for the buck") is crucial. Aside from the one-time political campaigning cost, voting reform is essentially free. Unlike, say, mosquito nets or medicines which have to be manufactured and distributed.

Full disclosure: Smith, Quinn, and myself are all former board members of the Center for Election Science, but I am no longer associated with them and am speaking only for myself.

Approval voting is vulnerable to tactical voting.

All deterministic voting methods are vulnerable to tactical voting. But computer simulation and game theoretical analysis shows that approval voting is especially resistant to tactical voting. For instance, as Warren Smith and Jameson Quinn showed in their computer simulations, approval voting worked very well with wide variances in assumptions about voter behavior and the preponderance of tactical behavior. The difference was so large that in some of Smith's models, approval voting performed better with 100% strategic voters than instant runoff voting (aka "IRV", the most prominent ranked method) did with 100% honest voters. There is even a mathematical theorem that, given plausible models of voter strategy, approval voting always elects a Condorcet winner (a candidate who beats every rival by a head-to-head majority) whenever one exists. This is a very mild, some would say beneficial, reaction to strategy.

It's also notable that approval voting was shown generally favorable to ranked methods in the William Poundstone book Gaming the Vote, and is specifically advocated by Steve Brams, an NYU professor of political science and game theory, who wrote such page turners as Mathematics and Democracy.

It fails the later-no-harm criterion: approving a second candidate can hurt your favourite.

At the outset, I want to suggest eschewing properties as a means for evaluating voting methods, and instead focus on voter satisfaction efficiency as described above. Focusing on properties is kind of analogous to evaluating race cars based on characteristics such as horsepower and aerodynamics. You might intuitively think a car with 10% more horsepower will be better, but once you perform a statistically significant number of timed trials, you may find instead that other factors such as aerodynamics or tire quality (or even properties you never thought to consider) have a countervailing effect that causes the more powerful car to surprisingly lose. Voter satisfaction efficiency (or Bayesian regret) simultaneously measures the combined effects of all those properties, even ones you forgot to consider. And indeed, those figures I cited already account for later-no-harm (LNH); and yet of the five alternative voting methods compared, IRV did the worst, even though it was the only one of those five methods to satisfy LNH.

Having said that, let's consider this failure of the later-no-harm criterion (LNH) more specifically. I actually contend that failing LNH is a benefit, not a flaw. Here's a thorough analysis by Warren Smith (again, full warning, Smith's writing is interspersed with venom for his enemies, but the content itself is high quality).

To summarize, later-ho-harm means that given you've started by showing support for your favorite, X, it cannot hurt X to indicate support for a lesser liked candidate, Y. E.g. suppose you rank the Green in first place. Now it cannot hurt the Green to rank the Democrat (or Labour) in second place. IRV is the only commonly discussed method that satisfies LNH. By contrast, if you cast a vote for the Green with approval voting, casting a second vote for the Democrat (or Labour) could cause the Green (your actual favorite) to lose. IRV proponents often argue that this creates an incentive for "bullet voting" only for one's favorite candidate. I admit this does seem problematic on its surface, but that goes away once you inspect a bit deeper.

See, all that assumed that you started by ranking your favorite candidate honestly in first place. E.g. you ranked the Green #1, and now you're considering whether to rank your honest second favorite as #2. But your best strategy with IRV is, similar to FPTP, to rank your favorite frontrunner in first place, not necessarily your favorite overall. We see this often in USA primary elections, where people are afraid to vote for their favorite candidate because they fear she'll lose the general election. For instance, right now my aunt in Iowa favors Democrat Elizabeth Warren over Joe Biden, but voted for Biden because she feels he's more likely to win in the next round against Trump. To convert this to its IRV analog, with all three of those candidates running on a single ranked ballot together, she would insincerely/strategically rank Biden in first place, to help ensure Warren (her actual favorite) is eliminated, thus giving the presumably more competitive Biden the chance to square off against Donald Trump in the next round. IRV fails the favorite betrayal criterion.

And contrary to those concerned about bullet voting with approval voting, the best strategy is actually to approve everyone you prefer to the expected utility of the winner. Bullet voting is absolutely not the best general strategy. Case in point, imagine a Green Party supporter who normally casts a strategic vote for the Democrat. With approval voting, she still casts that strategic vote for the Democrat, but then she also casts a sincere vote for her true favorite, the Green, plus anyone else she prefers to the Democrat. This is the underlying game theory that makes approval voting so robust against strategy. There's even empirical data showing that approval voting often has less bullet voting than comparable elections with IRV.

Moving beyond strategy, to the fundamental social choice theory behind LNH, the problem with LNH is that it forces a voting method to ignore important preference data. E.g.

Imagine preferences like these:

35% LRC
34% RCL
16% CLR
15% CRL

C is eliminated first with 31%, and L wins with 51%.

But suppose just 2%, from the CLR faction, swap their LR preference, creating:

35% LRC
34% RCL
14% CLR
17% CRL

C is still eliminated, but now R wins with 51%.

A tiny change in preferences changes the winner from L to R.

But now suppose a comparatively massive change in preferences occurs. The LRC voters find out something terrible about R, causing them to lower R to 3rd place. And the RCL voters find out something super positive about L, causing them to elevate L to 2nd place.

35% LCR
34% RLC
14% CLR
17% CRL

An enormous shift in public opinion just took place, positive for L and harmful for R. But this huge change didn't change the winner from R to L, even though a tiny change of preferences moved the winner from L to R in the first place. LNH causes this fundamental distortion in sensitivity to preference information.

The winner, then, may not be the candidate with the most support, but the one that’s best at manipulating the system.

Absolutely true. But also consider that:

A. This happens with IRV too, and in some ways more so. Since you still have to worry about electability with IRV, a candidate like Biden can convince Warren's supporters to drop her for him just by running ads that make voters fear her to be unelectable. That cannot possibly happen with approval voting. The best they could do is convince Warren's supporters to also vote for Biden.

B. Approval voting behaves so much better in the general case (again, see the voter satisfaction efficiency results above) that it gives substantial margin for error, such that even if this effect you describe happens, approval voting plausibly still comes out ahead.

Admittedly, we have to see approval voting in the real world to get a better handle on such campaign dynamics that are beyond the capacity for a computer to simulate.

Approval voting radically re-interprets the common-sense notion of "having a majority"...For instance, approval voting sometimes selects a candidate even though a majority of voters would, in a head-to-head contest, prefer any other candidate. (This is the Condorcet loser criterion.)

Again, approval voting tends to elect Condorcet winners whenever they exist, in practice. And most ranked methods, including most Condorcet methods, are extremely vulnerable to tactics, meaning they may in practice be worse at electing Condorcet winners. Indeed, IRV can elect candidate X even though candidate Y is preferred to X by a huge majority and also has twice as many first place votes as X.

And to go more esoteric and technical, it is mathematically proven that a group may prefer candidate X even though a majority of voters in that group prefer candidate Y. See here and here. So it is not inherently wrong to avoid electing the Condorcet winner, or even the majority winner for that matter. Here are even some examples where it seems bad to elect the Condorcet winner. I contend the goal of social choice is to maximize expected utility, i.e. maximize the net utility of the group, not to elect "majority winners" per se. We can talk about the biological origins of that grey decision-making machine between our ears, and how that makes us effectively utility maximization machines, but I suspect the EA community is already fairly on board with this.

Indicating support or opposition for each candidate is more expressive than just having a single vote, but it is still binary and does not allow voters to express more nuanced preferences between different candidates.

Yes, this is the expressiveness issue. Ranked ballots do provide more expressiveness, but this is counteracted by two other factors: 1. their increased vulnerability to strategy, and 2. their generally decreased tabulation efficiency (particularly in the case of IRV). This is why approval voting generally outperforms the ranked methods in computer models. Even in the circumstances where some ranked methods perform better, it's only a marginal amount that I do not think justifies the complexity. Especially given ranked voting methods have been repealed in something like 60 U.S. cities, apparently largely on account of their complexity.

There is almost no track record of approval voting being successfully used in competitive elections. Where it was used, approval voting was often repealed later on - e.g. in Dartmouth alumni elections and in internal IEEE (Institute of Electrical and Electronics Engineers) elections (search for IEEE here).

But all indications are that it worked well in those situations, and it was repealed for "political" reasons, plausibly because it worked. Granted, that's little consolation if it manages to be repealed in American political contests. But there are good reasons to believe that's less likely to happen in government elections. E.g. it's harder to imagine a city like Fargo, where approval voting was adopted by a 64% majority, voting to repeal it by a majority via another ballot initiative. And given ranked voting has already been repealed so many times in the U.S., it's not clear that approval voting is riskier in this regard. We'll just to have find out empirically by seeing how it plays out in Fargo this June, and hopefully in other cities in the coming years.

My view is that the urgency of voting reform demands small experiments limited in their scope. If it turns out approval voting actually is better, and its simplicity allows it to scale faster, then I feel it will have been worth it. I think the urgency of issues like climate change and authoritarianism demands a massive scaling out of "electoral technology" that can increasingly democratize the USA in something like a decade. If approval voting fizzles out and/or IRV or other methods turn out to scale faster, it wasn't that expensive of an experiment.

the tendency to favour moderate candidates could also be considered a bias and is not universally viewed as a positive feature of a voting system.

Again, the key here is to look at it through the lens of utility efficiency, which already measures "bias" and any other distortionary factors in terms of human welfare, which is the ultimate metric we want to look at.

It seems to me that effective altruism has not examined approval voting (or alternatives) in sufficient detail.

Speaking as someone who has spent countless hours studying this subject since 2006, whereupon I soon did my first exit poll, I think it has been studied voluminously. Organizational elections, exit polling, computer simulation, and all manner of years-long debates between math PhD's and various engineers have taken place. An NYU professor of game theory and political science has worked on it for four decades and written multiple books on the subject. I've personally visited Kenneth Arrow, who won the Nobel Prize in economics for his study of voting theory going back to the 1950s. We'll still find out new things from what we see in municipal elections like those in Fargo, but I do believe the general arguments you raise have been analyzed inside and out.

In general, my impression is that discussions of voting reform suffer from the problem that people tend to pick their favourite method and then cherry-pick one-sided arguments in favour of it.

Perhaps, but what's relevant is the veracity of the arguments, not the personality traits of people who favor one system or another.

The Center for Election Science often talks about no favourite betrayal (which approval voting satisfies) and not much about later-no-harm (which it fails). FairVote doesn't talk much about no favourite betrayal and talks a lot about later-no-harm - because their favoured method (instant runoff voting) satisfies later-no-harm but fails no favourite betrayal.

I would put this the other way around. Favorite betrayal matters for important game theoretical reasons that I described in detail above, whereas LNH is effectively an "anti-criterion". And from those observations, I form a relative assessment of approval voting and IRV. I do not start with the system and then try to make the facts fit it. Indeed, Warren Smith initially ran his computer simulations with no particular foreknowledge of how it would turn out. He thought the winning system would vary depending on the assumptions (the "knob settings" of the program), but it turned out that score voting won in all 720 different permutations of those settings. And that led him to become a supporter of score voting. When I came across his work, I was initially skeptical and I sent him an email berating him. Then over the course of some email correspondence, he refuted my arguments and made me a convert.

A few years back, an associate of mine added a top two runoff to score voting and "STAR voting" was born. At first I was skeptical that it was a needless additional complexity. But then I saw that Jameson Quinn's voter satisfaction efficiency calculations were quite favorable to it, so I've shifted my thinking substantially.

Since there is (some degree of) consensus that plurality voting is bad, but no consensus on which alternative is best, we should focus on the reform proposals that are most viable. That’s arguably instant runoff voting (IRV, called ranked choice voting / RCV in the US), which is championed by FairVote.

I don't know if there is "consensus", but I do feel the facts objectively show approval voting to be superior to IRV (if not every ranked method) according to essentially every metric we have, from voter satisfaction to ballot spoilage rates to voting machine complexity. I also dispute that IRV is more viable. Approval voting was adopted by a 64% majority in Fargo, and is polling at 72% support in St Louis. I suspect we are about to see that approval voting is more politically viable, due to its simplicity and transparency.

Unlike approval voting, IRV has a track record in competitive elections and is much more in line with conventional notions of “majority”.

But again, it is mathematically proven that majoritarianism is not the right metric. Maybe you're talking more about public perception, but in that case I would again cite the 2-1 margin by which approval voting managed to pass in Fargo, and the 72% support it's getting in St Louis. If this majority failure is a risk in terms of political viability, we're not seeing it.

My personal favourite voting system would be a Condorcet method such as Ranked Pairs, but there are no large organisations advocating this, and it’s unlikely that Condorcet methods will be adopted.

I know I'm repeating myself, but approval voting may in practice be a better Condorcet method than real Condorcet methods. And it performs better under models of significant voter strategy. And of course is much simper and thus politically and logistically easier to implement and scale.

IRV seems clearly superior to plurality voting and has stood the test of time

It was used in nearly two dozen U.S. cities and repealed in all but one of them, then adopted in several cities again, and then repealed in four of them. So it's not clear what its long term staying power is yet.

For parliamentary, I think it’s best to use a form of proportional representation rather than (or in addition to) first-past-the-post in single-seat constituencies.

Whether PR systems can outperform the best single-winner systems, such as STAR voting and approval voting, is very much an open question and highly speculative. But it's also very difficult to adopt in the USA without first getting a system like score voting or approval voting which is capable of ending two-party domination. That's because federal law makes multi-winner districts illegal, and the two-party system will make that impossible to change.

Proportional representation tends to lead to multi-party systems that require cross-party collaboration and reduce the team sport mentality that drives US polarisation.

One could expect that a congress full of moderate/centrist candidates would be even less polarized than one that includes every faction from socialists to fascists.

A steelman of plurality voting is that it grants power to the largest coherent political coalition (coherent in the sense of being able to coordinate on a single candidate).

Computer simulation shows that it is extremely bad. And as a 41-year-old American, I've seen first-hand how much its two-party lock-in fosters binary tribal thinking that makes it impossible to view issues like impeachment or climate change through an objective non-partisan lens. And combined with Gerrymandering, it virtually nullifies democracy. As FairVote says, elections become so predictable that, "Under our current system, we can predict 379 of the 435 House seats — or more than 87 percent of the total — with high confidence."

comment by Jc_Mourrat · 2020-02-19T01:33:18.117Z · score: 10 (6 votes) · EA(p) · GW(p)

Thanks for this interesting post! I particularly like your point that instant-runoff voting "has a track record in competitive elections and is much more in line with conventional notions of “majority”". Paraphrasing, the point is of course not to debate whether or not IRV produces a theoretically valid notion of majority; rather, it is about the psychological perception of the voting process and of the perceived legitimacy of the winner. I think these psychological aspects are very important, and are essentially impossible to capture by any theory.

Relatedly, I found this paragraph in Wikipedia's article on approval voting, which I find worrisome: "Approval voting was used for Dartmouth Alumni Association elections for seats on the College Board of Trustees, but after some controversy, it was replaced with traditional runoff elections by an alumni vote of 82% to 18% in 2009." My understanding is that voters in approval voting most often choose to support only one candidate, despite being given a much broader range of options; this, in elections with more than 2-3 possible candidates, often leads to a winner who collected only a small fraction of the votes, and who is then perceived as lacking legitimacy.

I have not studied the question in detail, but as of know my guess would be that instant-runoff voting should be preferred over approval voting.

comment by Matt_Lerner (mattlerner) · 2020-02-20T21:31:21.154Z · score: 6 (5 votes) · EA(p) · GW(p)

I agree that EAs should continue investigating and possibly advocating different voting methods, and I strongly agree that electoral reform writ large should be part of the "EA portfolio."

I don't think EAs (qua EAs, as opposed to as individuals concerned as a matter of principle with having their electoral preferences correctly represented) should advocate for different voting methods in isolation, even though essentially all options are conceptually superior to FPTP/plurality voting.

This is because A democratic system is not the same as a utility-maximizing one. The various criteria used to evaluate voting systems in social choice theory are, generally speaking, formal representations of widely-shared intuitions about how individuals' preferences should be aggregated or, more loosely, how democratic governments should function.

Obviously, the only preferences voting systems aggregate are those over the topic being voted on. But voters have preferences over lots of other areas as well, and the choice of voting system relates only to two of them: (a) their preferences over the choice in question and (b) their meta-preferences over how preferences are aggregated (e.g. how democratic their society is).

As others in this thread have pointed out, individuals' electoral preferences cannot be convincingly said to represent their preferences over all of the other areas their choice will influence.

So an individual gains utility from a voting system if and only if the utility gained by its superior representation of their preferences exceeds the utility lost in other areas lost by switching. I don't think this is a high bar to clear, but I do think that, beyond the contrast between broadly democratic and non-democratic systems, we have next-to-no good information about the relationship between electoral systems and non-electoral outcomes.

In the simplest terms possible: we know that some voting systems are better than others when it comes to meeting our intuitive conception of democratic government. But we're concerned about people's welfare beyond just having people's electoral preferences represented, and we don't know what the relationship between these things is.

It is totally possible that voting systems that violate the Condorcet criterion also dominate systems that meet the criterion with respect to social welfare. We simply don't know.

It's also not clear to what degree different voting systems induce a closer relationship between individuals' electoral preferences and their preferences over non-electoral topics, e.g. by incentivizing or disincentivizing voter education.

To reiterate, I strongly support the increased interest in approval voting and RCV that we're seeing, and I voted for it here in NYC. I want to see my own electoral preferences represented more accurately and I don't think there is a big risk that (at least here) my other preferences will suffer. But as consequentialists I think we are on very uncertain ground.

comment by ClayShentrup · 2020-02-25T20:35:33.255Z · score: -1 (2 votes) · EA(p) · GW(p)

@Matt_Lerner [EA · GW],

A democratic system is not the same as a utility-maximizing one.

In my utilitarian view, these are one in the same. An election is effectively just "a decision made by more than one person", thus the practical measure of democratic-ness is "expected utility of a voting procedure". I would argue it could be perfectly democratic to replace elections with a random sample of voter opinions over a statistically significant subset of the eligible voting population. This would probably be more democratic than the current system, which is distorted by demographic disparities in turnout. The issue would be making the process provably random, so as to ensure legitimacy.

The various criteria used to evaluate voting systems in social choice theory are, generally speaking, formal representations of widely-shared intuitions about how individuals' preferences should be aggregated or, more loosely, how democratic governments should function.

Yes, this is why the utilitarian camp within the electoral reform community eschews voting method criteria in favor of utility efficiency calculations, traditionally expressed as Bayesian regret, or more recently inverted into voter satisfaction efficiency. The procedure is pretty straightforward. We just start with a random utility distribution, then turn that into preferences by mangling it with an "ignorance factor", then turn that into a cast ballot by normalizing it and adding strategy. Then we compute the winner and measure the utility lost by not electing the social utility maximizer.

This allows us to property assess the combined effect of all criteria at once, even ones we never thought to consider, with their proper utility-decreasing weight, times frequency. There are of course externalities, like complexity and cost of voting machine upgrades, but luckily the better performing methods like approval voting tend to also be simpler than ranked voting methods too.

So an individual gains utility from a voting system if and only if the utility gained by its superior representation of their preferences exceeds the utility lost in other areas lost by switching.

I don't see how there is any appreciable utility lost by adopting approval voting. There might be a tiny amount lost from the physical cost of things like new voting machines if we upgrade to a more complex ranked system, but even then I believe the utility gain exceeds that by an order of magnitude.

In the simplest terms possible: we know that some voting systems are better than others when it comes to meeting our intuitive conception of democratic government. But we're concerned about people's welfare beyond just having people's electoral preferences represented, and we don't know what the relationship between these things is.

I have argued above that we do know. We have voter satisfaction efficiency and Bayesian regret. That is indeed the utilitarian lens through which many of the foundational members of the approval voting community see the world, and the basis of much of their support.

It is totally possible that voting systems that violate the Condorcet criterion also dominate systems that meet the criterion with respect to social welfare. We simply don't know.

This is in fact true! Score voting violates the Condorcet criterion, and also outperforms Condorcet methods in utility efficiency calculations.

comment by Matthew_Barnett · 2020-02-26T00:54:59.091Z · score: 1 (1 votes) · EA(p) · GW(p)
In my utilitarian view, [democracy and utility maximizing procedures] are one in the same. An election is effectively just "a decision made by more than one person", thus the practical measure of democratic-ness is "expected utility of a voting procedure".

Doesn't this ignore the irrational tendencies of voters?

comment by ClayShentrup · 2020-02-26T06:28:50.698Z · score: 1 (1 votes) · EA(p) · GW(p)

I discussed this in my post:

We just start with a random utility distribution, then turn that into preferences by mangling it with an "ignorance factor"

The ignorance factor represents a disparity between the actual utility impact a candidate will have on a voter, and the assumed utility impact which forms the basis for her vote. Even with lots of ignorance, there's still a significant difference in performance from one voting method to another.

In addition, I believe a lot of our ignorance comes from "tribal" thinking. If we have two parties (tribes), and each party must pick one side of any issue (abortion, guns, health care, etc.). Thus voters will tend to retroactively justify their beliefs about a given issue based on how it comports with their stated party affiliation. Note that this forced binary thinking is so powerful that we even have a party divide over the objective reality of climate change!

With a system like approval voting, candidates can easily run outside of the party system and still be viable. Thus they can take any arbitrary position on any issue, giving voters the freedom to move freely through the issue axes. A new offshoot of the GOP could form that is generally socially conservative and pro gun rights, but totally committed to addressing climate change. With 3-5 viable parties able to constantly adjust to changing realities, this is expected to reduce the amount of voter ignorance considerably, by allowing voters to consider issues which were once taken as given as part and parcel of their party affiliation.

comment by Reasonable Doubt · 2020-04-12T07:23:18.448Z · score: 1 (1 votes) · EA(p) · GW(p)

What do folks think of the relevance of the 17th Amendment to the U.S. Constitution?

Also, countries rarely make dramatic changes to their voting procedures once established, though there are exceptions (e.g. New Zealand’s switch to proportional representation).

U.S. senators were originally elected by state legislatures. Not until the early 20th century did reformists successfully amend the constitution and enable the popular vote election of senators. I doubt awareness of this history would lead to a sweeping belief in reform, but nonetheless I find this history encouraging.

comment by dpiepgrass · 2020-03-18T05:12:08.029Z · score: 1 (1 votes) · EA(p) · GW(p)

I've said for years that if there is a referendum / ballot initiative to switch from first-past-the-post to anything else, always say yes. Anything is better than first-past-the-post. Having said that... I have opinions.

First of all, before choosing a voting system you have to know if there will be a single winner or many. Single-winner voting systems should not be used to run multi-winner elections because single-winner district-based voting method cannot produce a fair outcome; gerrymandering is always possible. Also, these methods pretty reliably magnify the power of large parties over small parties, which has always been frustrating to me (because I consistently dislike large parties as well as most smaller parties, and feel like there is no one to represent me). Multi-winner elections should use multi-winner voting systems! Naturally, my favorite systems are the one I designed, Simple Direct Representation, and the one that inspired it, Direct Representation, but since these systems will never happen, I'd recommend good old fashioned Proportional Representation, Mixed-Member Proportional, STV or any other proportional system that seems politically viable. Sometimes at night I dream of a meta-voting system where a country splits its legislature into two voting systems and during every election there's a vote for which one people like better, which adjusts the relative influence of each system, and then ... but never mind, no one would vote for it: it's too democratic.

As for single-winner systems, I rank them clearly in this order:

1. Score voting (a.k.a. range voting, cardinal voting), where each candidate is rated on a scale (e.g. 0 to 5 stars, like the old Netflix. I was puzzled that Netflix killed off star-ratings; it seemed to produce more accurate and meaningful recommendations than the new up/down system. The reason given for the change was not that it didn't work well - the system worked quite well, but people didn't understand it. If it were up to me I'd focus on helping people understand it, rather than scrapping it.)

2. Condorcet methods, e.g. Ranked Pairs, which is based on preferential ballots (candidates in preferential order). A Condorcet method looks at each pair of candidates in isolation, with respect to all the ballots, and elects the candidate that wins a majority of the vote in every pairing against every other candidate. The problem is that there is not always a "condorcet winner". If there are three candidates A, B, and C, it can happen that A beats B, B beats C and C beats A. So a Condorcet system must also specify how to resolve such conflicts. Ignorant people often promote "the preferential ballot" as a voting system, but a preferential ballot is just a ballot, not a voting system. IRV is far more popular than Condorcet, but it seems strictly worse, because IRV has no underlying mathematical basis, and happens to have somewhat unstable behavior and fails the monotonicity criterion. Also, I believe voters should be allowed to rank two candidates as equal (no preference between them) or "no opinion"; Condorcet can support such features, while IRV cannot.

I used to prefer Condorcet, probably because I learned about it first and liked the intuitive idea that "if a candidate is preferred by a majority of voters over all others, that candidate should win." I changed my mind for the following reasons:

1. Range Voting, as well as its simpler cousin Approval Voting, allow the outcome of an election to be measured numerically, which lets voters understand the popularity of candidates, which is relevant in future elections. You can say things like "minor-party candidate M had an an average rating just one point behind the winner" or "the winner of the election had a lower average score than any other in history". Condorcet does not allow this. If somebody comes up with a way to turn Condorcet or IRV results into simple numbers, I think somebody else could come up with a different way to do that, allowing confusing, competing numerical narratives about the results.

2. Score Voting allows more nuance. I can say "I like X a little more than Y, but I like Y a lot more than Z".

3. Score Voting works far better in case the number of candidates is large. If there are 30 candidates, putting them in a single order is fairly impractical and burdensome for the voter unless ties are allowed.

4. Tallying results is easier with Score voting than Condorcet (though not as easy as Approval). Note that with computers we can calculate outcomes with an arbitrarily complex method, but computers can be hacked, so manual counting remains relevant.

5. If you wanted to know how happy people were with the outcome of an election, how might you ask them? "On a scale of 1 to 10, how happy are you with the outcome of the election?" That's asking for a Score! Score voting simply turns this question into ballot form, so that if people answer honestly, it will maximize the average answer to the happiness question! A criticism against Score voting might explain "if you raise the preference of a less-preferred candidate L on your ballot, you could cause L to beat your preferred candidate P who you rated higher". But if this happens because overall satisfaction of all voters is collectively higher, that's a fine outcome. I'm open to hearing about ways the Score voting system could be gamed, but such gaming is only interesting if other systems are not similarly vulnerable to gaming. (Edit: aha, here's the site where I learned about this idea.) The one "game" we can count on is something I'll call "spreading", where we spread out our true opinion on the ballot: if there are 3 candidates and my happiness would be 4/10 if A wins, 5/10 if B wins and 6/10 if C wins, I will spread this out to 0/10 for A, 5/10 for B and 10/10 for C. But every proposed voting system has something analogous to this.

Approval voting is technically a version of Score voting that gathers relatively little information from voters. Its virtues are that it is extremely simple and easy to implement, and I'm persuaded of its value on that basis. I suspect that, statistically, as a result of a large number of voters, Approval won't perform much worse than Score voting in practice. My intuition is this: consider one hundred voters who partially approve of a candidate C; they would like to rank this person as 5/10, but on an Approval ballot they can't. I suspect that roughly half of the people will "approve" of this person, so that overall the results are similar to what Score voting would produce.