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If I approve of two candidates, but I like one more than the other, approval voting doesn’t seem to allow me to express that preference. Do I vote for both candidates, or only the one I like the most? As a naive voter who isn’t going to research that question, will I make the right choice?

It's a hard question. I think it comes down to: are you more afraid of your top choice losing, or your least-favorite choice winning? If the former, then just vote for your first choice. If the latter, vote for everyone but your first choice. (This is an improvement over FPTP because you at least have the option to support multiple candidates if you want to.)

Some people don't like this aspect of approval voting, and really want to give an ordering or a score.

Score voting is like approval voting, but you give a score. All the scores are totaled up, and the winner has the highest total. This is a pretty good system, but it has a problem: honest voters who aren't enthusiastic about a candidate might rate their candidate 6/10, whereas a very opinionated partisan voter might rate their candidate 10/10. So, the people with the most extreme opinions have more influence: 6 partisans gives a score of 60, whereas ten unenthusiastic voters also gives an equal score of 60.

Under score voting, strategic voting means always maximizing your positions: always 10/10 or 0/10, nothing in-between. Basically this is the same as approval voting. So, I'd suggest that approval voting is usually better because it puts strategic voters and honest voters on an equal playing field.

There's another voting system called STAR (score then automatic runoff), in which you use score voting to select the top two candidates, and then you do an instant runoff by maximizing all the votes for the top two candidates. For instance, if our top two candidates are A and B and if someone marked candidate A as 7 and candidate B as 4, then that turns into A:10 and B:0. If another person has A as 6 and B as 6, then they don't have a preference and that ballot is dropped.

STAR isn't perfect (what if an extreme party runs two ideologically-similar candidates and they both make it to the runoff?) but it's a pretty reasonable compromise system that allows voters to score candidates rather than just making a yes/no choice.

you approve anyone who you approve of

approval voting is a special case of score voting where the range of scores is limited to 0 and 1. if you want to express different levels of preference, you can expand this range and get full score voting. the downside is this puts a heavier burden on the voter to decide on scores (if it's 0-99, i give my first choice 99, but what do i give my second choice? 98? 75? 50? my choice might depend on what i expect other voters to think makes sense as a score)

> RCV does have some serious problems. Eliminating the candidate with the least first-place votes at each round means a high probability of rejecting compromise candidates that may be a lot of voters' second choice. Also, placing your first-choice candidate first isn't always a safe choice. RCV is non-monotonic, which means it's possible that ranking someone first might actually cause them to lose. That's weird, and I think it's a good enough reason to investigate other options.

This is actually not true and the opposite of what happens. With RCV, people feel comfortable putting compromise or 3rd party candidates first because they know they aren't throwing away a vote. It creates a system where there is more middle ground and less black and white 2 party systems.

With IRV, you can put a compromise or third-party candidate first _only if they have no chance_. In other words, it's purely symbolic.

As soon as the third-party candidate starts to become competitive, the spoiler effect returns. It becomes risky to vote for your true favourite, and voters are forced to vote strategically as they do now. So IRV will not help us escape from polarized two-party politics; it will continue to entrench the duopoly.

IRV has other serious problems with fairness (a much higher spoiled ballot rate, disproportionately in low-income areas), practical implementation (requiring a redesign of ballots and counting software), and security (it isn't summable, which makes it harder to conduct a risk-limiting audit).

Approval is also imperfect, but it is simple, cheap, effective, and has none of these problems.

help me out here, I don't understand how the spoiler effect returns if the third party candidate becomes competitive. Wouldn't that just mean they have a chance of winning? Suppose Dave Chappelle ran in 2020 and 40% of people voted for him and they all had Biden ranked at #2. 15% rank Biden #1, and 45% rank Trump #1 with no #2 marked. Biden wins, no?

edit: found your explainer elsewhere, currently reading. edit edit: Huh, that is weird.

That's a pretty good example, because it illustrates a disconnect between how people expect IRV/RCV to work and how it actually works.

Biden would be eliminated first, because he had the fewest 1st choice votes in the first round.

The Dave Chappelle voters' 2nd choices for Biden don't matter: they're thrown out because Biden was eliminated.

So, it comes down to Chappelle with 40% and Trump with 45%. If none of the Biden voters listed Chappelle as their second choice, then Trump wins. If enough voters had Chappelle as their second choice, then Chappelle wins.

The lesson from this example is: it's quite possible that your second choices don't matter, because they're eliminated too early. We could come up with other examples that show that it isn't always safe to put your first choice first, either. IRV/RCV is non-monotonic, which means in some cases you can cause a candidate to lose by ranking them higher.

I agree with what /u/zestyping says in the other comment, so I won't repeat it. But here's a video explaining the strategic voting issue: https://www.youtube.com/watch?v=JtKAScORevQ

Also, wikipedia has an example of a non-monotonic result here: https://en.wikipedia.org/wiki/Monotonicity_criterion#Instant...

> RCV is non-monotonic, which means it's possible that ranking someone first might actually cause them to lose.

I'm intrigued. Can you explain how that works? I'm not saying I don't believe you- I'll bet it is possible, but I cannot see how, and I want to!

If you're a visual thinker, you might enjoy these:

http://zesty.ca/voting/voteline

http://zesty.ca/voting/sim

Or, if you prefer logic:

The intuition for "something strange could happen" is that IRV only uses some of the information on the ballots. Initially it uses just the top ranking on each ballot, and then at other points in the process, it might flip to using the second ranking on some of the ballots, and so on. There are these sudden trigger thresholds that cause big discontinuities in what gets counted—and that should feel weird. We have this pile of ballots that could all count for A or B; why should that decision depend on some unrelated other ballots?

That's the mechanism by which ranking someone higher can cause them to lose. Only some of the second ranks on the ballots will get to count, and depending which ones get counted, we could get a totally different outcome. Suppose A, B, and C are all competitive in an election, with no one having an outright majority, but A has a little more support than B, who has a little more support than C. It could be the case that A is in a winning position because C supporters mostly like A as their second choice; when C gets eliminated first, those ballots count for A and A wins. But let's say B supporters all like C as their second choice, and you persuade some B supporters to switch to A. If enough of them switch away from B that B is eliminated first, then all those B supporters' ballots will count for C, and that can cause C to win. So by campaigning for A, you made A lose!

The general idea is that if B and C are close, which way it tips can have a sweeping effect on whose second choices get counted, which can affect A. It should feel intuitively scary that a small shift in one part of the election can have a magnified effect on a different part. It's not good for systems to be unstable like that.

If some people change their vote from A-B-C to B-A-C, that can cause A to be eliminated instead of B in the first round, and B in the second (if C beats B but C doesn't beat A). Changing the winner from B to C.

https://www.fairvote.org/rcv_faq#monotonicity

Read "22. Does RCV satisfy the monotonicity criterion?"

Say, there's 3 candidates. You want A to win. You think A will lose to B in a 1-on-1 match, but would win C. So you vote C-A-B (or C-B-A, doesn't matter) to increase the likeliness that B got eliminated in the 1st round. Of course, you're now saying that you prefer C over A in a 1-on-1 race. But that's fine because other people will vote for A.

Concretely, let's say this is people's actual choice.

31 B-A-C; 39 A-B-C; 30 C-B-A

B wins.

Now, if 2 people preferring A (voted A-B-C) strategically change their vote to C-B-A.

31 B-A-C; 37 A-B-C; 32 C-B-A

Now, A wins.

I simply don't get why the person preferring A doesn't rank A first. This scenario only works if you have exactly 3 candidates and the numbers are tight and everyone is tactically voting instead of voting their conscience.

In reality most preferential voting schemes have many candidates, and there's too much chaos to coordinate this kind of scenario.

Meanwhile plurality voting has candidates winning with way less than 50% of the vote, and claiming some mandate from god.

The sooner we ditch FPTP the sooner we get to something like Condorcet, or STV with multimember districts.

> I simply don't get why the person preferring A doesn't rank A first.

Well, that's kind of the point of the example. A normal person who wants A to win would put A as their first choice. But doing that can actually cause their preferred candidate to lose, which is exactly the opposite of the voter's intent. FPTP has a different set of problems that one could argue are worse, but one of the few good things about FPTP is that you can't say about some election result "that candidate lost because I voted for him/her".

Non-monotonic results don't happen in every election, but they're something that can happen.

It just doesn't feel likely that this could be successfully coordinated or occur in a decentralized way organically in a sufficiently large election.

Consider how little trust a lot of people have in polling. You would need a very high amount of trust in it if you were going to dishonesty rank your choices based on it. And if strategic voting is going to be based on polling, wouldn't we expect people then start strategically lying to pollsters?

The system has too much chaos.

An individual person might not be able to coordinate such a thing, but you can bet that campaign strategists are going to be very interested in crafting their messages to get the results they want. I mean, right now we have campaigns and PACs that sometimes promote a minor candidate they're ideologically opposed to because they'll siphon votes away from their major-party opponent.

What strategies will they employ in RCV elections? I don't know, but given the way campaigns already operate with continuous polling, elaborate voter databases, and modern ad-tech that can target exactly the right message to exactly the right people to influence their behavior slightly, I see election systems with wonky outcomes as an attack surface against democracy.

> The system has too much chaos.

There's too much fog-of-war for individual voters to make optimal strategic voting choices, but the Cambridge Analyticas of the world can use that to their advantage. I don't like that information asymmetry, and it seems the best way to defend against it is to have voting systems that are as close to the ideal (which is that candidates win by having the most public support) as possible.

One important distinction to make is that RCV isn't the same as Instant Runoff Voting (IRV); rather, IRV is a specific (the most commonly championed, as far as I can tell) implementation of RCV, likely because it's the easiest to explain.

Note that all RCV implementations have limitations, per the oft-cited https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore... which outlines a number of ostensibly desirable attributes then demonstrates that no RCV implementation can satisfy all of them.

But that's not to say that approval voting methods are flawless, either. One often cited desirable property is the Condorcet criterion, namely, if one candidate beats all others in head-to-head matchups, that candidate should be the winner. (There's a related Condorcet Loser criterion which is the inverse: if one candidate loses to all others in head-to-head matchups, that candidate should not be elected.)

Suppose we applied approval voting to a simplified view of the 2016 election. (Y to indicate approval, N to indicate disapproval)

- 48%: Partisan R. Trump (Y) > Stein (N) > Clinton (N)

- 48%: Partisan D. Clinton (Y) > Stein (N) > Trump (N)

- 3%: 3rd-party, very slight D lean. Stein (Y) > Clinton (Y) > Trump (N)

- 1%: 3rd-party, very slight R lean. Stein (Y) > Trump (Y) > Clinton (N)

Stein beats both Clinton and Trump in head-to-head matchups, 52% to 48%. But with an approval voting system (selecting Clinton with 51% approval), this fails the Condorcet criterion! (IRV is no better here, to be clear. And Condorcet methods have their own pathologies.)

As far as I know, the label RCV as it's commonly used in the United States (and advocated most prominently by FairVote) usually means the same thing as IRV. Perhaps there are some minor differences in terms of specifying exactly what happens if a ballot doesn't rank all the candidates, or ranks two candidates equally. Perhaps using RCV to mean an exact system rather than a whole category of voting systems is imprecise, but I think that ship has already sailed.

It's also sometimes called alternative vote, and the Australians call it preferential voting.

I've wondered if IRV couldn't be substantially improved by using Borda count for the elimination step rather than eliminating the candidate with the least first-choice options. (I think there's an actual name for that system, but I don't remember what it is.)

Oh, I agree that in the US, RCV is (unfortunately) often conflated with IRV.

> I've wondered if IRV couldn't be substantially improved by using ... rather than eliminating the candidate with the least first-choice options.

This is exactly the family of RCV systems -- IRV merely defines one implementation by which a winner is selected from a ranked ballot.

Borda count has its own pathologies, too -- the usual cited problem is that it fails independence of irrelevant alternatives.

https://en.wikipedia.org/wiki/Independence_of_irrelevant_alt...

(Further, Borda count fails the majority criterion, namely there are situations where a candidate is the first pick of a majority of the electorate, yet fails to win. Some proponents of Borda count argue this is a feature, not a bug.)

The wiki article for Borda count has a solid table of various voting systems and whether they satisfy various criteria:

https://en.wikipedia.org/wiki/Borda_count#Other_properties

You're right that Borda count on its own isn't a great system. Though an RCV-style system that eliminates candidates on the basis of least-Borda count would be something else. It might be better than either normal IRV or plain Borda count on their own. (Though I still think I'd rather go with approval voting or STAR.)

It sounds like you're referring to

https://en.wikipedia.org/wiki/Nanson%27s_method

and the related Baldwin's method, which, while being Condorcet methods, both fail monotonicity.

I looks like what I was thinking of is Baldwin's method, actually. Failing monotonicity is still a problem, but it's actually pretty cool that it satisfies the Condorcet criterion. That seems like a pretty big step up from plain IRV.

Approval voting may lead to election of weak candidates, no? Like there's a strong right candidate, disapproved by left, there's strong left, disapproved by right, and there's meh candidate approved by both. Either strong right or strong left might be better for both left and right.

Thank you for pointing to the flaws of RCV though. It has flaws, but still looks like an improvement.

In London mayor they were using "Contingent vote" system, which is AFAIU RCV with only two options, which is weaker than RCV. And in the next elections they switched it to FPTP, which is unfortunate.

Regarding your comment about approval, isn't that the intended outcome? You elect the candidate that the most people approve of, regardless of whether or not there are other "stronger" candidates. The population would be better served than if one of the "strong" left or right candidates were elected.

You could also just not vote for any other candidates if you don't think they'd do a good job. In your example, the left or the right could just not vote for the "meh" candidate if they truly don't believe they would be a good person to lead, and if they do vote for them, then they should be happy at the outcome regardless.

Yeah, it's literally "elect the candidate with the highest approval rating" which seems like a fair and reasonable outcome.

(That's assuming that people vote honestly, but according to at least one analysis [1], the outcome isn't very much less democratically optimal if people vote strategically in approval voting rather than honestly.)

[1] https://electionscience.org/library/tactical-voting-basics/

> You elect the candidate that the most people approve of, regardless of whether or not there are other "stronger" candidates.

It may be a strategic voting: I approve anyone who is not democrat (or republican).

> The population would be better served than if one of the "strong" left or right candidates were elected.

Not necessarily. Perhaps it is better when left/right candidates alternate (driving important changes in their area of interests), than weak candidates elected every time.