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Comment by shawabawa3 | Hacker News Reader

Does Approval Voting really pass the "favourite betrayal criterion"?

There are scenarios where if you don't vote for both Good and Ideal, bad will win, and scenarios where if you do vote for both Good and Ideal, Good will win (over Ideal)

You obviously don't know which scenario you're in when you vote, so you don't know whether you should vote for both good+ideal or just ideal - both options can cause a worse result

I suppose the idea is that you use polling to decide which scenario is more likely and vote accordingly

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Yes, approval voting leaves the door open for some tactical voting.

So if candidate #1 would win a simple majority (50.01% of voters), but is absolutely hated by everyone else, but #2 is "acceptable" or second best to 100% of the voters, should #1 win?

We are used to the binary "simple majority takes all" in elections, but maybe the compromise "everybody is pretty OK with this one" _should_ win.

If it were a group of friends going to a restaurant, or playing a game, #2 sounds like a much better option.

I'm not totally convinced that particular compromise should win. The issue I have with it is whether political candidates should have to please everyone. Using that strategy would likely lead to a lot of charismatic but ineffective people getting elected. None of big issues would get any sort of resolution, because the candidates that the most people are ok with are the ones with the fewest controversial stances.

But, the alternative is the dysfunctional partisan mess we have in the US. If parties split government, nothing gets done (save a lot of finger-pointing and chest-thumping). If a single party controls government, "progress" is made, but that progress is likely to be extreme and to the displeasure of a massive portion of the electorate.

The "favorite betrayal" criterion is defined mathematically. In your scenario, as long as you approve Ideal, you are not betraying your favorite, even if you also approve Good. The only betrayal would be if you didn't approve Ideal. And in approval voting, there is no way others could be voting so that betrayal would be a good idea.

You are talking about a form of strategic voting — whether or not you approve Good. But it isn't favorite betrayal. In fact, it isn't betrayal at any level. All rational approval strategy (assuming a convex distribution over others' votes) is "semi-honest" in that you never approve a less-liked candidate but not a more-liked one. The only strategic choice is where to set your threshold, then honestly approve all candidates above it.

According to the Gibbard-Satterthwaite theorem, any voting method has some form of strategy, so in that sense the best you can possibly do is ensure that all strategy is semi-honest. Approval is optimal in this sense.

Using polling data to vote tactically is exactly what we want to avoid and gives undue power to pollsters (and the people paying them.)

Good winning over Ideal is a desired outcome when Ideal doesn't have the votes to win. That's one of the main attractions of non-plurality voting. The point of approval voting is not to rank candidates as Ideal > Good > Bad, that's what IRV is. Approval voting says, "These candidates are equally acceptable to me, so I'll be happy if any of them win over the candidates I didn't vote for."

Sure, but what the OP is saying is that in practice there's a massive tactical decision over whether to vote for "good" or not in a tight race, because "these candidates are equally acceptable to me" is a relatively rare situation

I don't think that's a rare situation at all. There's a large population out there that doesn't identify with R/D (in US politics), but does identify more closely with a 3rd party. But they never vote for them because "tactics". That doesn't mean those people wouldn't find R or D acceptable, it just means the're ideologically closer to a 3rd party. What AV is trying to get at is the situation where the most people are accepting of the outcome.

If a candidate is not acceptable, you don't vote for them. The situation you're describing is not one of selecting from Ideal, Good, Bad; it's the situation of selecting from Ideal, Somewhat Bad, Bad. If you're unwilling to vote for a candidate, they are by definition not "Good" to you. So you would just vote for the Ideal candidate in that situation.

In the worse case (everyone just votes for a single candidate), AV simply acts as FPTP. In the average and best case, the candidate that is acceptable to the most voters wins.

Look at it from the view of the US's extreme polarization: if I'm strongly for A, and you're strongly against A, nothing will be done if A wins. But I'm strongly for A, and we're both "meh" on B, then B might not get everything done that either of us wants, but at least the process won't completely break down.

But assuming most of these people consider R and D acceptable but actively prefer the third party (if they consider them equally acceptable FPTP isn't really depriving them of their ideal electoral choice), AV is inferior to most other non FPTP votes like IRV, which accurately represent their preference for the third party first, and the Rs and Ds only if that party can't win.

AV has a pretty significant "if I tick the good candidate box, am I impairing my ideal candidate's chances of winning?" problem.

IRV actually has the opposite problem: "If I vote for my ideal candidate, am I impairing the good candidate's chance of winning?" For instance, if it were Nader/Gore/Bush with 26%/25%/49%, and (hypothetically) all Nader voters preferred Gore over Bush but not all Gore voters preferred Nader over Bush, then voting for Nader instead of dishonestly choosing the "lesser evil" Gore would end up electing Bush.

No voting method can entirely escape both of these problems. But newer methods like STAR voting balance them against each other and manage to minimize both.

> No voting method can entirely escape both of these problems. But newer methods like STAR voting balance them against each other and manage to minimize both.

First you need to demonstrate that it's a problem in reality, there are very few times in history where it has been a real issue. Alternative to IRV are usually much more complex which is a terrible tradeoff for an almost entirely imaginary problem. Star voting has the same problem as star rating systems, almost everyone will score either a 5 or a 1.

almost everyone will score either a 5 or a 1

Then it will be similar to approval voting.

Previous comments complained that approval is bad because you cannot express detailed preferences, but you say no one wants to anyway? So then approval is ok?

These criteria are moot as regards popular systems. They cover cases where opinion is so mixed that no single-vote system can reliably pick a winner.

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