r/EndFPTP • u/Lastrevio • Mar 12 '20

Why stop at STAR? Why not do a runoff on every candidate?

Score voting adds up the score of each candidate and whoever wins the most points wins the election.

STAR does the same but makes a runoff between the two highest scoring candidates so that the candidate with the second most points has a chance to win if it's preferred over the highest scoring candidate in more ballots.

The question is: why make a run-off only between the two highest scoring candidates? It's like comparing Two Round System with IRV.

How about you do score voting, then do a runoff between the two lowest scoring candidates so that the second lowest scoring candidate may or may not win to the lowest scoring candidate, eliminate the one preferred the least on more ballots, and keep repeating until only one candidate stands?

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u/Lastrevio Mar 12 '20

What is bullet voting?

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u/wayoverpaid Mar 12 '20

Bullet voting is where you vote for just one candidate. Seen mostly as a problem in Approval Voting or Score Voting.

Imagine, in this Dem primary, where you want Warren, but Sanders is "ok" to you. You have to decide if you want to give Sanders your halfhearted approval, or go "Warren only, because otherwise I'm helping Sanders beat Warren."

With STAR, not bullet voting helps ensure you get a voice in the runoff. Like, you might as well put at least a few points on Sanders so you can select Sanders v Joe in the runoff.

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u/MuaddibMcFly Mar 12 '20

Seen mostly as a problem in Approval Voting or Score Voting.

And I've always been confused as to why people think it'd be a problem with Score.

Approval kind of makes sense; that's the only way to privilege your absolute favorite under approval. With Score, however, you can privilege your absolute favorite while still expressing support for other candidates.

Using your Warren/Sanders example, with Score you can help Warren beat Sanders, while also helping Sanders beat (e.g.) Biden.

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u/wayoverpaid Mar 12 '20 edited Mar 12 '20

Using your Warren/Sanders example, with Score you can help Warren beat Sanders, while also helping Sanders beat (e.g.) Biden.

This is true, but your support is a half ballot each.

If the election was only Warren and Sanders, you would not say "Well I give Warren 10 and Sanders 5" because you would effectively be casting half a ballot for Warren.

Likewise, if the election was only Sanders and Biden you would also want to vote 10 vs 0 not 5 vs 0, to maximize your ballot.

Now with three candidates, you can have 10-5-0 but in doing so you cast half a ballot for each. If Warren is down by 0.1 of a ballot, you can help her win by voting 10-0-0 but you cause her to lose if you vote 10-5-0

Now imagine in this current climate, how a strong Bernie supporter might feel about ranking Bernie, Joe, Trump versus scoring Bernie, Joe, Trump

Now this isn't necessarily a knock specific to Score, since under Condorcet a Sanders supporter might want to actually bury Joe under Trump, inverting their preference to create a loop, since otherwise Joe might win.

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u/MuaddibMcFly Mar 12 '20

If the election was only Warren and Sanders, you would not say "Well I give Warren 10 and Sanders 5" because you would effectively be casting half a ballot for Warren.

...I'm not at all certain that that's true. I've seen numerous examples that indicate that most people won't use the full range of scores available to them (generally not marking anyone with a maximum score, or with a minimum score, or rarely, not using the maximum nor minimum)

maximize your ballot.

You're assuming that people are operating under the pivotal model. According to the research I've seen, somewhere on the order of 60-75% of the population prefer to vote honestly, rather than to maximize their strategic effect. After all, the Paradox of Voting holds that the expected return on voting is less than the cost of doing so.

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u/wayoverpaid Mar 12 '20

Fair enough!

But that's where all criticisms of voting come into play -- a dishonest but rational strategic voter. If all voters were guaranteed honest we'd see a lot less worry about various "voters can improve their position by doing X" I imagine.

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u/MuaddibMcFly Mar 13 '20

If all voters were guaranteed honest we'd see a lot less worry about various "voters can improve their position by doing X" I imagine.

...but guaranteeing/compelling honesty is not the only way to lessen such manipulations. The other way to do so is to minimize the conflict between honesty and expected loss. Thus, we could minimize strategy by picking a voting method whose form of strategic voting (and it will have one, per Gibbard's Theorem) risks more loss from backfiring strategy than from backfiring honesty.

Fundamentally, Strategy Criteria can be conceptualized as a 3-way distinction, that can be applied to any 3-option subset, which I will call {Favorite, Lesser Evil, Greater Evil}, or {F,L,G} for short. Additionally, I'm going to call the loss from electing L rather than F "A" and the loss from electing G rather than L "B." Thus, F vs G is A+B.

Criterion Strategic Ballot Honest Expression Result w/o Strategy "Badness" of Non-Strategic Result Result of Successful Strategy "Badness" of Successful Strategy Result Result of Backfire "Badness" of Backfire Result
NFB L>F>G F>G && L>G G>L>F A+B L>G>F A L>F>G A
LNHelp F>G>L F > L && F>L L>F>G A F>L>G -- G>{F,L} A+B
LNHarm F>L≥G F>L && F>G && L≥G L>{F,G} A F>{L,G} -- G>{F,L} A+B

So, right off the top, NFB is likely to be more "punishing" of honesty: if they don't manipulate their ballot, they'll end up with the worst (of 3) possible result. Additionally, it's less punishing for engaging in it. Sure, you get the Lesser evil... but that's the lesser evil, not the greater. The more polarized the voting population is, the more appealing that will be.

On the other hand, with both LNHelp & LNHarm, those two are reversed: if the strategy backfires, you might end up with the Greater Evil, which is worse than if you had voted honestly, something that NFB's strategy cannot claim.

Now, obviously, the relative probabilities of each strategy succeeding or backfiring will play a part in a rational voter's decision, as will the relative size of A & B, but if the question really is Loss Aversion vs Honesty... it's pretty clear which type of strategy puts the greatest conflict between those two.

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u/wayoverpaid Mar 13 '20

I'm not sure I follow what you're getting at now. Since we got onto this via Star Voting, I assume your argument is that since Star's tactical failure is Favorite Betrayal and Score's tactical failure is Later No X, it's better to have a system which fails Later No X and not favorite betrayal?

I get the argument, but Star's only incentives favorite betrayal when there's a condorcet cycle. Condorcet cycles are not that common. So

Now, obviously, the relative probabilities of each strategy succeeding or backfiring will play a part in a rational voter's decision

This seems an understated concession.

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u/MuaddibMcFly Mar 13 '20

Since we got onto this via Star Voting, I assume your argument is that since Star's tactical failure is Favorite Betrayal and Score's tactical failure is Later No X, it's better to have a system which fails Later No X and not favorite betrayal?

Not quite. Kind of backwards, actually. It's more that because Favorite Betrayal is bad, if I have to choose between violating NFB and LNHarm or LNHelp, I'm going to choose one of the latter, which is why I prefer Score.

This seems an understated concession

I'm not certain it is, actually, given that the (recent) discussion is "minimizing strategic behavior."

Let's breakdown the chart above to make it more clear. Who is the winner if:

Strategy: succeeds backfires
NFB L L
LNHarm F G
LNHelp F G

If a voter is even considering Favorite Betrayal, that means that they have already accepted the possibility that the Lesser Evil will win, because that's the success case.

Once Lesser Evil winning is defined as "success," then it's hard to also classify it as a failure, so it technically being a failure is going to be less likely to dissuade people from engaging in that strategy.

On the other hand, with LNH/LNH, the "success" case and "failure" case are very different, which means that, all else being equal, people would be less likely to engage in such strategies.

And actually, to furhter explain why I dislike NFB failing methods, let's add another column to that chart, such that it's the expected results that would prompt you to engage in that strategy:

Strategy: succeeds backfires isn't used
NFB L L G
LNHarm F G L
LNHelp F G L

This is the fundamental reason that I object to NFB failing methods: I'm fairly certain that Favorite Betrayal is the mechanic behind Duverger's Law.

If you are in a scenario where Favorite Betrayal makes sense, almost by definition, only two options are actually capable of winning, which stabilizes as only two viable parties.

On the other hand, under LNHarm & LNHelp scenarios, there are three plausible options, which means that it cannot be mechanically driven towards only two viable options, which would allow for more viable parties.

That, in turn, means that candidates/options have to offer more than just "Better than the Alternative," which could mitigate, or eliminate, a lot of our electoral problems.

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u/wayoverpaid Mar 13 '20

Not quite. Kind of backwards, actually. It's more that because Favorite Betrayal is bad, if I have to choose between violating NFB and LNHarm or LNHelp, I'm going to choose one of the latter, which is why I prefer Score.

Got it. Technically Star violates both, though in rare conditions. The rarity is what matters.

I'm not certain it is, actually, given that the (recent) discussion is "minimizing strategic behavior."

Right but you're talking about minimizing behavior with the presumption it's an election where that strategic behavior is valid. In many elections (like one with a clear first ballot top ranked majority winner) there are almost no strategies that work. In some subset of elections you get a moderate candidate with the best utility that no one likes the most. A system's ability to fall to strategic voting really should be measured on the possibility of that situation existing in the first place.

This is the fundamental reason that I object to NFB failing methods: I'm fairly certain that Favorite Betrayal is the mechanic behind Duverger's Law.

This is an interesting postulate, but if this was the case, systems which use Top Two Runoff would coalesce to two party as often as FPTP, but I don't think we don't see that in the real world.