I'm just going to recenter that the entire basis of Approval as an effective and potentially-immediate compromise is that it doesn't require new ballots, machines, meaningfully different LEO procedures, noteworthy voter education, federal process certification, revised audit procedures, etc.

You just flip a switch. Uncheck the "discard overvotes" box, rewrite one sentence on the instructions line (in each language), and make sure the LEO guidance on tabulation reflects all this. The end. $0.

Extending the proposal to anything that actually requires a new ballot/process/everything defeats the entire point of the exercise. For that implementation cost, you could do practically any constitutionally valid single-winner system.

@casimir

A BTR monotonicity failure is pretty specific (4+ cycle dependent) and requires a plurality (first-rank) standing like so:

1. Paper Sr.
2. Paper Jr.
3. Scissors
4. Rock

The Paper candidates are both currently relying on Rock to take out Scissors early for them.

However, if some of Paper Jr. supporters switch their first-ranks to Paper Sr. (with no other changes) the first-ranks may now look like this:

1. Paper Sr.
2. Scissors
3. Paper Jr.
4. Rock

In this new ordering, Paper Jr. takes out Rock early, preventing Rock from taking out Scissors. Now Scissors wins.

This is, of course, an extremely specific scenario--and a good illustration of why focusing on absolute criteria is misleading. No one should care that something like BTR or Stable Voting are non-monotonic one-in-a-gazillion elections.

(On the other hand, competitive partisan primaries are egregiously non-monotonic all the time and no one bats an eye.)

@jack-waugh

Sort of; engineering is famously quantitative, wrestling with the myraid and complex nuances of reality. Most engineering constraints are built on pragmatic operational assumptions, like a realistic range of environmental conditions.

Constraints compete with standard criteria when they are too broad or abstract--"there should be absolutely no radioactive material allowed on premise" without specifying a tolerable level is banning all foods containing potassium, such as bananas. A set of food safety guidelines that that obsesses about radioactivity instead of saturated fat, processed sugars, overall caloric intake, or the many other more relevant factors would be pretty useless. So would a set of dietary standards asserting one-size-fits-all solutions that do not account for one's age, body composition, physical activity, or health conditions.

In programming, we see this with algorithm analysis a lot. Much academic emphasis is placed on a complexity classes on various algorithms, such a proving that mergesort has a O(n log n) worst-case performance while quicksort suffers from O(n^2). Yet in most empirical applications a software engineer knows they can get better performance out of a quicksort; the lower memory usage significantly decreases the circumstances that would require cache misses. (Just as your procedure for sorting papers might change depending on the size of your desk or how many hands you can use; these "harder" and more relevant constraints might be overlooked if one is fixated on comparison efficiency in a theoretical vacuum.)

So that brings us back to voting.

One of the more classic "absolute" criteria is participation: "Your participation in voting (at all) must never hurt your favorite candidate(s)."

The issue is that reality fails the participation criterion.

A Condorcet cycle is a thing that could conceivably exist in reality--it's super rare, but it could. And if it does, it's a consistent truth in that reality regardless of how you count the votes--it's a property of the electorate, not the method of measuring it.

And whenever there is a Condorcet cycle, it's possible that your vote for Scissors > Rock > Paper could be the pivotal deciding vote that makes everyone realize that Paper doesn't beat Rock. If this new information you have provided reveals that Rock beats everyone, your vote implies Rock should win--even if Scissors (your favorite) was winning before.

Any method sufficiently sensitive/accurate enough to reflect the possible existence of cycles in reality will automatically fail the participation criterion. This means that all Condorcet methods fail the participation criterion and all methods that pass the participation criterion must willfully ignore the possibility of cycles.

Another similar criteria is monotonicity--does improving your vote for a candidate never possibly hurt them, and reducing it never possibly help them? This one is more complicated. Methods that eliminate candidates one-by-one are typically non-monotonic. However, eliminating candidates one-by-one grants the most resistance to strategy and full immunity to clones.

Broadly speaking, I believe the latter is more important than monotonicity, and by several orders of magnitude. This is in part because simply being non-monotonic does not automatically imply a certain frequency of non-monotonic violation. I mentioned that BTR and Stable Voting are technically non-monotonic (both eliminate candidates one-by-one after all), but the odds of either exhibiting a non-monotonic situation are nearly astronomical. (And zero unless there are 4+ competitive candidates, or if the electorate preferences are single-peaked.)

I also mentioned the partisan primary elephant-and-donkey-in-the-room. It's frankly exhausting to discuss monotonicity's relevance in rare edge cases when our existing competitive partisan primaries are outright non-monotonic around a full 33% of the time. (That's about how often some of the primary votes hurt themselves, and would be ultimately more effective if cast "backwards" for candidate(s) in the other party.)

It's like hearing people argue over which brand of premium gas to buy for their car, when they are 6000 miles overdue for an oil change.

@jack-waugh

BTR with a cardinal ballot is the functionally the same as BTR with a ranked ballot so long as you have enough score options to distinguish all candidates. It will only resolve differently in cases where you both have a cycle and the ordering of iterated scores is different than iterated top-ranks, which is extremely specific.

And BTR is, pretty good. It's natural results are identical to Smith//Plurality outside of a 4+ cycle. This means the strategy resistance is the same as Smith//Plurality with 3 competitive candidates, and similar-but-slightly-better with 4+. It's functionally cloneproof and effectively monotonic.

I would categorize BTR as a hybrid method, and it continues a pattern of virtually all serious hybrid methods holistically outperforming all non-hybrid methods. Hybrid vigor truly is the law of the jungle.

@jack-waugh

I think you have the wrong guy. Insofar as I spoke about monotonicity, I was making the opposite argument.

If a court wishes to "ban non-monotonic voting methods", they would first have to declare all partisan primaries illegal.

@lime said in New voting method: Linear medians:

Well, there you go: Buttigieg could've either run as a write-in, or he could've launched a third-party candidacy instead of joining the Democrats.

As part of an experiment to see if it's possible for the Democrats to hate someone more than Trump, or just to set a Guinness World Record for biggest political career implosion?

@lime said in New voting method: Linear medians:

Also, I don't think sore loser laws apply to presidential candidates in most states, since RFK Jr. is on the ballot in lots of them right now.

Worm-brain man dropped out of the Democratic primaries last October, about 4 months before the first state primary.

He announced his independent candidacy the same day, and sore loser laws were his motivation for the preemptive move.

@lime said in New voting method: Linear medians:

That's the perfect information assumption: the post-hoc manipulability rate checks whether a one-sided strategy could possibly succeed, if a group of voters had perfect information and perfect coordination (which requires knowing all other voters' preferences).

Well, yes and no.

Pure compromise+burial is the optimal strategy in almost all methods, and essentially the only strategy in many. It requires minimal polling accuracy, voters find it intuitive, and is easily executed via ballot access given sufficient political infrastructure. Some authors have refered to it as "the trivial (but sufficient) strategy" or "the baseline strategy."

It is difficult to think of an election where either party failed to execute a compromise strategy at all. At best there are many examples where party leadership or public factors led to a greedy losing strategy, but even in the age of Trump endorsing Dr. Oz those cases are rare. And even then, these strategies didn't backfire, they were just probably worse than a better one--if the Pennsylvania Republican party nominated no one and told all their voters to just vote their honest gut, Fetterman wins even harder.

Tideman does include, in the papers I am thinking of, edge case strategies for applicable methods: pushover for IRV, extreme Borda optimization, and the same for Baldwin's. (I don't think he quantifies entry vulnerabilities, other than acknowledging them.)

I agree more with you that these edge cases can plausibly be disregarded. The very idea of anyone executing a pushover strategy is absurd--you would need exact polling, exact coordination, no counter-strategy, and face a worst-case backfire if you get any of that wrong.

Borda's most extreme solutions are similar and sort of moot contextually--it's one of the most vulnerable methods in existence to just basic compromise+burial, so who cares if some esoteric NP-hard ballot calculation can technically squeeze out a couple more percent? Whether or not we count these vulnerabilities, Borda is still a poor method no one should use.

Baldwin's is a ying-yang similarity, a method that is practically only impacted by said esoteric NP-hard strategies. (Simple compromise-burial does almost nothing.) These non-trivial Baldwin strategies are the hardest to calculate of any method, even with perfect [everything]. I think it's a fair and interesting academic question to quantify these, but I'd also raise an eyebrow (or two) at anyone listing them as a point against Baldwin's.

I don't know that Tideman including these edge cases would upset anyone other than perhaps a FairVote IRV-defender-of-the-faith. If anything, the biggest objection would be that he does not include entry/teaming.

@jack-waugh

First, I'll point out that Fargo is raw Approval and St. Louis is Approval-into-Runoff. These behave very differently. (Hint: the latter is way better, and is basically STAR's twin brother.)

Second, I am in complete agreement that the best path forward is simple improvements to IRV.

But you can do even simplier and better than BTR. You just slap a Condorcet check on it, the end.

Your ballots are now precinct summable and monotonic outside of cycles. The results are incredibly straightforward, ("Here's how much the winner beats everyone else by:") yet it also produces a complete pairwise matrix for any campaigns or political scientists who want it. It's 100% Condorcet efficient; no more center-squeeze, maximimally resistant to polarization. It's fully cloneproof.

And best of all, it exhibits the highest strategy resistance of any method. (Only Baldwin's comes close.)

BTR is good, but it should be regarded as strictly inferior to the more straightforward Condorcet//Hare alternatives unless you are somehow at a loss for computational speed.

@k98kurz

This is sort of a seperate question, even if it is a logical next one.

Think of it this way: We are talking about electing legislators with a new voting system. We are not talking about the legislators using a new voting system to vote on bills. That might also be a good idea, but it's an entirely seperate matter.

The electoral college is similar. Each electorate elects a (single) desired target for their state's delegation to vote for. We're not talking about how the delegations themselves vote. That might also be a good idea, but it's an entirely seperate matter.

Of course, there is more reason to address the latter than the former; legislature are deliberative bodies, while the Electoral College as currently set up is basically not. But the point is they are legally and functionally an independent system. In both examples, there is little reason for the representative body to conduct itself in the exact same way as the preceeding public vote.

@lime said in New voting method: Linear medians:

Pure cardinal voting strategies are almost-always sincere, i.e. they never involve rating a worse candidate higher than a better one. (This is Brams and Fishburn's terminology.)

Right, but this is a non-functional defintion to use for anything. It's asserting that the ballots:

Sanders - 10
Biden - 10
Trump - 0

and

Sanders - 10
Biden - 0
Trump - 0

...are equally "sincere" applications of identical preferences, simply because there is no inversion.

I do think this is a broader semantics issue, in which referring to different cardinal allocations as "strategic" or "honest" is too rigid; both lead to circular definitions. In my work, I introduce a middle layer and use the word "disposition" to refer to an individual voter's natural mapping of their (honest) preferences to a cardinal ballot. (I.e. we might have exactly identical preferences, but my 6 is your 7. We just say we have different dispositions, rather than asserting that only one of us is honest (and the other is a liar), or insisting our unequal ballots are identical.)

@lime said in New voting method: Linear medians:

I thought we were asking "why didn't Buttigieg run in the general?" to which the answer is "he wouldn't get any votes, because the party signaled to voters they should coordinate on Biden instead."
However, this is because the Democratic nomination provides information,

No, it is literally illegal for Buttigeig to run (as a non-write-in) in 47 states. The primary is a legally binding mechanism under sore loser laws. It is far from being a merely helpful suggestion.

(You do have edge cases who did revolt as a write-in (Lisa Murkowski, Byron Brown) in extenuating circumstances. Murkowski had the largest geographic bloc of independent voters in the US supporting her, and Byron's race had no other opponent to spoil + the tacit backing of the state Democrats. Both were incumbents, and decently liked. Both, when successful, became deeply despised by the non-centrists of their party to this day; while McConnell eventually came around as a Murkowski ally, at the time he and the rest of GOP leadership denounced her and stripped her position as vice char of the RSC.)

@lime said in New voting method: Linear medians:

All of the assumptions in Tideman's model are wrong:

I'm not sure that Tideman ever asserted a model in which it is assumed that anyone is acting with perfect information. (That seems pretty off-brand for him tbqh) Most his publications I'm familiar with (pertaining to strategy) merely address whether there exists possible successful one-sided strategies for a given context.

Tideman is pretty humble in interviews, and is quick to dismiss questions of human behavior on grounds that he is not a political scientist.

@lime said in New voting method: Linear medians:

On the other hand, I don't think this is all that irrational. It's all at least somewhat-reasonable behavior from Republicans, if they thought Begich and Palin had about the same chances of winning. That makes sense if you have:

Elections decided more by national environment than individual candidate quality,

I think this is the lynchpin. This was 100% a very real gap that the lower 48 thought Palin would win, and no one in Alaska thought she had a chance.

I'm pretty familiar with Alaska and its politics for a few reasons (not a resident though), and man was the mood on the ground sour. Palin hovered at around a roughly -45% favorability rating. She was seen as a quitter, someone who used Alaska as a stepping stone to TV shows and fame in the lower 48. And this was a pretty widespread rural sentiment, specifically. As Palin got endorsements exclusively from big names in the lower 48 (while Begich got the support of virtually every conservative group and legislator in Alaska), it only cemented this attitude. Even the Trump and Haley endorsements did surprisingly little to the polls.

But it did further advance the attitude outside of Alaska that wow gee, Palin must be a strong candidate.

Palin did outperform her polls in the special election, and her brutal attacks on Begich certainly made an impact on his numbers. But I can't think of a comparable US election where a candidate could come so numerically close yet have such a miniscule chance of ever winning.

@lime said in New voting method: Linear medians:

In that case we should probably just stick to approval voting (which is simple and sincere).

Wait what? Voting methods don't get less sincere than pure cardinal.

@lime said in New voting method: Linear medians:

I do think this needs to be emphasized: if you think voters engage in something close to fully-informed coalitional manipulation strategy, that implies the Condorcet winner always wins (no matter the system). That seems wildly unrealistic to me, since I'm pretty sure I've seen lots of elections where the Condorcet winner lost.

I think there must be some misunderstanding--this is the point I was making.

It doesn't matter much if optimal outcomes of strategic equilibirums are desirable. Imperfect strategy commonly leads to results that fall short of that, and even when it doesn't still leaves a trail of bloodstains and broken noses.

@lime said in New voting method: Linear medians:

That's why I think we need to be very careful to distinguish situations involving cooperation to coordinate on a single equilibrium (e.g. Democrats settling on Biden) from the idea of true "group strategy".

No, this is absolutely verbatim what a coalitional strategy is.

There is no strategy more pure than the selection of a party nominee, and no enforcement mechanism more straightforward than an agreement to only put that candidate on the ballot.

@lime said in New voting method: Linear medians:

since we have plenty of cases like Alaska 2022 where Republicans all should have supported Begich.

They should have! There are many, many, many, many partisan primaries in which a partisan echo chamber got greedy, overplayed their hand, and nominated an extremist who would lose rather than a moderate who would win. This has happened with both public primary electorates and the old days of men in backrooms with cigars.

Partisans and their donors are motivated to push the least-moderate candidate they think will still win, and it's easy to get that calculation wrong. Polls are weak, voters are fickle, and partisans are infamously prone to delusion.

Palin is a particularly extreme case of this. Her special election campaign was not only founded on the misconception that she was a good candidate, but spent the entire time attacking... Begich! Then the results are in, the false-dream was exposed, and the general election was looking far more difficult (pro-choice winds and higher turnout favored Peltola), Yet She Persisted. (Ultimately Begich would have lost in the general all the same, but it would have been a much better swing at the ball.)

Sarah Palin's House campaign was one long exercise in irrationality, and a great example of specific groups/leaders being pathologically incapable of compromise.

@isocratia

@isocratia said in score interval: score with additional protection against the chicken dilemma:

Isn't the chicken dilemma kind of a myth? It contradicts the theorem that approval and score voting elect the Condorcet winner under 100% tactical voting.

Perfectly-informed, perfectly-rational tactical voting generate a Condorcet winner. This is true of all (relevant) voting systems (including plurality), and is the inherent nature of a Condorcet winner.

The problem is that a very wide variety of factors stand in the way of "perfect." There is decent hindsight evidence suggesting that Gary Johnson would have been the Condorcet winner of the 2016 US Presidential election. Consider the informational, institutional, and political barriers preventing the Democrats from nominating Gary Johnson, advancing a Johnson strategy instead of a Clinton strategy. We'd sooner have held the election on Jupiter.

In prisoner's dilemma, it is just as rational for two criminals who have telepathy to have each other's backs as it is for two criminals who are isolated to sell each other out. Neither outcome should be surprising.

Chicken dilemma is similar. If Sanders voters have perfectly single-peaked preferences and only care about maximizing their preferences in this one election, then they will line their perfectly-rational and well-behaved butts up behind Clinton to beat Trump.

But man, political hostage-taking is so in right now. "No, screw that, you elect me if you don't want the other side to win!" This approach might even be mathematically rational if your previous assumptions about this person's utilities were wrong. Maybe Sanders and his voters care more about influencing future elections than winning just this one. Maybe Matt Gaetz just want to run for Florida Governor. Maybe someone is a full-on accelerationist, who believes the best way to address problems is to first make them worse.

I can't think of a point in American history where intra-group picking of "BETRAY" has ever been so prolific as it is right now.

I'm just going to recenter that the entire basis of Approval as an effective and potentially-immediate compromise is that it doesn't require new ballots, machines, meaningfully different LEO procedures, noteworthy voter education, federal process certification, revised audit procedures, etc.

You just flip a switch. Uncheck the "discard overvotes" box, rewrite one sentence on the instructions line (in each language), and make sure the LEO guidance on tabulation reflects all this. The end. $0.

Extending the proposal to anything that actually requires a new ballot/process/everything defeats the entire point of the exercise. For that implementation cost, you could do practically any constitutionally valid single-winner system.

@chocopi

BTW, my sims include "STAR3", which is literally BTR via Score among just the top 3 candidates.

You can see it's extremely similar in batch simulated results to BTR and Condorcet//Plurality or Smith//Plurality.

@jack-waugh

BTR with a cardinal ballot is the functionally the same as BTR with a ranked ballot so long as you have enough score options to distinguish all candidates. It will only resolve differently in cases where you both have a cycle and the ordering of iterated scores is different than iterated top-ranks, which is extremely specific.

And BTR is, pretty good. It's natural results are identical to Smith//Plurality outside of a 4+ cycle. This means the strategy resistance is the same as Smith//Plurality with 3 competitive candidates, and similar-but-slightly-better with 4+. It's functionally cloneproof and effectively monotonic.

I would categorize BTR as a hybrid method, and it continues a pattern of virtually all serious hybrid methods holistically outperforming all non-hybrid methods. Hybrid vigor truly is the law of the jungle.