Topics created by cfrank

@masiarek you're right, the "97/90/81/74" sequence was from a different experiment. The plots I shared have the accurate rates for the relevant experiments.

Your point about information is also important, because PSRO involves repeated optimization against mixed opponent strategies with effectively complete information about the modeled strategic environment, and a real election is definitely not like that. Present elections are probably better represented by the bounded-strategy region than by the PSRO endpoint, which does strengthen the practical case for Smith compliance. One could still speculate that declining computational and informational costs may move real strategic behavior toward that endpoint.

Also to clarify, the initial post was based entirely on the PSRO adaptive-strategy results. The later "human-like" bounded-strategy experiments were prompted by curiosity based on your feedback, and they changed the interpretation in the opposite direction. Unless we assume extremely capable strategic agents with very strong coordination and information, the PSRO results probably aren't descriptively realistic except as an approximation to a highly sophisticated strategic limit. It is interesting and somewhat unfortunate, though, that most formally Smith-compliant method seem basically unable to maintain a comparative advantage over non-Smith methods under the kind of strategic pressure PSRO simulates, at least in terms of preserving the sincere Smith structure.

Your last point about the fresh runoff aspect is also correct. I did also try several Smith-compliant methods with fresh runoffs during exploration, but those should be compared again systematically. In my exploratory simulations, most fresh runoffs showed only marginal improvements under PSRO, except for IRV vs runner up. There may be some interesting theoretical reasons for this, see Durand et al. 2026, "Super Condorcet Winners and Limit Coalitional Manipulability of IRV"--this uses Impartial Culture. I did not try fresh-runoff Smith methods in the later "human-like" analysis, so that would definitely be interesting to test as well.

And thank you for sharing your code base! I want to dig into this kind of thing more.

@masiarek I think this is a useful way of looking at it: sincere, consistent voting should lead to Smith//Approval, as long as the Approval (or score) round is conducted after the Smith set is already known. So I would push back somewhat on “same winner, no second election,” because in SSVV, the Smith set (as well as the Score winner set) is known before the scoring of candidates in step (2.2). That sequencing can matter, even if sincere voting ultimately produces the same outcome as Smith//Approval, unless voters have genuine independent approvals per candidate.

In fact, it may be that most strategic benefits of SSVV are caused by the score/approval in the Smith set being informed by the Smith set itself, which would mean Smith//Smith-informed-Approval is a reasonable comparator, and it may be superior.

I also agree that in the singleton case with sincere voters, the validation step is redundant. If the Score set is ({A}) and the Smith set is ({B}), then a majority vote consistently with sincere preferences should choose the Smith set, since that same majority sincerely prefers (B) to (A). Probably, often the Score winner and Condorcet winner will coincide anyway.

Where I think SSVV differs most substantially from Smith//Approval is in strategic behavior rather than sincere outcomes, particularly when strategic voting changes the composition of the reported Smith set. Smith methods like Smith//Approval automatically commit the electorate to choosing from the reported Smith set, whereas SSVV does not—since voters first see the Score and Smith sets, the majority can decide whether they actually want to validate a Smith set that may have been distorted by tactical voting.

That may matter specifically for burial. Suppose burial changes the Smith set from something relatively compelling into a larger or stranger set. The burial strategy has succeeded in manipulating the pairwise structure, but has also changed the object voters are being asked to validate. Voters who prefer the Score winner to every member of the Smith set obviously choose Score, but even some voters who prefer one Smith candidate to the Score winner might choose Score rather than risk one of the other Smith candidates winning.

So I think your observation points toward an interesting strategic question about the method. Manufacturing a cycle can indeed get a candidate into the Smith set or remove another candidate from it, but unlike under Smith//Approval, that does not automatically get the preferred candidate into the decisive election, nor does it necessarily eliminate the buried candidate from consideration altogether, since the manipulated Smith set has to survive validation by majority vote.

I don’t know yet whether that additional hurdle is strong enough to make enough of a difference to warrant it, but I think that’s the main distinction from Smith//Approval.

My simulations so far have been exploratory and conducted interactively through ChatGPT 5.6-Sol, using spatial and nonspatial electorates with coordinated factions iteratively trying various score-compression, compromise, and burial strategies, so I would not treat them as an equilibrium analysis. They do suggest that the validation stage can sometimes neutralize successful manipulation of the Smith set (primarily accomplished through burial), but that result needs more systematic investigation.

I also just experimented with public B and hidden A, or revealing only the mean score of A rather than candidate identity. This mostly improved behavior even more, because manipulating the Smith set becomes more risky in validation if the Score winner set is kept hidden. But it opens a can of worms in terms of “information engineering” to improve incentives. Even if the Score “escape hatch” isn’t used, its mere existence changes strategic incentives.

@toby-pereira makes sense, it seems Condorcet/Smith methods consistently rise to the top in multiple ways.

I think Smith//STAR (implicit) as mentioned above has some problems, but I think Smith//Approval (explicit) as denoted in the electorama vote is a very good method despite taking two rounds. I’m half surprised Smith//Approval (implicit) didn’t do better.

I understand the general aversion to two-stage methods, but in the USA, we often effectively do that with primaries anyway, and it seems commonly used elsewhere. I think introducing alternative methods into party primaries could be pretty significant change in itself.

Maybe I'll get to this when I've gone through the jury thread more thoroughly!

continued here.

I think it's fine to have it here, but being a US-specific thing, I probably don't have much to say on it!

@robla The feedback I've heard from various stakeholders and reformers across the landscape is that many people oppose narrowing the field too much, which can prevent minor parties from having a meaningful voice in the general or being seen as viable. Being on the general ballot is an important part of the path to becoming viable for a third party.

For that reason, I think there's more consensus around advancing a set number of candidates to the general (instead of setting an approval threshold). Given that the voting method does fine with multiple viable candidates, I think advancing the top 4, 5 or 6 is totally reasonable. The upper limit is set by voter fatigue.

I think two stage Approval is generally the way to go for Approval elections. Approval Top-Two makes a lot of sense for jurisdictions that already have Top-Two, but all other things being equal I'd recommend Approval Top-5 or Top-4. I'm not sure if an even number is better or not, but that's something that should be studied and modeled for each system.

For STAR I generally recommend having a conditional primary, where the top 5 (or 4) advance. And, if less candidates than that register you just skip the primary all together, which saves a bunch of money.

@jack-waugh I’m imagining the decisions could be automated by making assumptions about the group utility and computing the mixed strategy Nash equilibria of the game.

The deepest problem there is the utility function, since it would be an aggregate utility of some kind that we would have to presume emerged somehow from the individual utility functions of the voters that constitute the group.

All of that is definitely questionable, I don’t believe in utility functions, but I’m unsure how else to proceed in putting this kind of situation into an analytical framework.

@toby-pereira your interpretation is correct, and yes with an even number of voters and non-strict rankings, ties can occur and that can induce non-uniqueness. For example there may be two separate, disconnected Condorcet cycles of different sizes in the Smith set for instance. The proof of uniqueness in general is probably less straightforward than just the intuition, I haven’t dug into it.

With ties in other methods, the resolution of ties is typically standard because the set over which the ties occur is discrete—uniformly sample one from among the tied candidates. But for maximal lotteries, when non-uniqueness holds there is a continuum of admissible lotteries as you indicated. The analog of a uniform distribution in this case would be using Jeffrey’s prior, which is why I think that’s the “right” way to go.

But yes it ultimately doesn’t really matter how the maximal lottery used is chosen since they are all maximal, but that’s also kind of the issue, because a choice has to be made.

Hi @cfrank - as @Toby-Pereira mentioned, there is electowiki for consolidating ideas from over here. At this point, I'm already relying on some pretty substantial help from LLMs for the tools I use to put together the electorama news. The latest draft edition is here:

https://electowiki.org/wiki/ElectoramaNews/2026-January

The prose in the ElectoramaNews is pretty much all mine, but the code I've "written" to provide the summaries of each of the forums (like my summary of this forum) was mostly generated from a vibecoded script I run periodically. My hope is that I'll be able to provide a more-and-more sophisticated summary of the various forums every month, and maybe I can have my tools call the LLMs to provide the summaries of the discussions. Right now, the "summary" in many sections is basically just a link to every forum post or email or whatever.

Hopefully, by regularly publishing ElectoramaNews, we'll be able to drive some traffic over here to the Voting Theory forum.

@toby-pereira I see, it seems that the properties of maximal lotteries related to participation aren’t what I believed they were. Looking into this, I misunderstood the definition of an (x,y)-improvement, this is swapping the adjacent positions of x and y in a ballot that already exists in the election, not introducing a new ballot where x>y.

That’s unfortunate, but also makes sense.

@cfrank If others have examples, simulations, or citations for my claim that "over time the two opposing factions become more and more polarized” I'd love to have those on hand too. I'm not sure I'm referencing any one thing I've read or heard in particular, but more putting multiple things together to get the big picture.

On the math alone I think you're right that the center is an important block for the two parties to court as well, but in practice I think that that incentive is outweighed by the other perverse social incentives to demonize the other side, to punish "traitors" considering switching, and so on.

Cancelling people who question the party line costs center voters, but it also discourages others from following. I think this was the subliminal Democratic Party tactic over the last decade that paid dividends for a while but then ultimately lost them the "big-tent" advantage and the presidency. I'm not saying it was an intentional strategy. There are big cultural forces at play here. That's obviously my own personal opinion.

Back on topic: As the narrative gets dominated by two polarized factions and the middle is silenced, the real middle (the center of public opinion) almost ceases to be a part of the political spectrum because it's doesn't actually map on to the left, right, and swing voter boxes.

Identifying and presenting consensus win-win policy and then getting it passed is the goal. We need to incentivise and empower that one way or another.