Topics created by cfrank

@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 yes and that’s interesting in itself. I thought it would be about compensating disaffected majorities since that’s what the Chatbot said lol

@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.

@cfrank I’m bringing this topic up again, because it seems necessary to consider the implications of how alternative systems at lower levels of government translate effects upward, especially when higher levels maintain a winner-take-all style.

For instance, in a presidential election, say we adopt maximal lotteries (Condorcet compliant) to generate social choice rankings per state. For this to translate nicely to the federal level and accommodate the electoral college, the natural extension seems to be another maximal lottery where voters are states casting ranked choice ballots with electoral college weightings.

I think this could be a viable system in principle, but the question is about how feasible the structural and institutional changes would be to make.

The same sort of question comes up with approval voting. Essentially, my worry is that without upper-level criteria met, lower-level changes, while still locally impactful and potentially inducing long run changes, would not translate effectively upward in the short term, and may even destabilize upper levels of government.

@cfrank I revisited this concept, and I'm quite sure now that participation will not hold even with careful adjustments to the method. Several simple counterexamples were discovered involving the generation of a top Condorcet cycle. C'est la vie.

@jack-waugh but that’s always the tradeoff with score systems, which is why people bullet vote and/or min-max (translate to approval). I totally understand what you’re saying though.

I’m not saying the “Condorcet adversary” should be the score winner, just that they should be a strong alternative. Your approval-seeded Llull ballot could accommodate an approval winner as the Condorcet/Smith-method’s adversary, for example.

I think a “rank with approval cutoff” ballot makes sense. Then there could be the approval winner, and, say, the B2R (Smith compliant) winner, followed by an independent head-to-head.

https://forby.io/

@matija yeah, it seems that there were many factors that converged. I guess we never know what might have been or might be especially instrumental per se in the rise of anti-democratic regimes. As we’re seeing now in the USA, even supposedly “stable” vote-for-one systems are vulnerable to the most basic kind of fragmentation, namely splitting in half.

I’m not sure how stable these systems are then, considering the bipolar oscillations of government. The same gridlocks that make legislature impotent appear in a more blatant form. To me, that means vote-for-one is even less desirable than previously imagined, since even its claim to purported stability is moot.

Thank you both for keeping an eye on this and deleting the spam. If you have suggestions for the settings I'm open to whatever seems like the best option. I don't have strong opinions either way as long as people like you both are taking care of it if it does occur.

If that wasn't the case I'd say we should look into other options.

As said, voters can often face a dilemma of whether to approve someone or not. What counts as approval etc. If I approve my second favourite candidate, what if it turns out my favourite could have won after all?

Also under ranked voting, ranks have less of an obvious meaning so a voter doesn't have to feel they are explicitly endorsing a candidate when they rank them over someone else. Say my preference order is A>B>C and B and C are the frontrunners, but I hate both B and C while preferring B to C. I might happily rank A>B>C. But to explicitly approve B might be a step too far, even though it's the strategically optimal vote for me.

Also, it really invites people to say that it violates one person, one vote, and you have to explain why it doesn't.