I was wondering if anyone has written or thought about early elimination of candidates for the single transferable vote method.
I am aware STV is not precinct summable, nor can it be made precinct summable, because the outcome relies on the flows of ballots. However, I can imagine situations in which, even with only some ballots received, it's mathematically impossible for certain candidates to reach quota, and so we might wish to eliminated them early.
Unfortunately, depending on the counting method, even the order in which candidates are eliminated can affect the outcome of STV. So I suppose I'm actually looking for an answer to the question: is it possible to tell when a candidate can't win and can't change the count by being eliminated later, and if so, how.
Also, a related second question: I believe I have heard that the Meek counting rule makes elimination ordering not matter, but I can't find a source. Is this true, and if so, could someone point me at a good proof as to why this is so.
I was doing this when I was hoping that Codepen embedding would be added to this forum, not sure if that is in the works. But I think if it was, having a standard format would gain a lot of traction here.
implies that k is random (because if k is fixed, then this probability would have to be either 0 or 1), but this is not stated.
Assuming that there are finite possible seeds and that each seed is equally likely to be chosen, we could write:
P(f(k, e) = c) = sum over s in S (I_c(f(s, e)))/|S|,
where S is the set of seeds, I_c(f(s, e)) = 1 if f(s, e) = c and I_c(f(s, e)) = 0 otherwise.
For many methods, |S| might need to be chosen in a way that depends on some limited information about the election, in particular the number of candidates (since for there to be an even 3-way tiebreaker, |S| needs to be divisible by 3 and so on). Methods that are "routinely" non-deterministic (such as random ballot) might also require the number of votes to select |S|.
However I think it's still useful to study such methods, as you never know how voters' moods will change, and maybe a simpler method like one I listed can act as a stepping stone towards a more complex one.
Yeah, I'm ok with that. There's certainly nothing wrong with studying them, and it seems to be a good method if complexity isn't an issue.
And I totally understand why they published it the way they did. If all they did was provide a reason to switch to a better existing method, well.... that would be a pretty lame academic paper.
I just felt that their lead up was very good, they called out two real problems with IRV, then suggest that there are only two options:
we must consider which of the following approaches is preferable:
(1) deciding almost every election in a simple way—just elect the Condorcet winner—and rarely applying a more complicated backup plan, perhaps more complicated than IRV, or
(2) deciding many elections with a fairly complicated iterative elimination of candidates and transferring of votes, which may cause controversy when failing to elect a candidate who beats every other?
Without mentioning a third:
3) deciding almost every election in a simple way—just elect the Condorcet winner—and rarely applying the tried and tested IRV method
I should add, there are two kinds of complexity. IRV is complex in that it goes through this messy process which seems to delay election results (presumably because of its lack of precinct summability? I mean, computers are fast so that alone shouldn't be an issue. )
But IRV is easy enough to explain, and it has already been put into legislation, so all you have to do is copy and paste from, say, San Francisco's law.
The other kind of complexity is what we have with Stable Voting. It is recursive and seems pretty hard to explain, especially in a way that can be put into legal code.
@rob I like this concept, I was also trying to consider the prospect of interstate pacts. In the case of less competitive states, an alternative voting system pact might be set to go into effect only once a sufficiently "large" group of states enter into the agreement (maybe measured according to their electoral college points as you suggest), which could easily negate the difficulties of diminishing federal influence when competing with a large FPTP block.
I think electors tend to be mostly faithful to the interests of their states (at least as far as can be determined by the gerrymandered districts), especially I think since they have the pressure of public scrutiny to more-or-less rubber stamp the results as they come in, and hopefully they also have some humility in their own decision-making powers and confidence in the larger process. I do think it gets problematic because entrusting electors to distribute their votes according to a less black-and-white indication of state interests does give them significantly more political power and responsibility that they will also need to be held accountable for. Generally I don't mind the concept of electors/representative arbiters as long as the incentives are sorted out. The way I see it all we can hope for is a system that consistently gives results that are good enough for national success, and if such a system does the job that'd be just fine with me.
I also think it’s a good sign that we’re at the point of discussing potential issues with real large-scale implementation.
@multi_system_fan Thanks. I'm working on adding some new things that will make it better, as well as tie it to the more traditional pairwise matrix view. For instance I want to allow both this thing, and the pairwise matrix to appear side by side, and support mouse hover effects for both of them. (you could also just view one of the other)
I did some hover effects on the matrix some years back, but it would be especially cool if you could have the two things side by side, and when you hover over a pair of candidates on the matrix, or the connector line between the candidates on the "mesh" display, it would highlight relevant things in both graphics at once.
(this is for voting for restaurants, as we did at a previous job I had where they ordered lunch for us every day and we'd always waste time arguing about which one to get each day)
I'm convinced that allowing people to visualize this stuff quickly makes it less scary to them. Nobody wants to sort through tons of data, a picture can make a big difference.
A pairwise matrix without colors and hover effects / animation is extremely hard to make heads or tails of.... but all the better if you can show a simpler-seeming graphic that has each candidate on it only once.
@jack-waugh Depends on the context. I haven't spent a ton of time scouring their site because it infuriates me, but in my limited experience, their hard data on what voters actually put down on ballots tends to be pretty reliable. Their claims about what different voting methods do and don't do are usually pretty bunk all around, though.
A pair of concepts that might have use when we think about cast ballots is "ballot token" and "ballot type". A ballot token then would be an individual ballot and a ballot type would be the equivalence class of all the ballots that say the same thing.
@cfrank Geez I hate being boring and just agreeing with @Andy-Dienes again, but.... yeah. Cardinal ballots (i.e. 0-5) I think are the easiest for voters. Higher resolution cardinal ballots are even better, where it is practical. It makes sense for the votes I am proposing we do in this forum, since it gets more information out of each voter. (0-10 with as many decimal places as you want)
But really, the best methods will just ignore the information that goes beyond ranking, or if they do use it, it is as a last resort.
I'm not overly concerned with bullet voting, as those voters are choosing to not use all the power granted to them. I wouldn't characterize it as a vulnerability, any more than people choosing not to vote, or choosing to equally rank candidates (if that is allowed).
As for what I think is most sellable to the public: probably ranked not cardinal ballots, simply because RCV is a thing. I think you could sell a Condorcet method while just calling it RCV. Bottom-2-runoff is good in that it is the smallest change to RCV. A simple version of minimax is good because it can be based on a pairwise matrix alone, which makes it most easily precinct summable.
Recursive IRV is.... well I'm kinda obsessing over it at the moment. But I won't say more at the moment until I understand it better.
@rob I think it would also be interesting to get votes on what forum users consider the most important aspects of a voting system.
It would also probably be useful to get some kind of informal map of different voting systems plotted on a spectrum of relative characteristics. I think a triangular spectrum of stable vs. simple vs. consensual could be a good place to start.