If there are only two candidates, could FPTP be improved upon?
Most people -- at least in the general public -- tend to think that if exactly two candidates are running, there is nothing better than simply voting for your favorite, and the method will choose the one with the most votes.
(This is assuming that the election is independent from all other elections. You are just voting for these two candidates, nothing more.)
I saw in this thread -- https://www.votingtheory.org/forum/topic/141/mars-mixed-absolute-and-relative-score -- this set of score ballots for a two candidate race:
99: A B 1: A B
@Casimir noted that "Here 99% prefer A over B, but score elects B." (I should mention that he also noted that it was a contrived, ridiculous example)
****** Pairwise wins ****** A: 1 B: 0 ****** Score ****** B: 100 (1.0000) A: 99 (0.9900) ****** STAR ****** A: 99 B: 1
In the real world, of course, those 99 people aren't going to bother going to the polls just to give their favorite candidate a 1 out of 100. So if they voted a bit more smartly, Score would pick the same candidate as FPTP, Condorcet, STAR, etc. (in this case)
So anyway, the question is, is FPTP effectively "perfect" in the case of there being exactly 2 candidates? If we can agree on this, I think this has implications for elections with 3 or more candidates.
If we can agree on this,
I think this has implications for elections with 3 or more candidates.
What might those be?
rob Banned last edited by
What might those be?
I come around to that, but I don't want to jump ahead of myself quite yet. I don't want to bias anyone else who wants to weigh in on it.
Anyway I'm glad to know that you agree that you agree that the winner in a two candidate race should be the one with the most votes. It sounds obvious, of course, but I think it is significant.
We talked about a culture of shooting things down and I don’t want to be that guy, I hope this doesn’t come off that way and I don’t think it should, I just want to express my own personal thoughts about this topic. I do think what “improvement” means exactly is not clear, and that it depends on your paradigm. We obviously all mostly agree about what improvement entails, but I have the feeling that we lack a sufficient consensus and maybe we can address that with this thread opening the discussion.
For example, it is not clear what is meant socially by the indicated score ballots. If the second-lowest score indicates, “I like candidate A more than candidate B, but my preference is very weak, so if there are any people who would strongly prefer B to A, I am willing to forego my marginal preference for their benefit,” then it seems to me that the score ballot actually may be an improvement, because it somewhat takes into account more nuanced social relationships implicated in the construction of the ballots. Like we talked about, if there are people who are allergic to peanuts, we shouldn’t only serve peanut butter sandwiches at the team lunch. This kind of thing really makes me interested in proportional representation systems, do you know of any good arguments against PR or why it is contentious? I understand the issue of party collusion, I just wonder if there are ways to mitigate that effectively.
What do you think “improvement” should mean? My thinking is that an improved system would reduce the differences between the outcome of the election and the expected outcome of a lengthier, civil, pro-social engagement between the members of the group who might come to a maximally consensual arrangement without any formal voting system at all. After all, isn’t that what a voting system is supposed to be a substitute for?
This of course gets philosophically difficult, and a bit self-referential, since it may very likely be that a large group of actual humans will devise their own voting systems (or worse) if left to their own devices. What does that imply to you?
To me, a voting system has the function of increasing the consensuality and reducing conflicts of interest in group decision-making and its consequences. It could very well be that a score-based system would operate better even with only two candidates. I would actually challenge the idea that there is a good definition of “majority rules” even with only two candidates, unless the decision-making method is a priori restricted to the scope of a specific paradigm.
We talked about a culture of shooting things down and I don’t want to be that guy,
Since this isn't actually a proposal, but just a request that we weigh in on theoretical baselines, that's not really a problem. (but I do appreciate the concern for that issue! )
I do think what “improvement” means exactly is not clear, and that it depends on your paradigm.
Well, I have my own ideas as to what is an improvement, but I was kinda asking for yours....
Since you participate in a forum dedicated to better election methods, and have submitted your own proposals, is it fair to assume you have some idea for what might be an "improvement" for voting methods, at least in the general (3 or more candidate) case? (and is it possible you are overthinking this? )
You use the term "maximally consensual arrangement" to basically indicate your ideal. So, moving it closer to that ideal would be an improvement. Right?
But here's the thing: it seems like you're suggesting that a "lengthier, civil, pro-social engagement between the members of the group" would naturally tend toward that sort of ideal. I am not so optimistic, in fact I think that lengthy social engagement might well be warfare or other violence (or, I guess whatever you get when they just argue until someone gives up). Ok, warfare isn't civil, but.... I just don't see how you can assume that parties which don't agree can just agree to be civil and come to a fair agreement, unless .... well unless they agree to hold a vote or the like. Which brings us back to square one.
If you agree that working it out socially is not necessarily going to produce good results, then we're left still asking what is ideal. So... I appreciate your attempt to answer what I asked, but it still feels more like kicking the can down the road to me. You haven't really defined "maximally consensual arrangement", only suggested that things other than voting might actually get better results, albeit less efficiently.
(keep in mind, with respect to my "overthinking" comment, that my answer to this is indeed simple, and is identical to @Jack-Waugh's: "yes I think majority vote on a binary choice is ideal". Another possible answer -- which is also simple, and concretely answers the question -- might be that you could do Score ballots and tabulation, and hope that some portion of people don't exaggerate, so that strength of preference might be better factored in. I don't agree with that latter one, but at least it is a concrete alternative to a simple majority vote, and therefore more what I was hoping for in terms of answering the question with some specifics)
@rob Your question was answered by Ken Arrow (of Arrow's impossibility theorem fame). AIT is more formally called Arrow's general possibility theorem, and is the second theorem in his Social Choice and Individual Values. His theorem 1 (Possibility Theorem for Two Alternatives) covers exactly this situation, and unlike his General Possibility theorem, the answer is affirmative. It is possible for a society to choose between two alternatives without violating any of his desirable conditions. The method to use is simple majority rule.
After Arrow published his book, Kenneth May published an article in Econometrica (1952) titled, A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision. That paper augmented Arrow's result and states that not only does simple majority rules satisfies Arrow's conditions, but every voting system that satisfies those conditions is equivalent to simple majority rule.
In essence, choosing between two alternatives is easy. The problem comes when you try to expand beyond two alternatives. That's what AIT shows and what Gibbard and Satterthwaite expanded upon.
So when limited to two alternatives simple majority decision works, and any other reasonable voting system devolves into simple majority decision when restricted to two alternatives.
Thanks @tec, I certainly agree with you and Arrow on this. I always got the impression that Arrow's conditions were actually based on this case, in other words, it was treated as a given that majority rule for a binary choice was the standard that other systems (with 3 or more candidates) were being compared to (and of course failing in one way or another)
any other reasonable voting system devolves into simple majority decision when restricted to two alternatives.
The one I can think of that doesn't is Score, as given in @Casimir's example where voters don't give their favorite a maximum score. I believe some people actually like this property of Score. (I don't)
The one I can think of that doesn't is Score, as given in @Casimir's example where voters don't give their favorite a maximum score.
I think this depends on the context in which Score is being used. In US politics, we now have one faction threatening the lives of the children of school and election officials. Stakeholders are not going to give up power voluntarily. Once they come to understand how Score works, they can be counted on to use both ends of the range, assuming they are willing to put down their weapons and trust an election of any kind.
On the other hand, in a political action group (equivalently a political-action group or a political action-group) characterized by mutual respect, gratitude, and love among the participants, a question can come up where some participants choose to defer to their comrades to a greater or lesser degree.
@rob I think majoritarianism is definitely a problem and not a virtue, it's intrinsically competitive as opposed to cooperative. If it happens as a contingency regarding the outcome of an election, fine. But it definitely shouldn't be a mechanical aspect of the system. That's exactly what the founders were afraid of. Direct and majoritarian democracy are both terrible ideas for the same reason: they pit large mobs against each other and lead to tyranny, the very situation we find ourselves in. Two huge parties taking turns oppressing each other, a pump that inflates the wealth of apathetic plutocrats.
@cfrank So what's your answer? If you've got a binary choice, which alternative do you choose if not the one preferred by the majority?
I'd prefer it if we didn't have only two choices, but in cases where we do, how do we resolve it as fairly and reasonably as possible?
I'm with @tec that "choosing between two alternatives is easy" and "when limited to two alternatives simple majority decision works, and any other reasonable voting system devolves into simple majority decision when restricted to two alternatives." (which is one reason I'm not a big fan of Score, which doesn't do this)
I suspect that the vast majority of scholarship on voting theory agrees with this position, but it is certainly interesting to see who does and who doesn't agree. I admit to being surprised when anyone with knowledge of the field disagrees with it.
Do you have a proposal for a better system for choosing between two alternatives?
@rob I have already mentioned that the definition of a majority only applies in a constrained paradigm. My answer is that the question preconceives a paradigm that may be inappropriate, and that alternatives may be superior.
For example, let’s say we have two choices for lunch: peanut butter and jelly sandwiches, or fruit cups.
51% of the people at the lunch marginally prefer peanut butter and jelly sandwiches to fruit cups, but 10% of the people are allergic to peanuts. Furthermore, let’s say that 49% even strongly prefer the fruit cups to peanut butter.
Do you really think it’s a better idea to have peanut butter sandwiches than to have fruit cups?
I think it’s clear that empathy is necessary here to come to a sociable solution. A selfish majority rules paradigm doesn’t make any sense here and doesn’t produce a good outcome.
I don’t know of a good system, I have suggested one before involving allowing voters to send in ballots, making the candidates anonymous except for their score distributions, and then having the electorate vote on which candidate to select according to those score distributions only. I actually do think this would be a better system than straight up majoritarianism. Unfortunately it requires more effort on the part of the electorate.
Do you really think it’s a better idea to have peanut butter sandwiches than to have fruit cups?
Food allergies are a special case where we "override democracy" for some greater ideal. That's very different and I don't think can be accounted for by voting.
Should I be able to claim an allergy (real or metaphorical) to a certain candidate? Claim that if that candidate gets elected, it will cause me to get physically sick or otherwise is simply intolerable? I think we'd have complete chaos, and it would no longer be democracy if such absolutes can be allowed. If someone is on the ballot, they should be considered a viable candidate, full stop.
I think it’s clear that empathy is necessary here to come to a sociable solution
I wish everyone was fully empathetic and cared for everyone else, rather than being selfish. Meanwhile my daughter wishes that unicorns were real and that cotton candy rained from the sky. Seriously, though, that just sounds like wishful thinking, and the realization that that sort of thing doesn't work for large numbers of people is why voting was invented in the first place.
I'm all for systems that bring people together rather than driving them apart. There are ways to align people's interests with the goal being social harmony. But assuming they are that way to begin with? I don't see how that is going to work at all.
I have suggested one before involving allowing voters to send in ballots, making the candidates anonymous except for their score distributions, and then having the electorate vote on which candidate to select according to those score distributions only
Ok I missed that one but I don't understand it from your short description. Is this two votes? I don't understand why people would vote on score distributions when they don't know who the candidates are. Seems more efficient, and just as good, to just agree upon a formula for it ahead of time, so you don't spend millions of dollars bringing people in just to vote on how to resolve votes, for every single election. It sounds like all that would do would be make it more complex, and obscure any potential bad effects from being directly analyzed. But mostly, who is going to want to go in and vote on anonymous score distributions? I also don't see it having a positive effect with regard to the food allergy example, it's not like people would see someone giving a particularly low score to PB&J (not knowing that the choice is PB&J) and conclude that they must have an allergy, rather than just being picky.
Also, are you suggesting it would be better than majority vote for a simple binary choice, i.e. two candidates? It doesn't seem like you could vote on score distributions for two candidates, so if not, this really doesn't apply.