But what happens in your cardinal voting system, if D and C are the front runners in competition for a single seat? Imagine the final results were
A: 30 points, B: 20 points, C: 50 points, D: 51 points.
If only you had given the realistic challenger to D your full support (5) instead of being expressive in your preference and docked them 2 points. Now D will rule for another 4 years and the C supporters will call you a traitor for voting your honest preference, just like in the present system.
And this scenario is easy to imagine. You usually know who the front-runners are, and because not only you, but everyone else, wants to avoid that scenario, belief about who the front runners are has a self-reinforcing effect.
A scenario where you're glad you didn't award the full 5 points, though, is much harder to imagine. And a scenario where you are BOTH glad that you didn't award them 5, yet glad that you didn't award them 0, is as far as I can see never going to happen in a single candidate election.
While this is easy to write down it isn't easy to tabulate. You must provide a new tallying algorithm (you'll find that important features break).
> But what happens in your cardinal voting system, if D and C are the front runners in competition for a single seat?
I'm a bit confused what you're asking here. There are no voting systems where a single vote/rank permutation/rating will not change the outcome of an election. To do so would mean votes are being wasted. Yes, there are people that will be upset in these situations just like people are upset in a close sports game. But unlike a close sports game we have a higher expectation that the teams that win like this are more likely to be similar. That is candidate C's voters frequently like candidate D (your ordering even suggests that despite the example ballot being from someone on the other side of the political isle). The point is to get someone that is the most representative. In the end, it shouldn't matter what a single voter's preference is, it matters what the collective preference is. That's why we vote in the first place. So that's why I'm confused.
But maybe you should click on the montonicity link. You may also find this link[0] interesting. It is also extremely important that we remember that no voting system is perfect. So if you're going to put down a voting system because you've found a flaw you'll never be happy with a system unless you lie to yourself. It also means that if you're arguing with someone and point out a flaw you need to attempt to convince the person why that flaw (and others) are important in comparison to the upsides/downsides of the other competing system/s. Discussing voting systems is difficult because there are no global optima but it is also more difficult to discuss because proof by counter-example is meaningless and will only convince a novice. If you're wondering the motivation I'm giving in my arguments, click the links.
[0] https://web.archive.org/web/20180721221826/https://www.starv...
Ranked pairs etc. have no problem tabulating it. If the change to allow equal ranking breaks some obscure metric, that's a sign the metric isn't very important. After all people can just rank everyone if they worry about it.
I've read a lot about this, and I argue with the usual suspects range people every time the topic shows up.
I don't understand how you don't understand the argument. You can come into situations where you'll regret you didn't min-max your choice (rank everyone 0 or 100). You can't come into situations where you say, "gee, I'm glad I ranked that candidate somewhere in between". Consequently, everyone will do that, whether it's good for the collective or not. Sure, I want what's best for society, but I'm not volunteering to have my vote diluted for the common good - especially since I know that the people I disagree with most, certainly won't do it.
> I don't understand how you don't understand the argument.
Because pure honesty is never an optimal strategy? I'm not aware of a system where that's the optimal strategy. But as we showed here in range, the best strategies are some form of honesty. The dishonest part is that you rescale, which I don't think most people would be upset about. What is frustrating to me is that you appear (I'm willing to admit a misread because these conversations are difficult and it is clear you're primed on my position given your usual suspects statement) to be ignoring identical strategic issues in ordinal systems. But I've also stated pretty clearly why I have a preference of cardinal systems. It is because I care a lot about the resolve complexity (the thread topic is a good example), monotonicity (something IRV/RCV fail (RP and Schultz pass but fail the prior criteria)), favorite betrayer/strong spoiler effect (again IRV/RCV fails), and an important factor is the embedding aspect. That the distance between all preference is not identical. We just can't have as richly expressive latent embedding as we can in a rated system. This has a lot of benefits that I think we need to discuss, including a smoother VSE solution space[0]. That dictates how resistant a system is to dishonest strategies and how representative we are.
It's not in a system alone. Strategies are something you have when you have information about the other players and their payoffs.
As it happens, honesty is an excellent strategy in Condorcet methods (even the "bad" ones, like those who aren't monotonic) when you have a realistic amount of information about other people's preferences/strategies. People who are honest because they can't be bothered to be strategic, do great with those methods.
In approval, even the information about who the front runners are, causes trouble.
And in range, even with NO information, you'll know it's better to just use the max and min values.
Those systems don't encourage honesty, and the "extra information" range sneaks in from self-reported strength of preferences on an absolute scale, is junk information. Nothing good can come of using it. Certainly it's no good to use it to reject a candidate that is preferred by a majority over all the other candidates.
There are so many ways to lie with simulation. When you took away even the most obvious lie in the simulations painting range in a good light - namely when you took away the simulated people's magical ability to honestly compare interpersonal utility on an absolute scale, so they always ranked their most preferred 100 and their least preferred 0, no matter where they were in "opinion space" - then most of the good properties of score vanished. Smith for a while conceded that, and advocated range with top-2 runoff if you were concerned with that (as if this was some obscure technicality).
Second, those simulations had lousy ideas of "strategy", as if strategy was just a percentage slide. Strategies are inherently dynamic, and require coordination - if I see you instructing your supporters how to vote, I can take that into account in how instruct my supporters to vote.
Suppose there are three candidates, A, B, C, and D. We have a strong preference for A, we like B and C equally, and strongly dislike D. How do we express these?
- Ordinal: A > B > C > D
- Cardinal (5 points): A:5, B:3, C:3, D: 0
We can see the embedding issue here pretty clearly. In an ordinal system there cannot be a means for us to express that we have no strong preference of B over C. We also can't express how much we like C over D because we're forced to place them equidistant from one another. This is a big problem because in the ordinal system we say that our preference of B over C is identical to our preference of C over D. There is a clear advantage here to cardinal systems that have a lot of downstream effects that lead to cardinal systems passing the favorite betrayer criteria -- aka strong spoiler -- (ordinal fails) and is why these systems are monotonic (ordinal systems aren't).
I argue strongly in favor of cardinal systems but I often find that people are strongly invested in ordinal systems. Unfortunately fair vote has done a great job at advocating for RCV and people get passionate about things they are not passionate about learning about. But I need to note that there are downsides to cardinal systems too. Voting systems are over constrained and so it really depends on what criteria you are optimizing for. If we strictly want the best VSE over everything else, there's ordinal systems that out perform cardinals. There is nuance here that we need to recognize and be aware of in these discussions, especially when passion is abound. We'll also see if Clay shows up. If it stays on the front page long enough he'll probably see it (hi Clay ;) He's the real expert here.