> Score voting doesn't violate Arrow's Theorem (because it's not a ranked-choice system).

This is very much like the idea that radix-sort can run in linear time worst-case, because it's not a comparison sort. While absolutely true, both statements can be misleading without context. Just as radix-sort has the weakness of depending on the size of the keyspace (and therefore being poorly suited for sorting small vectors of large numbers), score voting has some issues that do not appear in ranked-choice systems.

Most obvious: There is incentive to vote tactically (as is always the case), but the tactics are more complicated than in most other systems. Most serious: Not using a ranked-choice system prevents us from reliably finding a Condorcet winner.

One could make the case that these disadvantages aren't as bad as those of ranked-choice systems, just as one can make the case that radix-sort is a generally good way to sort records by a lexographic key. Simply listing advantages doesn't do that, though.

> Score voting doesn't violate Arrow's Theorem (because it's not a ranked-choice system).

Right, but it could still have those problems that Arrow's theorem talks about. Do we have a proof to the contrary? I have a hunch that it promotes strategic voting, like plurality voting ("first past the post") does.

It's fairly straightforward to prove that score voting does not violate the conditions of Arrow.

For example, adding an additional candidate should not affect the average score of the rest of the candidates, hence there is no problem with "independence of irrelevant alternatives". (I leave the rest of the conditions as an exercise to the interested reader.)

That having been said, all voting systems can be vulnerable to strategic considerations. However, simulations and theory suggest it's much less the case for score voting compared to ranked choice systems. See electology.org for some pointers to research.

> For example, adding an additional candidate should not affect the average score of the rest of the candidates, hence there is no problem with "independence of irrelevant alternatives".

It is non-obvious to me that rational voters in such a situation should not adjust their scores for the initial candidates. In fact, it seems like you should adjust scores in the prototypical situation where you prefer candidate A to candidate B, and detest candidate C. With only A and B present, you give A a high score and B a low score. When C enters the picture, you change your score for B to a high one, so that you make it maximally difficult for C to win.

Range/score voting suffers from the vary serious problem that there is no consistent mapping from subjective preferences to ballot markings; it suffers from the cultural variability that affects numeric ratibg systems in general; approval voting has a similar problem.

These systems can be very good in situations different from common public elections where there is a consistent meaning for ballot markings (e.g., approval makes good sense in non-secret-ballot elections where a vote to approve an option is a binding commitment to participate if the option is selected.)

It sounds appealing, but I wonder if in practice range voting tends to collapse into first-past-the-post, with people voting tactically to maximize the chances of a popular candidate winning (instead of voting for the candidate they most prefer). This is why systems such as optional preferential voting appeal to me despite their (different) flaws. I wonder if monotonicity and trying to avoid circular electoral preferences are slightly overrated goals. I suspect that a good electoral system might involve a bit of satisficing, of producing great outcomes even when the theoretically best outcome isn't consistently achieved.

In fact it collapses into aproval voting, which is like range voting except every score is 0 or 1, or equivalenty like FPTP except that you can vote for more than one person.

But it turns out that approval voting is itself considered a very good voting system (I remember reading an article about how a conference of experts voted on their favourite voting systems and approval voting won, but I can't find it because "voting system vote" isn't a very good Google search).

I think The main theoretical problem with most approval and range voting methods is that they fail the Condorcet and majority criteria. A candidate who is preferred over every other candidate by a majority of voters can lose, which sucks, but in practice it is debatable how common such an occurrence would be.

> I wonder if in practice range voting tends to collapse into first-past-the-post

Of course it will. The fundamental problem is selecting only one representative per voting district. However fancy and complicated voting algorithm you make, it will most probably collapse anyway. It's the size of the voting districts that leads to a two-party system, not the voting mechanics.

But then: Just pool nearest 20 voting districts [x] into one large voting district, from which you elect 20 representatives, and any kind of simple proportional voting mechanics [xx] will do. If you elect 20 representatives, any party that manages to get at least 5% of the voes will get their representative to the Parliament. New political parties start to appear, and a multi-party system emerges on its own.

[x] Or 15, or 30 or whatever.

[xx] Such as the D'Hondt method, https://en.wikipedia.org/wiki/D%27Hondt_method

It’s hard for me to imagine that the actual outcome of such a proportional representative system would be worse (in my judgment) than the current US federal district system, but the theoretical criticisms are obvious. For instance, it makes sense to have representatives represent a specific area who were supported by a majority of voters from that area. That way, the representative can in theory represent specific interests that are disproportionately important to citizens from that specific area (e.g. agricultural issues for rural areas or public transportation issues for urban areas).

Of course, drawing these districts (in either system) is an inherently arbitrary process which can lead to counterintuive or obviously unideal results, the most obvious example of which being gerrymandering. But at the end of the day, unless we have a one world democracy, borders must be drawn. National borders are “easy” in the sense that they tend to be formed not by a democratic political process but rather historical conflict.

" people voting tactically to maximize the chances of a popular candidate winning (instead of voting for the candidate they most prefer)"

I'm not sure I understand your comment. There is no "instead" -- you can vote honestly for both your preferred candidate and the popular candidate.

So in the U.S. then Dems will vote 0-10 and Republican 10-0. I'm not sure I see the difference as long as there is only one winner

What the U.S. really needs is proportional representation, similar to parlimentary systems of other countries

> So in the U.S. then Dems will vote 0-10 and Republican 10-0.

Then someone who identifies as neither could get a 6 on average and get elected. (Assuming both other candidates are close to tied.)

That said as a Canadian I'm down with almost any change in the voting system.

Why give a 6 when you could give a 0 or a 10 depending on advance polling data? Score voting devolves into approval voting for sufficiently informed and tactical voters, and provides less impactful ballots to the tactically naive.

No, a new single winner election system is a distraction. What we need is proportional representation, to ensure that more people actually have representatives in proportion to their political desires.

You didn't understand the parent's point. The independent has 60% of the population giving him a 10.

You replace the claim about voting method with a claim about who can get on the ballot. That is as big of a change as changing the voting method.

There are options for managing ballot access:

* Since there is no spoiler effect, you could just let everyone on the ballot. Letting abstentions count as zero votes, obscure candidates cannot win. (Less severely, abstention could count as a fractional zero vote, i.e. 0 in the numerator of the average and 0<x<1 (say x = .25) in the denominator...)

* Or require a certain number of signatures to let a candidate on the ballot.

What stops everyone from voting 0 for everyone and 10 for one candidate? It's how like our system is now, where no one votes for who they want, but the person they can tolerate most, and can win.

I think you misunderstand the system. It's not that you have 10 points to distribute across the candidates, but that you give each candidate a score. What score you've given to other candidates doesn't constrain what score you can give this candidate - you pick separately from the whole range for each.

So if 10 is the maximum (0-1 was the range given above, but whatevs), then sure if I prefer Hillary to Trump and they're the only two that seem likely to win, maybe I'll give her a 10. But for anyone I prefer to Hillary, why would I give them a zero? Of course I should give them a 10 as well!

Yeah I understand that. I still feel that voters will eventually converge to giving other candidates the lowest score possible because it increases the likely hood of their candidate getting elected.

edit: definitely willing to try the system though :D

The problem I have with this is that the score from 0 to 1 isn't tied to any strong foundation.

Suppose that I rate a candidate 0.7, and my neighbor ranks the candidate 0.6 . Does this mean that I like the candidate more than my neighbor does? What does that mean? How can we tell?

Suppose you take two people who would vote in the same way, but then you take all the scores of one of the people, and square them. These are all still scores between 0 and 1, and so a valid way to vote, and it keeps the preference order in place. But what do the difference in these scores mean? "amount of happiness"? How could we quantify this?

The way that seems to make the most sense to me is a normalized vNM utility. A person's least favorite candidate (or least favorite candidates if some tie for this position) get(s) the rating 0, and their favorite candidate(s) get(s) the score 1. All other candidates are scored as the probability r such that the voter is indifferent between that candidate, and (probability (1-r) of [least favorite candidate]) and (probability r of [most favorite candidate]).

This gives a well defined foundation for what score a voter would give a candidate, a clear definition for what a 0.6 means vs a 0.7 .

The system where you just pick the candidate with the highest average rating though, does not incentivize voting in this manner.

I have an idea for a system which I think would incentivize voting this way, and which would optimize the expected value of a weighted sum of everyone's vNM utility. (it is a weighted sum because the utilities are normalized between 0 and 1, and different people's vNM utilities are incommensurate. The weighting is in the normalization. It is I think the most neutral weighting it can be.)

However, it would probably be entirely impractical.

The idea is this:

Each person states their utility for each of the candidates listed, and the system makes sure that these utilities are normalized.

Then, each voter gets 1 (arbitrarily subdivisible) point of voting probability.

Then, a bunch of "trading" is automatically done, where say, as an example, if two people have different first picks, but would both prefer some other candidate as a close second, they could both give up some "undifferentiated" voting probability in exchange for some which is restricted in some way, based on whatever deal they made.

All the deals would probably be made automatically, because it would just be so incredibly inconvenient otherwise, and also having the result be biased towards voters who are better at trading probably wouldn't be great.

Once there are no more trades to be done, all the remaining undifferentiated voting probability goes to the voters' first choice.

Then, the winner is chosen randomly, with the probability of winning corresponding to the proportion of the voting probability that was assigned to them in the end.

Assuming an efficient market, this should optimize the expected value of a weighted sum of the voters' vNM utility (assuming rational voters).

Unfortunately, it is rather complicated, and I think it would probably be too computationally intensive to run.

Oh well.

> Suppose that I rate a candidate 0.7, and my neighbor ranks the candidate 0.6 . Does this mean that I like the candidate more than my neighbor does? What does that mean? How can we tell?

Each voter should rationally vote in whatever way maximises the expected value of his utility of the outcome. The extent to which your vote "looks like your actual preferences" depends on how the voting system is designed.

Sure. My point was that the "pick the one with the highest average rating" doesn't obviously incentivize a particularly meaningful way to vote.

I think that ideally, if it is possible without giving up too much, it is desirable that how a person would rationally vote doesn't depend very much on what they know about how other people will probably vote (though this probably isn't the most important consideration).

If the system is based on people giving ratings, and there isn't anything that these ratings are designed to exactly mean, then it seems likely to me that the system wouldn't just so happen to be such that the way people are incentivized to vote would mostly not depend on how others are expected to, and also unlikely that the way people would rationally vote would match particularly well with the way that the designers of the voting system imagined.

The system I gave was intended to be one in which the way people would be incentivized to vote would correspond to their preferences in a clearly defined (and sensible) way.