> That said, things like Approval have the opposite problem, in which moderates are given an advantage (some approval people will say this is a feature, not a bug).

This is a weird way to say that representing the population is a bug.

Your example election would be a compelling argument if population preference was more of a multimodal distribution rather than closer to a unimodal distribution. Despite the US's current division, it is nowhere near as divided as your scenario.

To be clear, I personally prefer approval to IRV. But raw approval gives undue advantage to moderates. Approval-to-runoff being clearly superior than raw approval, for this reason. And STAR being a little bit better than that.

The RCV people's main criticism of Approval is that it doesn't allow you to express different levels of support, and they aren't totally wrong (even though their preferred mechanism of IRV doesn't get them there, either).

I think (without data, happy to be proven wrong) that the US population is fairly strongly bimodal on most issues. Many issues that people care a lot about (for better or worse...) have two clear centers of gravity,

e.g. for gun control and abortion most people are in the orbit of a "mostly ban" or "mostly allow" group, with very few people falling into some nuanced middle ground.

> But raw approval gives undue advantage to moderates.

If by "moderates" you mean "most liked" then I'm not sure what the problem is here. The point of voting is to find the most universally agreed upon ruler. You may call this unfair, but I would say that it is MORE unfair to give advantage to fringe groups rather than giving advantage to the masses. I thought the point of democracies was about having rule by the masses. If you think fringe groups should have the advantage I'd like to hear your argument.

> If you think fringe groups should have the advantage I'd like to hear your argument.

I'm not sure what gave you the impression I think that. My comments clearly suggest that my view is that STAR > Approval-to-runoff > Approval > RCV-IRV > Plurality. My reasoning is that I place a very high value on the condorcet and favorite betrayal criteria.

My apologies then. It was the italicized "undue" that made me think that this was your position. I read it as "undeserving".

As for the condorcet winner, that is quite hard actually. But if we consider a weak condorcet winner (where it is true 90+% of the time), that isn't as hard. I do think simplicity, transparency, and reduced vulnerability to strategy is a worthwhile trade-off for a strong condorcet winner. But of course, this is just my personal opinion and what's the preferred optima depends a lot on personal preferences.

> I think (without data, happy to be proven wrong) that the US population is fairly strongly bimodal on most issues. Many issues that people care a lot about (for better or worse...) have two clear centers of gravity,

We'll you'll be happy then! :)

Because this is commonly believed but actually totally untrue. There's an entire book about it, "Culture War? The Myth of a Polarized America" by Morris P. Fiorina.

The upshot is basically that if you ask people binary yes/no questions (or binary left/right votes), the population appears divided, bimodal. But whenever you give a sliding scale in surveys, it becomes abundantly clear that the population is centrist -- unimodal. Even for gun control and abortion, the most hot-button issues.

> The upshot is basically that if you ask people binary yes/no questions (or binary left/right votes), the population appears divided, bimodal.

SHOCKING! (I laughed a little too much at this comment)

But this is also why surveyists tend to ask the "strongly disagree, disagree, neutral, agree, strongly agree" questions. Because it can measure the temperature better. This is effectively a type of cardinal voting too. After all, voting theory is also known as "social choice theory."

But I definitely agree that in practice we find more normal like distributions in preference. Which is why I find it odd when commenters argue that other voting systems "give advantage" to "moderates" or "centrists" as if this is not in reality "gives 'advantage' to candidates that have low variance to the mean opinion." (aka, the most representative). Isn't that the goal of voting systems? To be the most representative?

It's actually really interesting, when you look at political science literature and essayists.

You have those insisting that the population is divided and there just aren't that many centrists, and then you have those insisting that the population is centrist and there aren't that many extremists.

And they're always looking at the same exact bell curve, and then the first group decides the center is only an arbitrary 10% wide so most people are divided (45% on either side), and the second group decides that the center is an arbitrary 80% wide, so only a small number of people are extremist (10% on either side).

It's the same damn bell curve.

I don't think I see as much of a problem out of academic literature (there are clear problem groups though, not denying that), but more that the problem is how the information is conveyed to the population. Both the media perception as well as how radicals present information. I'm always reminded of John Cleese's skit on extremism[0]. When he lists the enemies of liberals and conservatives "moderates" are included in both. I think we see this a lot as we often paint people that are moderates as "on the fence." We see this with the popularity of subreddits like r/ENLIGHTENEDCENTRISM[1]. With one of the top posts suggesting that centrists see "compromise" and "a little genocide" as okay.[2] But is this not the playbook of authoritarians (right or left)? To remove all nuance from the conversation. Centrists aren't people who go to the middle of divisive opinions, they just don't cleanly fit into either camp but pull elements from both. I think nuance is the most important thing we can do to fight extremism in either direction.

[0] https://www.youtube.com/watch?v=wXCkxlqFd90

[1] https://www.reddit.com/r/ENLIGHTENEDCENTRISM/top/?t=all

[2] https://www.reddit.com/r/ENLIGHTENEDCENTRISM/comments/cw2bbh...

Voters will realize that approval gives benefits to centrists, and they will change their voting strategies and stop approving centrists. None of the math analyses shared here take that into account.

For example, say three fictitious candidates are running for dogcatcher, Bernie, Hillary, and Trump. Does your hardcore Bernie supporter friend believe that approving Hillary doesn't hurt Bernie? Will they choose not to approve centrist candidates, leading to extreme results in elections?

If centrist is defined by the minimization of distance between a population's preference and a candidate's position then I don't see the problem. Why would you want an extremist? Or why would you want someone that is less representative of the population as a whole? Isn't the point of democracy to minimize this distance?

I'd actually argue that if approval was used Bernie would have won. One can vote Bernie honestly but also approve of Hillary as a safety. And this would have had a larger edge with Score or STAR. Bernie was quite popular and frankly a lot of people that also voted Trump also liked Bernie because he was an outsider.

> One can vote Bernie honestly but also approve of Hillary as a safety.

No, that's the thing. Many people want to express their preference, and really really didn't want to "approve" of these two people at the same level. It's exactly the same with...

> Bernie was quite popular and frankly a lot of people that also voted Trump also liked Bernie because he was an outsider.

...where these people may have felt positively about Bernie, but they really really preferred Trump, and they would not have "approved" of Bernie if that meant putting him at the same level as Trump.

So now you have two groups of people who would have preferred Bernie as their 2nd place choice, but decide not to "approve" him in order to help their 1st place choices win. Supporters of approval voting just keep ignoring this dynamic of how real people vote in the real world.

So I think your points are valid. I also just want to state that pretty much every cardinal voter I know prefers STAR then Score then Approval. I'm STAR 5, Score 5, approval 4 (only slight preference of STAR over Score). But I think that resolves your concerns. It is just that in practice we find that Approval is easier to argue for and is good enough. From a personal stand point I'll argue with technical people about voting systems if we got approval but I wouldn't be an evangelist anymore.

It's an iterated event, voters would learn that voting a single candidate generally gives them less influence.

Millions of Jill Stein voters would disagree with that.