Recounting my comment from a previous article[1], comparing all these voting systems is not really the right way to think about it. First, you need to separate the mechanism used to express voter preference (i.e the ballot design), from the method used to choose the winner. Those are separate things that, in theory, can be mixed-and-matched to produce various voting systems.
In terms of ballot designs, they are basically all just restricted subsets of the "score" voting ballot. That is, any voter preference that can be expressed in an "approval", "ranked choice", "ranked choice with ties", or traditional "single choice" ballot, can also be expressed with a "score" ballot.
That means every voting system is a "score ballot" system with some restrictions applied to the ballot. This means that, for example, you could have an election where you allow the voter to choose whichever ballot they are most comfortable with. Then you just interpret the ballot as a score ballot.
There are multiple ways to choose a winner from a set of score ballots. But debating between them is counterproductive to getting better voting systems adopted. Just start off with one that's easy to understand (i.e. "sum of ratings", or "only the first choice counts"), and worry about improving it later.
The important thing is to give the voter the option to use a more expressive ballot. Whichever one they feel most comfortable with. You could even make it so that initially, all ballots are converted to traditional "single choice" ballots for tallying, but let voters know how the vote would have turned out under other evaluation methods (like "sum of ratings" and Schulze). I think voters would quickly realize the value of counting all of their expressed preferences.
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But that is a very cool site. Probably the kind of site the web was intended for, don't you think?
The issue with that is any change, especially how a winner is chosen from a ballot, is a long and politically fraught process so whatever is changed to shouldn't just be 'eh it's not great but we'll change it in a few years' because that's really unlikely to actually happen.
So first of all, I think that only three evaluation methods should be considered - ballot conversion/reduction to traditional "single choice", "sum of ratings", and Schulze. You might need to start off with conversion to traditional "single choice", because it's hard to argue against adopting it. That is, you're not actually changing the election system at all. You're just allowing people to optionally express extra information about their preferences in a way that does not affect the election. But it will give each voter a chance to, if they want, try out more expressive ballots (which will presumably be appealing to most people once they get the hang of it), and the public will be told how the election would have resulted under the other two evaluation systems. Presumably, a more "centrist" candidate would generally have won. And after a few election cycles, people will be able to form an opinion on which evaluation system they think produces the best results.
I think the reason why electoral system change has so often been met with public resistance is that most people don't have a feel for how the results would change, and nobody is offering them a chance to get familiar with a different election system without an up-front commitment to the change.
If you can get people to accept the "sum of ratings" evaluation method, then I say be happy with that. The fact that "sum of ratings" is arguably not as good as Schulze is a very high class problem to have. (Btw I'm using Schulze as a stand-in for any "good but complex" evaluation system.) Anyway, I'm not sure the improvement in evaluation is worth having an evaluation system that most people wouldn't understand.
So just to sum up, I think what I'm proposing is different and more acceptable in that:
i) It allows people to use whichever ballot they feel most comfortable with, knowing that no matter which ballot they choose, their vote will count as much as any other voter.
ii) It allows voters, if they so choose, to get familiar with the more expressive ballots and different evaluation methods without committing to any change in the election system.
In terms of ballot designs, they are basically all just restricted subsets of the "score" voting ballot. That is, any voter preference that can be expressed in an "approval", "ranked choice", "ranked choice with ties", or traditional "single choice" ballot, can also be expressed with a "score" ballot.
That means every voting system is a "score ballot" system with some restrictions applied to the ballot. This means that, for example, you could have an election where you allow the voter to choose whichever ballot they are most comfortable with. Then you just interpret the ballot as a score ballot.
There are multiple ways to choose a winner from a set of score ballots. But debating between them is counterproductive to getting better voting systems adopted. Just start off with one that's easy to understand (i.e. "sum of ratings", or "only the first choice counts"), and worry about improving it later.
The important thing is to give the voter the option to use a more expressive ballot. Whichever one they feel most comfortable with. You could even make it so that initially, all ballots are converted to traditional "single choice" ballots for tallying, but let voters know how the vote would have turned out under other evaluation methods (like "sum of ratings" and Schulze). I think voters would quickly realize the value of counting all of their expressed preferences.
...
But that is a very cool site. Probably the kind of site the web was intended for, don't you think?
[1] https://news.ycombinator.com/item?id=12950566#score_12952384