[Matt Q]

Hi Max,

Originally Posted by Max Goodman

If that's the definition of failing to produce a [deserving] winner, then, when voters have paradoxical preferences, no system can produce one; the voters' preferences make it impossible. This isn't a weakness of ranked choice unless we agree that concealing paradoxical preferences is a strength. (I see pros and cons.)

I guess there are a number of criteria by which a method of electing a president can be judged. One of them, for very practical reasons, would be that the method ultimately generates a winner. For that reason, a method which may not produce a winner, such as the Condorcet method, has a weakness: There's a risk that either you end up with no president, or worse, you're stuck with Trump indefinitely! So, I'd say if we want to guarantee electing a president, then this is a weakness of the Condorcet model. I think we're agreed on that.

The definition of failing to produce a winner I'm using is simply that the system fails to produce a winner. The ballot is taken, the votes are processed, the method is applied, and the person announcing the winner stands up and says, "Sorry folks, we don't have a winner". "Deserving" wasn't related to the point I was making.

But yes, if we define a deserving winner as a Condorcet winner, and there is actually no Condorcet winner (due to paradoxical averaged population preferences), then clearly no other method will find a Condorcet winner, because one doesn't simply exist. I agree with you on this.

[We may have to agree to disagree about whether paradoxical preferences exist equally whether or not the voting system allows them to be expressed. On that issue, we're writing in circles.]

I think we also agree on this: if paradoxical preferences exist in the population, they exist irrespective of whether or not the chosen voting method is capable of measuring them. They will only show up under some methods, and not under others, but they'll still be there. If that's your point I also agree.

However that's different from saying:

A paradoxical result (posts 36 and 37) is not the same as failure to produce a winner (39), and neither of those outcomes is any more likely under ranked choice than under a vote-only-for-your-favorite-candidate system. (A paradoxical result may feel more likely under ranked choice, but only because that system can reveal a paradox that would otherwise have remained hidden. Ranked choice may therefore be more interesting to those intrigued by paradoxes and probability, but that's not a weakness.)

You can only get a paradoxical result if you use a particular method, like the Condorcet method, that's capable of generating such a result. You literally can't get a paradoxical result if you use a vote-only-for-your-favorite-candidate system. It's not one of the possible outcomes of applying that system. So getting a paradoxical result is more likely under the Condorcet method, since it's impossible to get one under the vote-only-for-your-favorite-candidate system. However, not getting a paradoxical result doesn't mean that population doesn't have paradoxical average preferences. It just means that the vote-only-for-your-favorite-candidate system won't register these, because it's not measuring ranked preferences on the ballot paper. I think we're agreed on this too.

So, hopefully we're not disagreeing about anything, but I apologise if I'm missing your point again!

best,

Matt