[EM] Approval vs Condorcet. Voting in Approval.

[Kristofer Munsterhjelm]

On 2024-05-16 08:04, Michael Ossipoff wrote:

> I’m glad you brought up the desire for the method to do it all for us 
> (as Condorcet does)…taking our sincere rankings as input, & outputting 
> the legalistic right choice. …because I’ve been meaning to address that 
> matter.
> 
> …& that’s not even counting the much less expensive implementation 
> (could be zero cost, without even needing new count-software), easier 
> less expensive administration, & easier simpler explanation with 
> consequent easier enactment.
> 
> Approval isn’t as difficult to vote as it opponents claim.  There are 
> many ways to choose what or whom to approve. That variety is a good 
> thing, because you can choose how you like.
> 
> Condorcet is legalistic, but we don’t have to be legalistic! Approval 
> guarantees election of the candidate who maximizes the number of voters 
> for whom the outcome is in their preferred of the two merit-subsets, 
> however the voter designates them.
> 
> e.g. If people approve what they like, Approval maximizes the number of 
> people who like the outcome.
> 
> If people approve what’s acceptable, then Approval maximizes the number 
> of people for whom the outcome is acceptable.
> 
> If people approve above expectation, then Approval maximizes the number 
> of people for whom the outcome is above expectation…maximizes the number 
> of people pleasantly surprised.
> 
> You don’t know the objectively-optimal vote? Neither does anyone else, 
> so don’t worry about it!

This makes it very hard to reason about or define any relative 
properties about Approval, though, because it kicks the can down the 
road to the voter instead.

This is perhaps a bit exaggerated, but to show a point: does Approval 
really pass clone independence? Suppose more candidates of a wing show 
up, which embolden people to be more discerning than just approving 
what's acceptable. Then the winner changes.

Is "Approval"[1] *really* FBC, or monotone? If it converges to the 
Condorcet winner, then nope, because you can't have FBC and Condorcet. 
If it converges to the essential set, then nope, because the essential 
set is nonmonotone.

By saying "don't sweat it, people will do what they will do, there's no 
objective meaning to the ballot except what the voters like", voter 
behavior becomes so much more intermixed with the method. And then, for 
criteria to compare apples to apples, they should take this intermixing 
into account. Not being legalistic shouldn't let Approval off the hook.

But how?

What I want is to have each method equally on the hook for what its 
behavior implies. To paraphrase a reply I made to rb-j: if the winner of 
an election can change when non-winners drop out, we don't really care 
if the method passes IIA as such. It's a nice thing to have in a 
box-ticking way, but that's it.

If a method wants to open up the can of worms to say "nope, this method 
isn't meant to be used in isolation, it's supposed to be used with 
/whatever/ internal way of going from utilities to the types of 
expression the ballot accepts", then okay, let's take it at face value. 
Let's ask the questions that matter. Can this make someone lose if some 
of the honest voters like the candidate more? Can it make a non-winner 
change who the winner is?

For ranking, this is easy, courtesy of the "legalism". For Approval, not 
so much.

-km

[1] or rather, the method induced by iterating Approval or by combining 
Approval with one or more thresholding strategies implicitly chosen by a 
voter.