[EM] Approval vs Condorcet. Voting in Approval.

[Closed Limelike Curves]

>
> 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.

If that's the case, the voters would be irrational; adding a clone to an
approval election doesn't change the optimal strategy. If the voters are
individually irrational then all bets are off for any voting system. So
yes, it's definitely clone-independent under any sensible model of
strategic voting. Sadly not IIA, but nothing is under strategy. (Also, I
think the Bipartisan Set, as a set, is cloneproof.)

Is "Approval"[1] *really* FBC, or monotone? If it converges to the
> Condorcet winner, then nope, because you can't have FBC and Condorcet.
>
First, I'd argue you can, because majority-strength Condorcet seems like a
more reasonable definition of a Condorcet winner under strategic voting:
you can't determine from the ballots whether Alice or Bob would win a
paired-matchup if a substantial number of voters refuse to disclose which
they prefer. (With honest voting, tied-ranks should never occur; they form
a set of measure 0. Tied ranks don't really indicate indifference;
they indicate a voter is strategically pleading the 5th, and we can make
rational inferences from their refusal to disclose which candidate they
prefer.)

However, you can't have FBC and *ballot* Condorcet, i.e. always elect the
"apparent" Condorcet winner as calculated by naively assuming all the
ballots are honest. I think that's fine. If the Condorcet winner is
different from the "apparent" Condorcet winner on the ballots, I think we
should elect the actual Condorcet winner, rather than the fake Condorcet
winner.

If it converges to the essential set, then nope, because the essential
> set is nonmonotone.

The bipartisan set itself is monotone
<https://doi.org/10.1006/game.1993.1010> (it's the probabilities of a
maximal lottery that aren't).

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.

I agree. I think we should be putting a lot more effort into identifying
results about the Poisson game equilibria of various voting
systems, because the Poisson game models like Myerson-Weber are the most
realistic models we have of voter behavior—or more precisely, voters are
probably using some mix of Poisson game strategy (they want to cast the
tiebreaking vote), level strategy (goal of showing support for a
candidate), and sincere voting.

One very important fact: I'm not aware of a single "Condorcet" method that
satisfies the Condorcet criterion under the Poisson game model. Monroe
proved none of the common defeat-dropping methods or Nanson's method
satisfy it. The idea of any Condorcet-Smith hybrids satisfying it strikes
me as dubious when IRV doesn't and parties have an incentive to squeeze out
the Condorcet winner.

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.
>
I care about it (in a non-box-ticking way): satisfying IIA makes spoiler
effects *less likely, *so long as some voters are honest.

On Sun, May 26, 2024 at 2:50 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> 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.
> ----
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>
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