[EM] A proxy for Monroe's "strategic election of universally loathed candidates" criterion

[Kristofer Munsterhjelm]

On 2024-08-04 19:26, Closed Limelike Curves wrote:
> Thank you so much for all of your hard work+analysis Kris :)
> 
>     Smith passes DH2, but (surprisingly) Schwartz fails!
> 
> Could you clarify what you mean by Smith/Schwartz passing/failing?

Sure :-) Suppose we have

N: A>B>C
N: B>A>C
1: C>A>B
1: C>B>A

The Smith and Schwartz sets are {A, B}. Now suppose that A buries:

N: A>C>B
N: B>A>C
1: C>A>B
1: C>B>A

The Smith set is still {A, B}, but the Schwartz set is {A} (unless 
there's a bug in my code - and rbvote).

Hence there exist Smith methods that pass DH2.[1] But there don't exist 
Schwartz methods that do so, because unilateral burial will lead the 
buriers' candidate to win, and bilateral burial makes C the CW.

As I have stated, I wouldn't put *too* much into this kind of knife edge 
election. It's not going to make me throw away RP or Schulze. But if 
you're going by the letter of the criterion, then Schwartz does seem to 
imply failure.

> ————
> That said, I'd like to offer some clarification. My concern isn't 
> actually with DH2 or DH3 scenarios.

[...]

> Second, I reject the idea of looking at individual scenarios like DH3 or 
> Burr, then judging if a voting system fails or succeeds in such a 
> scenario. (Or rather, using this to rule electoral systems in, not out). 
> This feels like declaring a theorem proven after trying a few numbers 
> and not finding a counterexample.
(I'll get to the rest at a later point)

I find this surprising. What initially got me to investigate this was 
your reply to my post about resistant set performance, where I showed 
that even Resistant,Borda had low manipulability. You said something 
like, and I'm paraphrasing, "but how do I know that the remaining share 
of manipulable elections isn't all turkey-raising of no-hope 
candidates?", and then pointed at Monroe's analysis.

If you have no concern about DH2 or DH3, then it would seem that you 
have no concern with Monroe's NIA either, because my whole point was 
that we could reduce all this complicated thinking about M-W equilibria 
in Monroe's scenario with a much simpler mechanically approximable 
criterion.

But if you weren't interested in Monroe's NIA to begin with, you should 
have made that more clear when you replied to my resistant set post.

> (The Burr dilemma should be the poster boy for this kind of bad 
> strategic analysis: it focuses on a single scenario, /and/ on group 
> strategy, /and/ it completely ignores the possibility of correlated 
> equilibria and mixed strategies...)

I may get into why I don't think that's an accurate depiction, either, 
later. But before I do that, I would like to know if single scenarios 
concern you when it comes to ruling methods out.

Do you consider concrete criteria and/or single scenario analyses 
valuable in making sure a method doesn't blow up on its users after 
implementation (or as a proxy for the risk that such an event may occur)?

And do you consider statistical analyses like manipulability and VSE 
useful to determine the viability of a method? Or are you more 
fundamentally saying that we can only rule methods out, but we can't 
rule them in by either approach?

-km

[1] Strictly speaking, all that this argument shows is that there may 
exist such a method. But since Smith,X preserves X's DH2 resistance, we 
can just let X=IRV and so we know that one exists.