[EM] A family of easy-to-explain Condorcet methods

[Kristofer Munsterhjelm]

On 7/2/21 5:16 AM, Daniel Carrera wrote:
> 
> On Thu, Jul 1, 2021 at 5:51 PM Kristofer Munsterhjelm 
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
> 
>>     You probably need to define the list-creating procedure and explicitly
>>     refer to striking candidates off the list, so as not to confuse the
>>     method with IRV. I did a cursory check of Reddit and cmb3248 said "IRV
>>     is literally the same thing [as Pb] except instead of Condorcet winners
>>     it uses majority winners, something people already get". The
>>     remove/eliminate distinction seems to be a subtle one that not
>>     everybody
>>     gets.
> 
> 
> Indeed, I'm sure most people would say that "remove" and "eliminate" are 
> synonyms. Even now I honestly don't understand why you assign them 
> different meanings (a dictionary says that they're synonyms). I simply 
> accepted the different meanings that you assigned to them for the sake 
> of communication.

I may have been a little imprecise in either what I thought or said. 
What I mean, or what I should've said at least, is that I understand 
that the way you use "remove" doesn't mean what most people in voting 
methods call "eliminate", so it makes sense to distinguish between the 
two. But you're also very right in that, to most people, the two words 
are synonyms. So when you describe the method, you should specify 
exactly what you mean by remove, because otherwise their minds will go 
directly to IRV.

> 
>     In a three-cycle, Pb would elect the candidate among the top two who
>     beats the other one pairwise - kind of like top-two runoff within the
>     Smith set, now that I think of it.
> 
>     It's possible that in a cycle situation, a party A can split its
>     vote so
>     that instead of the Plurality ranking being A>B>C, it becomes
>     B>C>A1>A2,
>     and then the clones are kicked off the list early, after which B
>     beats C
>     pairwise and wins.
> 
> 
> That's a bit similar to how Minimax is not clone independent either. I 
> think a similar example shows that Pb is not ISDA either. Imagine that 
> A2 is not quite a clone but is similar enough to siphon a few 
> first-choice votes. So the Smith set is still {A,B,C} but Plurality now 
> ranks 'A' lower.

ISDA failure is pretty easy, I think. If the base method isn't ISDA (and 
Plurality isn't), then eliminating the Smith set before doing the base 
method can alter the order that the candidates appear in the cycle, and 
thus who wins.

If you absolutely need ISDA, then you can just eliminate everybody 
outside the Smith set first before running Plurality and Pb. This will 
give you additional nonmonotonicity, though, and give up summability, so 
I wouldn't recommend it.

> I suspect that in practice Pb would work great. I once read that >90% of 
> elections have a Condorcet winner anyway (I think that came from Tideman 
> but I forget).

Yeah, you're most likely right, though remember that the voting patterns 
might change. If the method supports a more diverse arrangement of 
candidates, then more candidates may well appear, and the chance of 
hard-to-resolve situations may increase.

I'll try to find a better method -- my optimization simulations suggest 
that monotonicity doesn't affect manipulability much, and so there 
should be a DMTBR Smith monotone method out there somewhere. It's just 
very hard to get the pieces to fit.

But in the meantime, if you want to advocate for Pb, go ahead :-)