[EM] Couple of comments (AMS, Why the fuss)

[Kristofer Munsterhjelm]

On 06.03.2023 06:26, Kevin Venzke wrote:
> Hello,
> 
> Colin wrote:
>> Their specification doesn't say what to do if two pairs have equal margins, although other
>> forms of tie are at least vaguely described. I assume "there is a tie" means "the margin is
>> zero", but the language is slightly misleading. Maybe whenever two pairs had equal margins
>> the AMS resorted to a coin toss between all candidates.
> 
> Incidentally I think this is a considerable advantage of Schulze, that no matter which
> approach you use, i.e. the beatpath algorithm or the Schwartz sequential dropping one, you
> are able to go through the calculation a single time and you will know whether ultimately
> there is a tie and who was in it.
> 
> I recently made a calculator that tries to show the steps to solve Ranked Pairs and River
> and I couldn't come up with a satisfying way to dedupe all the possible ways that one could
> traverse the propositions when there are tied strengths, and potentially many. I settled on
> showing up to two traversals per possible winner.

IIRC, Tideman originally proposed a method where X wins if there exists 
a way to break ties so that X comes unambiguously first in Ranked Pairs. 
This method is neutral, but it's also (as Colin said) NP-complete. In 
practice, people just break ties in some way. I think that the AMS 
method (just a coin flip) fails clone independence and that random voter 
hierarchy, while cloneproof, fails summability. But I'm not entirely 
sure about either.

(E.g. part of my intuition says: "if you pick a random voter and rank 
A>B over B>A if that voter ranks A over B... isn't that the same as a 
coin toss? Because imagine you eliminate everybody but A and B, then the 
number of voters who rank A above B is just A>B, and the number of 
voters who rank B above A is B>A; and by presumption that there's a tie, 
A>B must be equal to B>A, so the chance of picking a voter who prefers A 
to B is 50%". If it were that simple, then there would be no need for 
random voter hierarchy, so clearly I'm missing something.)

Maybe there exist cloneproof summable tiebreaking rules. But practically 
speaking, I imagine public elections would produce enough noise in the 
ballots that it would be very unlikely for two pairwise relations 
involving candidates in the Smith set to have exactly equal strength.

I agree that Schulze doesn't have this problem, though I have the 
impression it's considered to be more complex and harder to explain to 
non-mathematicians. (However, the evidence is ambiguous: both Ranked 
Pairs and Schulze have been used by organizations to do their elections. 
And Schulze is used by a Spanish city for referenda, but I'm not aware 
of any public elections using RP. So who knows?)

> One thing I could do is provide a bunch of examples on what methods 
> look like in my framework, taking the form of a Python 3 class, and 
> then people could just send me methods if they want. I'm not sure if
> there would be any takers for that. It would probably be more 
> interesting if I was maintaining and publishing a big list of 
> results, which at the moment I'm not. (Partly due to the sensitivity 
> of results to scenario parameters.)
I've had similar ideas myself, that surely it should be possible to not 
be duplicating each other's efforts as much. Strictly speaking, my 
quadelect simulator is extensible, but I wouldn't call it very easy to 
use and C++ has its own quirks.

Would you be interested in putting your code on a version control system 
of some kind?

> The idea of making some new visuals is interesting. I would like to 
> somehow map the correlations or apparent trade-offs present in
> methods' compromise, burial, and truncation incentive. That's
> seemingly a 3D plot though.

My Python voting simulator uses stacked bar charts to show 
susceptibility to compromise, burial, and two-way strategy (both at 
once). Unfortunately its results are sometimes wrong and I can't find 
the bug that distorts them. But that might be a way to show just what 
type of strategy works - e.g. Plurality is all compromise, Antiplurality 
is all burial.

-km