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

[Colin Champion]

I think Tideman's original description calls for the implementor to 
recursively exhaust over all permutations of tied margins, and to 
construct a winner set as the union of winners under all recursive 
extensions. This is no fun. The Handbook of Computational Social Choice 
(one of my few books on the subject) says "Whether a given alternative 
is a ranked pairs winner... turns out to be NP-complete". (p100.)
    I agree that Schulze's method cuts out a lot of pain. I don't think 
Tideman himself ever proposed his method for practical use.
       CJC

On 06/03/2023 05:26, 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.
>
> Kristofer wrote under "Why all the fuss?":
>> (Of course, it's not that easy: someone has to actually implement the method -- and the
>> simulations!)
> Yes, implementing a complicated method can take some time, and I'm often unsure of the
> prospects for a method to be good in some way. (This might even cause me to implement it
> wrong due to bad intuition.)
>
> I've seen skimming the recent posts that Forest is proposing a number of methods where
> you're pretty much going to look at all the pairwise contests, and there are a number of
> points within the course of following the algorithm where the method can take a turn and
> lead to a change in outcome. I feel pretty confident at least that such a method, from a
> burial incentive standpoint, is not going to be very interesting to Kristofer. It might
> work for me, that's true.
>
> 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.)
>
> 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.
>
> Kevin
> votingmethods.net
> ----
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