[EM] halp!

[Kristofer Munsterhjelm]

On 05.08.2021 03:08, robert bristow-johnson wrote:
> i just got offa the phone with a Dr. Tideman.  you guys might know him.  could someone here, who is more qualified than me, put in a new line into this table at Wikipedia:
> 
> https://en.wikipedia.org/wiki/Comparison_of_electoral_systems#Compliance_of_selected_single-winner_methods 
> 
> for BTR-STV ?   https://electowiki.org/wiki/Bottom-Two-Runoff_IRV
> 
> I know that BTR is Condorcet-compliant (which means that it cannot be LNH) and that, strictly, it's not precinct summable (if there was a cycle, you don't know from the summable defeat data who wins).  But I am not qualified to get the facts and authoritatively evaluate each criterion and say "yea" or "nay" to it.
> 
> geez, i can't pay you, but i can beg.

This is what I know:

Every monotonicity property IRV fails, BTR-STV/BTR-IRV also fails.
Majority, Condorcet: pass (obviously; all implied by Condorcet)
Smith, Mutual majority, majority loser, Condorcet loser: pass (Smith
implies the rest)
Clone independence: fail (crowding: https://www.rangevoting.org/BtrIrv.html)
IIA: fail
Reversal symmetry: fail (because IRV fails it)
Consistency: fail (winner consistency incompatible with Condorcet, and
no Condorcet method but Kemeny passes social order consistency)
Participation, favorite betrayal: fail (incompatible with Condorcet)
Later-no-help, later-no-harm: fail (ditto)
Polynomial runtime: O(n^2)
Summable: O(n!)
Resolvability (Woodall's version): pass if the elimination count breaks
ties by second preference (then third, fourth, etc), otherwise I don't know.

Also (not mentioned on the list):
Plurality: pass
Mono-add-top: fail (incompatible with having both Smith and Plurality)

These I'm not 100% certain about:

LIIA: Pretty sure this is a fail, though I could be wrong.
ISDA: Not sure, but I would expect fail.

So all we need to do is to find a LIIA failure and an ISDA failure.
Anyone got such failures?

I'm kinda thinking I should make a simple Python program "How Your
Method Sucks" that finds criterion failures.

I kid :-) About the title, at least. It *would* be nice to just throw a
method at some program and get "definitely fails these".

-km