[EM] Method X

Kristofer Munsterhjelm km_elmet at t-online.de
Tue Aug 1 16:20:51 PDT 2023


This is method X, the monotone burial-resistant method from the previous 
post: (It doesn't really have a name yet.)

- Each candidate A obtains his score by eliminating candidates in 
rounds, one candidate per round, until one other candidate (B) remains 
or A himself is forced to be eliminated. In the former case, A's score 
is A>B. In the latter case, A's score is zero.

- When figuring out A's score, the method chooses the sequence of 
candidates to eliminate so as to maximize that score.

- In a round, the method can never eliminate a candidate who has more 
than 1/n of the total number of (non-exhausted) first preferences, where 
n is the number of remaining candidates in the round in question.

- Unlike IFPP, it never eliminates more than one candidate per round.

- Highest score wins.

That's it!

Now for the bad news:
	- it's not summable (a summary takes O(n2^n) space),
	- it's not polytime (ditto),
	- its use of quotas means it would probably fail IIB,
	- and I have no idea why it works.

I can't say I wasn't tempted to name it after myself since it's kind of 
a big deal (if I can verify its monotonicity), but given its drawbacks, 
maybe it's not a good idea? It's like the Kemeny of monotone 
burial-resistant methods: slow and impractical, but it shows what's 
*possible*.

I would very much like some independent verification or replication, though.

-km


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