[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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