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Rank consistency

KM
Kristofer Munsterhjelm
Mon, Feb 19, 2024 6:18 PM

Given the subtleties about what "sincerity" means, that led to the
Gibbard-Satterthwaite discussion earlier, I'd like to suggest the
following property, based on an off-the-cuff naming in that thread:

Rank consistency: A method is strongly rank-consistent (passes strong
rank consistency) if there exists no situation where a voter who prefers
A to B can obtain a more preferred outcome by voting in a way that
indicates B>A or A>=B than by voting A>B.

A method is weakly rank-consistent if a voter who prefers A to B can
never get a better outcome (defined as above) by voting consistent with
B>A than by voting consistent with A>B or A=B.

(This by analog to strong and weak FBC, which are the same thing for
first preferences that this is for ranks.)

Range and Approval pass weak rank consistency. Strategy-proof ranked
methods like random pair and random favorite pass strong rank consistency.

Hopefully this should be more helpful than getting confused over
technical terms of sincerity (e.g.
https://old.reddit.com/r/EndFPTP/comments/1arr7bc/utah_lawmakers_advance_bill_to_drop_ranked_choice/kr28m85/).

What do you think? (I'm not wedded to the name.)

(By analog we could also define vNM-utility consistency, which requires
the voter's ballot to be some affine scaling of his honest utilities.
The weak analog would allow the scaled values to be rounded to integers
first. Hay voting passes this, but nothing else I know of does. Gibbard
precludes deterministic rated methods from passing this.)

-km

Given the subtleties about what "sincerity" means, that led to the Gibbard-Satterthwaite discussion earlier, I'd like to suggest the following property, based on an off-the-cuff naming in that thread: Rank consistency: A method is strongly rank-consistent (passes strong rank consistency) if there exists no situation where a voter who prefers A to B can obtain a more preferred outcome by voting in a way that indicates B>A or A>=B than by voting A>B. A method is weakly rank-consistent if a voter who prefers A to B can never get a better outcome (defined as above) by voting consistent with B>A than by voting consistent with A>B or A=B. (This by analog to strong and weak FBC, which are the same thing for first preferences that this is for ranks.) Range and Approval pass weak rank consistency. Strategy-proof ranked methods like random pair and random favorite pass strong rank consistency. Hopefully this should be more helpful than getting confused over technical terms of sincerity (e.g. https://old.reddit.com/r/EndFPTP/comments/1arr7bc/utah_lawmakers_advance_bill_to_drop_ranked_choice/kr28m85/). What do you think? (I'm not wedded to the name.) (By analog we could also define vNM-utility consistency, which requires the voter's ballot to be some affine scaling of his honest utilities. The weak analog would allow the scaled values to be rounded to integers first. Hay voting passes this, but nothing else I know of does. Gibbard precludes deterministic rated methods from passing this.) -km