[EM] Rank consistency

[Kristofer Munsterhjelm]

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