[EM] Gradual Information Approval

[Simmons, Forest]

A while back Kevin came up with an interesting method that he called Gradual Information Approval.
 
There are both ranked ballot and ratings versions of this method.
 
If there are K candidates then K-1 approval rounds are simulated.
 
In round m, the 1+K-m most approved candidates in the previous round are given equal weight in determining the approval cutoffs for the next round.
 
In the ratings version, above mean strategy is used.
 
In the ordinal version, above median strategy is used.
 
What if we used ballots that are intermediate between ratings and rankings?
 
I refer to what I call "Ranked Strength Voting Preferences."
 
For these RSVP ballots you don't have to have any absolute strengths for the intensity of preferences.  But you are able to indicate which of two preferences you consider stronger, if you feel that one is stronger than another.
 
So the ballot
 
A>>>B>>>>C>>>D>E>F>>G
 
does not imply that A is preferred over B with three times the intensity of the D over E preference.   It only means that the strongest preference is B over C, then next strongest is A over B, which is about the same as the C over D  preference, etc.
 
I say that RSVP ballots are somewhere between Ratings and Rankings because Rankings can be inferred from RSVP, which in turn can be inferred from high resolution Ratings.
 
Now, how would RSVP ballots be used for Gradual Information Approval?
 
If every preference has a different strength, then the approval cutoff would be the highest strength preference that is straddled by the set of 1+K-m most approved candidates  from the previous round.
 
If there are no distinctions in strength of preferences straddled, then we're back to the above median strategy.
 
Otherwise, we use a hybrid of these two strategies, using above median for the highest strength preferences straddled by the previous step approval standouts, etc.
 
Kevin, did Gradual Information Approval turn out to be monotone?  Probably not.
 
What other applications would be good for these RSVP ballots?  [I mean besides invitations to parties.]
 
Forest
 
 
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