[EM] Eight FBCs

[MIKE OSSIPOFF]

I've said that ERBucklin(whole) passes Strong FBC, while Alex said that only 
Reverse Plurality passes it. Aside from the fact that I didn't prove my 
statetement on that, and it could be mistaken, though I doubt that it is, 
the explanation for the contradictory statements is that Alex and I are 
defining Strong FBC slightly differently. And defining ordinary FBC slightly 
differently.

Alex defined it in terms of incentive. He said that no one should have 
incentive to vote someone over his/her favorite. I myself often say it that 
way, but I define it in terms of what a voter can do, given a configuration 
of other people's votes.

My ordinary definition hasn't changed, but I've iimproved its wording:

For a particular election, and for a particular voter who has a unique 
favorite, it shouldn't be possible to contrive a configuration of other 
people's ballots such that that voter can optimize his outcome only by 
voting someone over his unique favorite.

A voter optimizes his outcome, for a particular configuration of other 
people's ballots, if s/he votes so as to gain an outcome to which she 
doesn't prefer any other outcome that she could gain with that configuration 
of other people's ballots.

A voter's unique favorite candidate is a candidate whom s/he prefers to each 
of the other candidates.

[end of FBC definition]

Alex's definition is more demanding than mine. Approval passes even the most 
demanding interpretation of Alex's defilnition, and so I think that Alex's 
definition the more useful one.

But there may be methods, such as Bucklin versions, that pass my FBCs but 
not Alex's, so my FBC and Strong FBC definitions could still be useful.

Alex's defilnlition needs a definition of incentive. I suggest:

Given hir predictive information and candidate ratings,

A voter has strong incentive to vote a certain way if, ,  no other way for 
hir to vote gives hir a higher utility expectation.

A voter has a strongest incentive to vote a certain way if no other way for 
hir to vote gives hir as
high a utiilty expectation.

A voter has some incentive to vote a certain way if that way of voting isn't 
dominated for hir by another way of voting.

[end of incentive definitions]

Of course the weakest incentive gives the most demanding FBC. Approval 
passes the especiallly demanding some-incentive FBC.

I suggest the following naming of FBCs:

Follow "FBC" with a 2-digit decimal number. The 1's digit is 0 if it's only 
about not voting someone over your favorite. It's 1 if it's about not voting 
someone equal to or over your favorite. The digit of larger value is 0 if 
it's about what the voter can do in a particular configuration of other 
people's votes. It's 1 if it's about strongest incentive. It's 2 if it's 
about strong incentive, and it's 3 if it's about some incentive.

Approval meets the especially demanding FBC30. Maybe Bucklin doesn't. I'm 
not sure. It seems to, at first glance. Buckliln with AERLO seems to meet 
FBC01, but I haven't proved it. Bucklin with AERLO may well not meet FBC11, 
FBC21 or FBC31.  I haven't checked those things, and haven't proved my 
claims about Bucklin meeting FBC00, or Bucklin with AERLO meeting FBC01.

Mike Ossipoff

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