Assumptions about BSB’s Preferences
A1: S= {-1,1}d, d ?{1, 2, ...}. Let ? be the power set of S.
A2: BSB Preference Relation R ? ? x? connected & transitive (implies existence of ?(?|?) : ??? for (S, ?, R))
A3: Assume ?(B|A) = G [?(?B|A)]
A4: Assume G is sufficiently smooth so A3 is “stable”
A5: Assume ?(C ? B| A) = F [?(C|A ? B), ?(B|A) ]
A6: Assume F is sufficiently smooth so A5 is “stable”
A7: Assume certain preferences Boolean Algebra Consistent
A8: Assume ?({x}|?) > 0 for all x?S. (“positivity assumption”)
A9: Assume only “pair-wise” cliques for neighborhood graph