27 April 2007, Computational Social Choice Seminar, Joel Uckelman
Sets of weighted formulas---known as goal bases---are a useful formalism for representing agent preferences. We exhibit restrictions on formulas or weights which correspond to well-known classes of utility functions. We give a proof that a particular fully-expressive language (positive clauses, arbitrary weights) admits of only a single representation for each utility function, and thereby show this language to be strictly less succinct than one of its superlanguages (clauses, arbitrary weights). We describe Max-Util, the decision version of the problem of finding states with optimal utility, and summarize known complexity results for different goal base languages. Finally, we describe an application of goal bases to committee elections, where they may be used as a voting language.