Designer path independent choice functions

This paper provides an algorithm for the construction of all PICFs on a finite set of alternatives, V, designed by an a priori given set I of initial choices as well as the determination of whether the initial set I is consistent with path independence. The algorithm is based on a new characterization result for path independent choice functions (PICF) on finite domains and uses that characterization as the basis of the algorithm. The characterization result identifies two properties of a partition of the Boolean algebra as necessary and sufficient for a choice function C to be a PICF: (i): For every subset A of V the set <InlineEquation ID="Equ1"> <EquationSource Format="TEX">${\rm arc}(A)={\{}B: C (B)=C(A){\}}$</EquationSource> </InlineEquation> is an interval in the Boolean algebra 2<Superscript> V </Superscript>. (ii): If A/B is an interval in the Boolean algebra such that C(A)=C(B) and if M/N is an upper transpose of A/B then C(M)=C(N). The algorithm proceeds by expanding on the implications of these two properties. Copyright Springer-Verlag Berlin/Heidelberg 2005