Optimal collective dichotomous choice under partial order constraints

Abstract This paper generalizes optimal collective dichotomous choices by including constraints which limit combinations of acceptance and rejection decisions for m projects under consideration. Two types of constraints are examined. The first type occurs when acceptance of some projects requires acceptance of others. This type reduces the choice problem to the tractable (solvable in polynomial time) problem of finding a maximum weight closed subset of a directed acyclic graph. The second type occurs when some projects must be accepted when certain others are rejected. We show that this type renders the choice problem to be NP-complete by reduction from the problem of Vertex Cover. Applicability of the generalization to information filtering is discussed.

[1]  R. K. Sah,et al.  Qualitative Properties of Profit-Maximizing K-Out-of-N Systems Subject to Two Kinds of Failures , 1988 .

[2]  G. Owen,et al.  Thirteen theorems in search of the truth , 1983 .

[3]  Christopher Winship,et al.  Information Processing and Jury Decisionmaking , 1984 .

[4]  Janny G. de Wit,et al.  Rational choice and the Condorcet jury theorem , 1998 .

[5]  T. Feddersen,et al.  Convicting the Innocent: The Inferiority of Unanimous Jury Verdicts under Strategic Voting , 1996, American Political Science Review.

[6]  J. Stiglitz,et al.  Committees, hierarchies and polyarchies , 1987 .

[7]  D. Kleinman,et al.  Optimal team and individual decision rules in uncertain dichotomous situations , 1993 .

[8]  L. Shapley,et al.  Optimizing group judgmental accuracy in the presence of interdependencies , 1984 .

[9]  R. Myerson.  Extended Poisson Games and the Condorcet Jury Theorem , 1998 .

[10]  Raaj Kumar Sah,et al.  An Explicit Closed-Form Formula for Profit-Maximizing k-Out-Of-n Systems Subject to Two Kinds of Failures , 1990 .

[11]  Shmuel Nitzan,et al.  Are qualified majority rules special? , 1984 .

[12]  T. Feddersen,et al.  Voting Behavior and Information Aggregation in Elections with Private Information , 1997 .

[13]  Shimon Even,et al.  Graph Algorithms , 1979 .

[14]  T. Feddersen,et al.  The Swing Voter's Curse , 1996 .

[15]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[16]  A. McLennan.  Consequences of the Condorcet Jury Theorem for Beneficial Information Aggregation by Rational Agents , 1998, American Political Science Review.

[17]  J. Stiglitz,et al.  The Architecture of Economic Systems: Hierarchies and Polyarchies , 1984 .

[18]  Shmuel Nitzan,et al.  Optimal Decision Rules in Uncertain Dichotomous Choice Situations , 1982 .

[19]  Shmuel Nitzan,et al.  The Optimal Decision Rule for Fixed-Size Committees in Dichotomous Choice Situations: The General Result , 1997 .

[20]  Scott E. Page,et al.  An appending efficient algorithm for allocating public projects with positive complementarities , 1997 .

[21]  Raaj Kumar Sah,et al.  Fallibility in Human Organizations and Political Systems , 1991 .

[22]  Pattie Maes,et al.  Social information filtering: algorithms for automating “word of mouth” , 1995, CHI '95.

[23]  Shmuel Nitzan,et al.  A general theorem and eight corollaries in search of correct decision , 1994 .

[24]  J. Banks,et al.  Information Aggregation, Rationality, and the Condorcet Jury Theorem , 1996, American Political Science Review.