A model of path-dependence in decisions over multiple propositions

Abstract

I develop a new model of sequential decision processes over multiple interconnected propositions, combining social choice theory and propositional logic. I focus on so-called priority-to-the-past decision processes. A sequential decision over multiple propositions is path-dependent if its outcome depends on the order in which the propositions are considered. I prove three main results. (1) Path-dependence of a strong kind occurs if and only if the propositional attitudes of an agent (individual or group) on a set of propositions violate strong consistency. Path-dependence of a weaker kind occurs if and only if these propositional attitudes are strongly consistent, but violate deductive closure. (2) If we impose universal domain, anonymity and completeness on a collective priority-to-the-past decision process, pathdependencies are unavoidable. (3) Path-dependence makes sequential decision processes vulnerable to manipulation by changes of the decision-path and to manipulation by expression of untruthful views on the propositions. I discuss three escape-routes from the problem of path-dependence: the special support, dictatorship and domain restriction approaches. Show more