Individual Powers and Social Consent

We introduce a notion of conditionally decisive powers of which the exercise depends on social consent. Decisive powers, or the so-called libertarian rights, are examples and much weaker forms of powers are covered by our notion. We provide an axiomatic characterization of existence of a system of powers and its uniqueness as well as characterizations of various families of rules represented by systems of powers. Critical axioms are monotonicity, independence, and symmetric linkage (person i and i's issues should be treated symmetrically to person j and j's issues for at least one linkage between issues and persons). Considering a domain of simple preference relations (trichotomous or dichotomous preferences), we show under a certain assumption on the model that a rule satis¯es Pareto e±ciency, independence, and symmetric linkage if and only if it is represented by a \quasi-plurality system of powers". For the exercise of a power under a quasi-plurality system, at least either a majority (or (n + 1)=2) consent or a 50% (or (n ¡ 1)=2) consent is needed.