| Abstract: |
We formalize 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. Main results provide an axiomatic characterization for existence of a
system of powers and its uniqueness as well as characterizations of various
families of rules represented by systems of powers. In particular, we show
that a rule satisfies 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) if and only if
there is a system of powers representing the rule and that the system is
unique up to a natural equivalence relation. Considering a domain of simple
preference relations (trichotomous or dichotomous preferences), we show that a
rule satisfies Pareto efficiency, independence, and symmetry (the symmetric
treatment condition in a model with an exogenous linkage between issues and
persons) 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. |