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.
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Sen, Amartya K, 1976.
"Liberty, Unanimity and Rights,"
Economica,
London School of Economics and Political Science, vol. 43(171), pages 217-45, August.
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Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991.
"Voting by Committees,"
Econometrica,
Econometric Society, vol. 59(3), pages 595-609, May.
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Gaertner, Wulf & Pattanaik, Prasanta K & Suzumura, Kotaro, 1992.
"Individual Rights Revisited,"
Economica,
London School of Economics and Political Science, vol. 59(234), pages 161-77, May.
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