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A social decision function (SDF) is nonmanipulable if it is impossible for an individual, by misrepresenting his/her preferences, to secure a social outcome preferable to one secured through honesty. Examined are nonmanipulable SDFs that transform individual preferences & agendas into sets of best alternatives rather than unique best alternatives, ie, multivalued SDFs. Several reasonable criteria might be imposed on these SDFs: (1) neutrality, or unbiasedness among alternatives; (2) anonymity, or unbiasedness among alternatives; (3) nonimposition; & (4) normality, or consistency of choice under expansion & contraction of agendas. The main result is this: if a nonmanipulable, multivalued SDF satisfies all four reasonable criteria, then every choice set must contain a most preferred alternative for every individual, & every choice set must be contained in the set of Pareto optima. Dropping some of the criteria produces weaker but nonetheless interesting results. AA.

In this paper we discuss a new tort liability rule, which we call super-symmetric comparative negligence and vigilance. When both injurer and victim in an accident are negligent, it provides for liability shares that depend on the degrees of negligence of the two parties, similar to the standard comparative negligence rule. Unlike standard liability rules, however, when both parties are vigilant (i.e., taking more care than is efficient), the rule provides for liability shares that depend on the parties' degrees of vigilance. Moreover, when one party is negligent and the other is non-negligent, our rule provides for variable liability shares, that respond to both carefulness and carelessness of the parties. Our liability rule is equitable; it has no discontinuity at the efficient point where both parties are just meeting their standards of care; and it provides incentives that guarantee the injurer and victim will choose the efficient care levels. This paper does not include theorems and proofs; rather it explains the results with the aid of a simple example, laid out in an easy 3 x 3 table.