Uniform estimates for Fourier restriction to polynomial curves in Rd\mathbb R^d

We prove uniform $L^p \to L^q$ bounds for Fourier restriction to polynomial curves in $\mathbb R^d$ with affine arclength measure, in the conjectured range.Comment: This is a preprint version of a published article. The final version is in Amer. J. Math. 138 (2016), no. 2, 449--47

Collective rationality and monotone path division rules

We impose the axiom Independence of Irrelevant Alternatives on division rules for the conflicting claims problem. With the addition of Consistency and Resource Monotonicity, this characterizes a family of rules which can be described in three different but intuitive ways. First, a rule is identified with a fixed monotone path in the space of awards, and for a given claims vector, the path of awards for that claims vector is simply the monotone path truncated by the claims vector. Second, a rule is identified with a set of parametric functions indexed by the claimants, and for a given claims problem, each claimant receives the value of his parametric function at a common parameter value, but truncated by his claim. Third, a rule is identified with an additively separable, strictly concave social welfare function, and for a given claims problem, the amount awarded is the maximizer of the social welfare function subject to the constraint of choosing a feasible award. This third way of describing the family of rules is similar to Lensberg's (1987) solution for bargaining problems applied to conflicting claims problems

Asymmetric parametric division rules

We describe and characterize the family of asymmetric parametric division rules for the adjudication of conflicting claims. We use two approaches to characterize this family. The first approach follows the existing literature in defining a claims problem. As part of the characterization in this setting, we present two novel axioms which restrict how a division rule indirectly allocates between different versions of the same claimant. The second approach departs from the existing literature by expanding the definition of a claims problem to allow claimants to have multiple claims. The characterization in this setting uses the same set of axioms, though modified for this expanded domain, used by Young (1987) to characterize the family of symmetric parametric division rules. We show that these two approaches are essentially equivalent

Temptation with uncertain normative preferences

We model a decision maker who anticipates being affected by temptation but is also uncertain about what is normatively best. Our model is an extended version of Gul and Pesendorfer's (2001) where there are three time periods: in the ex-ante period the agent chooses a set of menus, in the interim period she chooses a menu from this set, and in the final period she chooses from the menu. We posit axioms from the ex-ante perspective. Our main axiom on preference states that the agent prefers to have the option to commit in the interim period. Our representation is a generalization of Dekel et al.'s (2009) and identifies the agent's multiple normative preferences and multiple temptations. We also characterize the uncertain normative preference analogue to the representation in Stovall (2010). Finally, we characterize the special case where normative preference is not uncertain. This special case allows us to uniquely identify the representations of Dekel et al. (2009) and Stovall (2010)