Working papers/Works in progress

A long-standing foundational problem in the spatial theory of politicsis the generic emptiness of the majority core when there is more than one dimension in the policy space. This implies that, in general, we cannot predict where win-motivated candidates will locate in an electoral contest decided by majority rule. We assume that the candidates face some uncertainty: they observe each voter's ideal point in the policy space but not their indifference surfaces. Given any proper spatial voting game, we first identify the set of imprudent positions in the space. If a candidate adopts an imprudent position, then there exists a position for their opponent that will defeat them for certain (i.e., irrespective of the shape of the indifference surfaces). We introduce a new concept, the prudent core, as the set of positions that are not imprudent in this sense. We show that the prudent core is always non-empty. With majority voting and an odd number of voters, the prudent core equals the dimension-by-dimension median. The prudent core equals the majority core whenever the latter is non-empty.

Keywords: Spatial theory of politics, median voter theorem, prudent core, prudence.

In spatial voting games, the valence is traditionally modeled as a non-ideological attribute that is uniformly assigned to a candidate by all voters, independent of their policy preferences. In its original formulation, additive valence is assumed to be entirely detached from the candidate policy considerations. In this paper, we explore an alternative framework in which additive valence interacts with the candidates’ policy platforms. Each candidate possesses an individual valence level, but voters choose to recognize this valence only if the candidate is perceived as competent in defending their proposed policy. This perceived competence is assumed to be common knowledge among voters. The core objective of this study is to determine the conditions under which Nash equilibria arise in the context of electoral competition with policy-dependent additive valence.

Keywords: Spatial voting, Electoral competition, Dual valence, Equilibrium.

We study how to measure the utility an individual derives from the alignment between their preferred ranking and a noisy or random external ranking—for example, an investor comparing her ideal asset ordering to fluctuating market valuations, or a sports fan evaluating league standings against personal team rankings. In such settings, agents form hyperpreferences—preferences over rankings—derived from their own preferences. We formalize this through hyperpreference rules over lotteries on rankings by extending the von Neumann-Morgenstern expected utility framework. We provide a new set of axiomatic conditions under which these rules admit an expected utility representation. Our main results characterize this class via hyperutility functions defined over pairs of preferred and random rankings and identify conditions for metric-based representations, notably as expectations of ranking distances. The framework unifies preference uncertainty, consequentialist reasoning, and utility theory and applies broadly to finance, policy, sports, and household decisions, offering a foundation for quantifying utility when outcomes are expressed as rankings rather than absolute payoffs.

Keywords: Hyperpreference rule, Hyperutility, Expected-utility, Metric utility

The joint enforcement of rules creates a fundamental tension between rewarding historical contribution and maintaining future prevention incentives. We use the Shapley value as a benchmark for allocating enforcement revenues among actors possessing complementary detection channels. When an actor's preventive vigilance reduces the incidence of violations, assigning it a large share of recoverable sanctions can conflict with its private interest in compliance, making zero vigilance optimal. We determine this individual negligence threshold without relying on a specific functional form for the prevention technology. We then characterize the unique efficient allocation rule that respects these thresholds as upper bounds while preserving the relative Shapley proportions among unconstrained actors. The resulting formula coincides with Moulin’s weighted gains method but, both the weights and constraints derive endogenously from the enforcement context. As the stakes associated with enforcement rise, individual constraints become binding in a precise order determined by compliance stakes relative to Shapley weights. Applications involving platform fraud and a shared data registry illustrates the practical scope of this framework.

 This paper characterizes stable allocations under collective decision-making with single-peaked and single-dipped preferences. We prove necessary and sufficient conditions for stability in both frameworks, showing that stability requires either resource-scarce coalitions to receive everything (without exceeding peaks) or resource-abundant coalitions to receive exactly their ideal points. Applications to the UN Security Council and EU Council reveal how veto power and majority requirements create institutional friction, forcing negotiation and compromise while preventing unilateral domination.

In this paper, we study how preferences defined over a set of alternatives can be extended to preferences over committees of fixed size drawn from that set, when each committee member is assigned a distinct task that cannot be shared or partially performed by another member. We adopt an axiomatic approach grounded in observable choice behavior. Within this framework, we derive conditions under which an aggregation (selection) rule satisfies strategy-proofness and/or efficiency. 

Coming soon...