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.

Understanding how individuals and groups differ in their opinions and preferences is central to analyzing disagreement, measuring polarization, designing institutions, and predicting collective outcomes. Yet comparing preferences requires more than observing how each person ranks alternatives---it requires a method for comparing preference orderings themselves. This paper develops a formal framework to infer how individuals might rank different preference orderings based solely on their observed preferences. We introduce a set of natural and behaviorally plausible axioms---Independence (I), Disagreement Aversion (DA), and Symmetry (S)---and show that they uniquely characterize a class of hyperpreference relations and their associated utility representations. We apply this framework to the study of aggregation mechanisms, deriving necessary and sufficient conditions on utility structures that induce truthful preference reporting in equilibrium and guarantee efficiency. The results provide new insights into the design of strategyproof mechanisms under preference heterogeneity.

Keywords: Preference, Hyperpreference, Hyperutility, Strategy-proofness, Efficiency

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

 Coming soon...