Characterizing lexicographic preferences, Journal of Mathematical Economics, March 2016 (with Mark Voorneveld) (Link to publication here)
Abstract: We characterize lexicographic preferences on product sets of finitely many coordinates. The main new axiom is a robustness property. It roughly requires this: Suppose x is preferred to y; many of its coordinates indicate that the former is better and only a few indicate the opposite. Then the decision maker is allowed a change of mind turning one coordinate in favor of x to an indifference: even if one less argument supports the preference, the fact that we started with many arguments in favour of x suggests that such a small change is not enough to give rise to the opposite preference.
A "three-sentence proof" of Hansson's theorem, Forthcoming in Economic Theory Bulletin (Link to publication here)
We provide a new proof of Hansson's theorem: every preorder has a complete preorder extending it. The proof boils down to showing that the lexicographic order extends the Pareto order.
Choice by Incomplete Checklist (PDF) (New version coming soon!)
Abstract: A decision maker chooses alternatives from menus by proceeding sequentially through a checklist of properties. In contrast to the standard framework her ranking of properties is not necessarily complete. We characterize the model in terms of observed choices. As another main result of the paper we show that an important special case of our model is exactly equivalent to the maximization of an incomplete preference relation. We also relate the model to the choice model resulting from the maximization of a multi-utility (also called multi-criteria) function. Our results suggest a close relationship between the degree of completeness of the order by which properties in a checklist are looked at, and the degree of completeness of the revealed preference relation maximizing the corresponding choice function.
No Bullying! A playful proof of Brouwer's fixed-point theorem (with Mark Voorneveld)
Abstract: We give an elementary proof of Brouwer's fixed-point theorem. The only mathematical prerequisite is a version of the Bolzano-Weierstrass theorem: a sequence in a compact subset of n-dimensional Euclidean space has a convergent subsequence with a limit in that set. Our main tool is a `no-bullying' lemma for agents with preferences over indivisible goods. What does this lemma claim? Consider a finite number of children, each with a single indivisible good (a toy) and preferences over those toys. Let's say that a group of children, possibly after exchanging toys, could bully some poor kid if all group members find their own current toy better than the toy of this victim. The no-bullying lemma asserts that some group S of children can redistribute their toys among themselves in such a way that all members of S get their favorite toy from S, but they cannot bully anyone.
Asymptotic properties of welfare relations (PDF) (This version: June 2017)
Abstract: We introduce and discuss notions of efficiency in the aggregation of infinite utility streams. For any utility streams x and y, our efficiency criteria roughly requires this: If a utility stream x dominates another utility stream y and if the asymptotic density of the set of coordinates in favor of x is strictly positive, then x is socially preferred to y. As a robustness check of the proposed efficency axioms we explore the consistency of the axioms with notions of equity. Our main results characterize one period utility domains, i.e. the set of utilities Y attainable by each generation, admitting a social welfare aggregator with the desired properties.
Lexicographic Majority (PDF) (This version: June 2017)
Abstract: We propose a descriptive theory of lexicographic choice, lexicographic majority, where a decision maker's ranking of attributes is not necessarily strict. Thus we allow an agent to assign the same rank to a set of attributes. If a decision maker assigns the same rank to a set of attributes, it is assumed that the simple majority heuristic is used, within the set, to discriminate between pairs of vectors. Our model is general enough to account for intransitive preferences. Moreover, it includes as special cases: pure lexicographic preferences, simple majority preferences and lexicographic semiorders. We justify lexicographic majority preferences by providing an axiomatization in terms of behavioral properties. As a further justification we characterize lexicographic majority preferences as a subset of the class of weighted majority preferences.