Arbitrary Preferences Research Articles

Recovering the Anchoring of Economic Valuations

We revisit the interpretation of the anchoring effect as evidence for nonexisting or arbitrary preferences. A theory of endogenous information acquisition (i.e., deliberation) is developed to rationalize the causal dependence of economic valuations on arbitrary anchor numbers. We identify theory-driven moderators to reconcile seemingly discrepant findings among original and follow-up anchoring experiments. We demonstrate in a meta-analysis that the anchoring effect may be systematically moderated by unintended experimental/individual differences. Moreover, apparent replication failure of the anchoring effect may be a false negative for self-countervailing treatment effects, because an anchoring treatment may cast opposite effects on different subjects within an experiment. (JEL C90, D11, D83)

Stability in Large Markets

Abstract In matching models, pairwise-stable outcomes do not generally exist without substantial restrictions on both preferences and the topology of the network of contracts. We address the foundations of matching markets by developing a matching model with a continuum of agents that allows for arbitrary preferences and network structures. We show that pairwise-stable outcomes are guaranteed to exist. When agents can interact with multiple other counterparties, pairwise stability is too weak of a solution concept, and we argue that a refinement of it called tree stability is the most appropriate solution concept in this setting. Our main results show that tree-stable outcomes exist for arbitrary preferences and network topologies.

Measuring Growth in Consumer Welfare with Income-Dependent Preferences: Nonparametric Methods and Estimates for the United States

Abstract How should we measure changes in consumer welfare given observed data on prices and expenditures? This article proposes a nonparametric approach that holds under arbitrary preferences that may depend on observable consumer characteristics, for example, when expenditure shares vary with income. Using total expenditures under a constant set of prices as our money metric for real consumption (welfare), we derive a principled measure of real consumption growth featuring a correction term relative to conventional measures. We show that the correction can be nonparametrically estimated with an algorithm leveraging the observed, cross-sectional relationship between household-level price indices and household characteristics such as income. We demonstrate the accuracy of our algorithm in simulations. Applying our approach to data from the United States, we find that the magnitude of the correction can be large because of the combination of fast growth and lower inflation for income-elastic products. Setting reference prices in 2019, we find that (i) the uncorrected measure underestimates average real consumption per household in 1955 by 11.5%, and (ii) the correction reduces the annual growth rate from 1955 to 2019 by 18 basis points, which is larger than the well-known “expenditure-switching bias” over the same time horizon.

Cutting a Cake Fairly for Groups Revisited

Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to partition the players into groups of any desired size and divide the cake among the groups so that each group receives a single contiguous piece and every player is envy-free. For two groups, we characterize the group sizes for which such an assignment can be computed by a finite algorithm, showing that the task is possible exactly when one of the groups is a singleton. We also establish an analogous existence result for chore division, and show that the result does not hold for a mixed cake.

Higher-Order Optimality Conditions in Set-Valued Optimization with Respect to General Preference Mappings

We present higher order necessary conditions for a model of welfare economics, where the preference mapping has a star-shape property. We assume that the preferences can be satiable and can be described by an arbitrary preference set, without the use of utility functions. These conditions are formulated in terms of higher-order directional derivatives of multivalued mappings, and the variable domination structure is not given by cones.

Core and top trading cycles in a market with indivisible goods and externalities

In this paper, we incorporate externalities into Shapley–Scarf housing markets, expressing agents’ preferences as defined over allocations rather than houses. We introduce a class of preferences called hedonic preferences, extend the top trading cycles (TTC) algorithm to housing markets with hedonic preferences, and investigate the existence and core properties of TTC allocations. In order to further expand the applicability of the TTC algorithm, we consider a class of preferences called trading-cycle-lexicographic preferences, and we also construct worst-case hedonic preferences from arbitrary preferences. Lastly, we study the properties of the TTC algorithm as a mechanism on the domain of preferences called egocentric preferences. Our results show that many desirable properties of the TTC algorithm for housing markets without externalities can be extended to housing markets with certain kinds of externalities.

Continuity and closedness of constraint and solution set mappings in unified parametric semi-infinite vector optimization

The main aim of the paper is to study continuity properties of the constraint and solution set mappings of a semi-infinite vector optimization problem. The problem is studied in a general setting of topological spaces and the solution concept used is a unified notion, which unifies many solution concepts in literature. This unified notion is given using an arbitrary preference relation, which is not necessarily a preorder. We establish the closedness, upper and lower continuity of the constraint set mapping governed by inequality constraints. These results are further used to establish the closedness and continuity of solution sets both in the image and given spaces. The results are further justified with the help of examples.

State Authority, Parental Authority, and the Rights of Mature Minors.

When mature minors face a decision with important consequences, such as whether to undergo a risky but potentially life-saving medical procedure, who should decide? Relying on liberal political theory’s account of the importance of decisional autonomy for adults, and given the scalar nature of the capacities needed to exercise decisional autonomy, I argue that mature minors with the requisite capacities and commitments have a right to decisional autonomy though they are not yet 18. I argue for this right using a ‘balancing of interest’ account of rights: the interest mature minors have in decisional autonomy outweighs their parents’ interest in shaping their children as a means of ‘creative self-extension’. But I propose two limitations on this right: requests for waivers of the rule that one must be at least 18 to decide cannot be so numerous as to make adjudication impractical; and though a competent adult’s voluntary decision to refuse medical treatment should generally be respected, the state may reject a mature minor’s decision upon review by an indifferent judge of the minor’s capacities and reasons. The judge reviews not the substantive merits or prudence of the decision, but whether the decision promotes the interest in decisional autonomy, by asking among other things whether the decision is the minor’s own, is tethered to core commitments rather than based on arbitrary preferences, and could be regarded as reasonable to the minor’s ‘future self’.

Cautious farsighted stability in network formation games with streams of payoffs

We propose a new notion of farsighted pairwise stability for dynamic network formation which includes two notable features: consideration of intermediate payoffs and cautiousness. This differs from existing concepts which typically consider either only immediate or final payoffs, and which often require that players are optimistic in any environment without full communication and commitment. For arbitrary (and possibly heterogeneous) preferences over the process of network formation, a non-empty cautious path stable set of networks always exists. Furthermore, some general relationships exist between cautious path stability and other farsighted concepts.

Essential stability in unified vector optimization

The emphasis of the paper is to examine the essential stability of efficient solutions for semicontinuous vector optimization problems, subject to the perturbation of objective function and feasible set. We obtain sufficient conditions for existence and characterization of essential efficient solutions, essential sets and essential components, where the efficient solutions are governed by an arbitrary preference relation in a real normed linear space. Further, we establish the density of the set of stable vector optimization problems in the sense of Baire category. We also exhibit that essential stability is weaker than examining continuity aspects of solution sets.

How to Cut a Cake Fairly: A Generalization to Groups

A fundamental result in cake cutting states that for any number of players with arbitrary preferences over a cake, there exists a division of the cake such that every player receives a single contiguous piece and no player is left envious. We generalize this result by showing that it is possible to partition the players into groups of any desired sizes and divide the cake among the groups so that each group receives a single contiguous piece, and no player finds the piece of another group better than that of the player’s own group.

Endogenous Leverage in a Binomial Economy: The Irrelevance of Actual Default

We show that binomial economies with financial assets are an informative and tractable model to study endogenous leverage and collateral equilibrium: endogenous leverage can be highly volatile, but it is always easy to compute. The possibility of default can have a dramatic effect on equilibrium, if collateral is scarce, yet we prove the No-Default Theorem asserting that, without loss of generality, there is no default in equilibrium. Thus potential default has a dramatic effect on equilibrium, but actual default does not. This result is valid with arbitrary preferences, contingent promises, many assets and consumption goods, production, and multiple periods. On the other hand, we show that the theorem fails in trinomial models. For example, in a CAPM model, we find that default is robust. In a model with heterogeneous beliefs, we find that different agents might borrow on the same asset with different LTVs.

Efficient and Strategy-Proof Multi-Unit Object Allocation with Money: (Non)decreasing Marginal Valuations without Qquasi-Linearity

We consider the problem of allocating multiple units of an indivisible object among agents and collecting payments. Each agent can receive multiple units of the object, and his (consumption) bundle is a pair of the units he receives and his payment. An agent's preference over bundles may be non-quasi-linear, which accommodates income effects or soft budget constraints. We show that the generalized Vickrey rule is the only rule satisfying efficiency, strategy-proofness, individual rationality, and no subsidy for losers on rich domains with non-decreasing marginal valuations. We further show that if a domain is minimally rich and includes an arbitrary preference exhibiting both decreasing marginal valuations and a positive income effect, then no rule satisfies the same four properties. Our results suggest that in non-quasi-linear environments, the design of an efficient multi-unit auction mechanism is possible only when agents have non-decreasing marginal valuations.

Arrovian Aggregation of Convex Preferences

We consider social welfare functions that satisfy Arrow's classic axioms ofindependence of irrelevant alternativesandPareto optimalitywhen the outcome space is the convex hull of some finite set of alternatives. Individual and collective preferences are assumed to be continuous and convex, which guarantees the existence of maximal elements and the consistency of choice functions that return these elements, even without insisting on transitivity. We provide characterizations of both the domains of preferences and the social welfare functions that allow for anonymous Arrovian aggregation. The domains admit arbitrary preferences over alternatives, which completely determine an agent's preferences over all mixed outcomes. On these domains, Arrow's impossibility turns into a complete characterization of a unique social welfare function, which can be readily applied in settings involving divisible resources such as probability, time, or money.

Strongly sincere best responses under approval voting and arbitrary preferences

Approval voting allows voters to support as many candidates as they wish. One advantage is that voters have weak or no incentives to vote insincerely. However, the exact meaning of this statement depends on how the voters' preferences over candidates are extended to sets. We show that, under a combination of standard, well-established assumptions on extended preferences, voters always have a strongly sincere best response (a best response ballot such that every approved candidate is strictly preferred to every disapproved one) given other voters' ballots. An analogous result for sincere best responses obtains under weaker conditions. The results hold for arbitrary preferences over candidates, allowing for indifferences but covering the extreme cases of dichotomous or strict preferences. As a corollary, we show that the classical strategy-proofness result for dichotomous preferences (Brams and Fishburn, 1978) holds for a larger class of preferences on sets than originally assumed.

Limiting Sender's information in Bayesian persuasion

I study how the outcome of Bayesian persuasion depends on Sender's information. I consider a game in which, prior to Sender's information disclosure, Designer can restrict the most informative signal that Sender can generate. In the binary action case, I consider arbitrary preferences of Designer and characterize all equilibrium outcomes. As a corollary, I derive an information restriction that maximizes Receiver's payoffs: Whenever Designer can increase Receiver's payoffs by restricting Sender's information, the Receiver-optimal way coincides with an equilibrium of a hypothetical game in which Receiver persuades Sender.

Ranking objects from a preference relation over their subsets

In many everyday situations, we need to rank individuals or single items having the possibility to observe the behavior of groups. In this paper we propose a way to get this ranking over the elements of a set X, starting from an arbitrary preference relation over the subsets of X and taking into account the information provided by this ranking over the subsets. To this purpose, we use a very common approach in the social choice framework: we single out some properties that a general solution should satisfy, and we prove that these properties characterize a unique solution. Given the generality of the approach, we believe that this paper is only a starting point for a more extended analysis. In particular, it is clear that different contexts can suggest other properties, thus identifying alternative ranking methods.

An impossibility theorem for paired comparisons

In several decision-making problems, alternatives should be ranked on the basis of paired comparisons between them. We present an axiomatic approach for the universal ranking problem with arbitrary preference intensities, incomplete and multiple comparisons. In particular, two basic properties -- independence of irrelevant matches and self-consistency -- are considered. It is revealed that there exists no ranking method satisfying both requirements at the same time. The impossibility result holds under various restrictions on the set of ranking problems, however, it does not emerge in the case of round-robin tournaments. An interesting and more general possibility result is obtained by restricting the domain of independence of irrelevant matches through the concept of macrovertex.

Coalition Manipulation of Gale-Shapley Algorithm

It is well-known that the Gale-Shapley algorithm is not truthful for all agents. Previous studies in this category concentrate on manipulations using incomplete preference lists by a single woman and by the set of all women. Little is known about manipulations by a subset of women. In this paper, we consider manipulations by any subset of women with arbitrary preferences. We show that a strong Nash equilibrium of the induced manipulation game always exists among the manipulators and the equilibrium outcome is unique and Pareto-dominant. In addition, the set of matchings achievable by manipulations has a lattice structure. We also examine the super-strong Nash equilibrium in the end.

Constructing and Repairing Our Bridges: Statistical Considerations When Placing Agents into Legislative Preference Space

A statistical test of hypotheses regarding the strategic interaction between legislators and third-party agents, such as lobbyists, bureaucrats, or experts, requires some ``bridging'' method to place each type of actor into preference spaces that are comparable. Current solutions to the bridging problem either attempt to place both legislators and agents into an arbitrary preference space entirely disconnected from the institutional setting, or they attempt to place agents into a legislative roll-call preference space mistakenly as if agents were themselves legislators. I propose a new method that leverages the observed behavioral hypotheses to identify a set of agent-specific bridging parameters that place agents directly into legislative roll-call preference space as agents, rather than counterfactually as legislators. I apply my method to test whether members of Congress condition their questioning of witnesses in committee hearings on preference similarity within the legislator-witness dyad, as a test of lobbying models for strategic information transmission.