arXiv subjects

Christopher P. Chambers

Publications and source records attributed to Christopher P. Chambers.

At least 19 recordsLinked to original sources

arXiv2026

Acceptant Expansions of Path-Independent Choice Rules

A choice rule is $q$-acceptant if it chooses $\min\{q,|X|\}$ alternatives from each set $X$. We show that a path-independent rule of maximum cardinality at most $q$ need not have a $q$-acceptant path-independent expansion, refuting Chambers and Yenmez (2017, Theorem 4). We construct a one-school matching market whose unique stable matching leaves a seat vacant that no path-independent expansion of the school's rule fills. Every path-independent rule satisfying the law of aggregate demand has such an expansion. We characterize the choice rules admitting an acceptant expansion by monotone selections of rejected alternatives.

econ.TH↗

arXiv2026

Belief Identification in Populations

We study the identification of belief distributions in a population of Bayesian agents from anonymous aggregate belief data. While a single Bayesian agent's full belief can be recovered from beliefs over a suitable collection of binary events, this principle need not extend to populations: event-by-event distributions of beliefs may fail to identify the underlying distribution of priors. We study when this failure is generic and when it is exceptional. Identification is governed by the graph-theoretic structure induced by the observed family of events on the state space. Among $n$-agent distributions, identification is generic if the induced graph is nonseparable, while non-identification is generic if the graph is separable. The results establish both limits and design principles for recovering belief heterogeneity from aggregate belief data.

econ.TH↗

arXiv2026

In Search of Lost Correlation: Correlated Equilibrium via Marginal Actions

In this paper, we study which data can be induced by a correlated equilibrium given a known finite simultaneous move game. We assume that an analyst has access to the frequency of each agent's actions but does not have access to the distribution over joint action profiles. We characterize which sets of marginal distributions over actions arise from some correlated equilibria via a type of no arbitrage condition. An outside observer is unable to make a profit in expectation by independently contracting with each agent and collecting a portion of the total utility gained via unilateral deviation. This characterization naturally extends to Nash equilibria.

econ.TH↗

arXiv2025

Invariant Modeling for Joint Distributions

A common theme underlying many problems in statistics and economics involves the determination of a systematic method of selecting a joint distribution consistent with a specified list of categorical marginals, some of which have an ordinal structure. We propose guidance in narrowing down the set of possible methods by introducing Invariant Aggregation (IA), a natural property that requires merging adjacent categories in one marginal not to alter the joint distribution over unaffected values. We prove that a model satisfies IA if and only if it is a copula model. This characterization ensures i) robustness against data manipulation and survey design, and ii) allows seamless incorporation of new variables. Our results provide both theoretical clarity and practical safeguards for inference under marginal constraints.

econ.TH↗

arXiv2025

Ordered Probabilistic Choice

We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be associated with a copula, enabling the analysis of representations through established results from copula theory. We provide functional forms to describe the "extremal" representations of an ordered probabilistic choice behavior and their distinctive structural properties. The resulting functional forms act as an "identification method" that uniquely generates heterogeneous choice types and their weights. These results provide valuable tools for analysts to identify micro-level behavioral heterogeneity from macro-level observable data.

econ.TH↗

arXiv2025

Revealed Social Networks

The linear-in-means model is the standard empirical model of peer effects and asks that an agent's choice or outcome is a combination of their ideal point and the mean outcome of their group. Using choice data and exogenous group variation, we develop a revealed preference style test for the linear-in-means model. This test is formulated as a linear program and can be interpreted as a condition about differentiating the behavior of each agent in a consistent manner. We then study the identification properties of the linear-in-means model. A key takeaway from our analysis is the close relationship between the dimension of the outcome variable and identification. When the outcome variable is one-dimensional, failures of identification are generic. When the outcome variable is multi-dimensional, we provide natural conditions under which identification is generic.

econ.TH↗

arXiv2024

Revealed Invariant Preference

We consider the problem of rationalizing choice data by a preference satisfying an arbitrary collection of invariance axioms. Examples of such axioms include quasilinearity, homotheticity, independence-type axioms for mixture spaces, constant relative/absolute risk and ambiguity aversion axioms, stationarity for dated rewards or consumption streams, separability, and many others. We provide necessary and sufficient conditions for invariant rationalizability via a novel approach which relies on tools from the theoretical computer science literature on automated theorem proving. We also establish a generalization of the Dushnik-Miller theorem, which we use to give a complete description of the out-of-sample predictions generated by the data under any such collection of axioms.

econ.TH↗

arXiv2024

Coherent Distorted Beliefs

Many models of economics assume that individuals distort objective probabilities. We propose a simple consistency condition on distortion functions, which we term distortion coherence, that ensures that the function commutes with conditioning on an event. We show that distortion coherence restricts belief distortions to have a particular function form: power-weighted distortions, where distorted beliefs are proportional to the original beliefs raised to a power and weighted by a state-specific value. We generalize our findings to allow for distortions of the probabilities assigned to both states and signals, which nests the functional forms widely used in studying probabilistic biases (e.g., Grether, 1980 and Benjamin, 2019). We show how coherent distorted beliefs are tightly related to several extant models of motivated beliefs: they are the outcome of maximizing anticipated expected utility subject to a generalized Kullback-Liebler cost of distortion. Moreover, in the domain of lottery choice, we link coherent distortions to explanations of non-expected utility like the Allais paradox: individuals who maximize subjective expected utility maximizers conditional on coherent distorted beliefs are equivalent to the weighted utility maximizers studied by Chew [1983].

econ.TH↗

arXiv2024

Success functions in large contests

We consider contests with a large set (continuum) of participants and axiomatize contest success functions that arise when performance is composed of both effort and a random element, and when winners are those whose performance exceeds a cutoff determined by a market clearing condition. A co-monotonicity property is essentially all that is needed for a representation in the general case, but significantly stronger conditions must hold to obtain an additive structure. We illustrate the usefulness of this framework by revisiting some of the classic questions in the contests literature.

econ.TH↗

arXiv2024

Manipulation of Belief Aggregation Rules

This paper studies manipulation of belief aggregation rules in the setting where the society first collects individual's probabilistic opinions and then solves a public portfolio choice problem with common utility based on the aggregate belief. First, we show that belief reporting in Nash equilibrium under the linear opinion pool and log utility is identified as the profile of state-contingent wealth shares in parimutuel equilibrium with risk-neutral preference. Then we characterize belief aggregation rules which are Nash-implementable. We provide a necessary and essentially sufficient condition for implementability, which is independent of the common risk attitude.

econ.TH↗

arXiv2024

The Limits of Identification in Discrete Choice

This paper uncovers tight bounds on the number of preferences permissible in identified random utility models. We show that as the number of alternatives in a discrete choice model becomes large, the fraction of preferences admissible in an identified model rapidly tends to zero. We propose a novel sufficient condition ensuring identification, which is strictly weaker than some of those existing in the literature. While this sufficient condition reaches our upper bound, an example demonstrates that this condition is not necessary for identification. Using our new condition, we show that the classic ``Latin Square" example from social choice theory is identified from stochastic choice data.

econ.TH↗

arXiv2024

A duality between utility transforms and probability distortions

In this paper, we establish a mathematical duality between utility transforms and probability distortions. These transforms play a central role in decision under risk by forming the foundation for the classic theories of expected utility, dual utility, and rank-dependent utility. Our main results establish that probability distortions are characterized by commutation with utility transforms, and utility transforms are characterized by commutation with probability distortions. These results require no additional conditions, and hence each class can be axiomatized with only one property. Moreover, under monotonicity, rank-dependent utility transforms can be characterized by set commutation with either utility transforms or probability distortions.

econ.TH↗

arXiv2023

Linearity, Geometry, and Substitution in Aggregate Production

We study aggregate production under efficient input allocation across heterogeneous production units. With constant returns to scale, every profit-maximizing allocation generates a cone on which the aggregate production function is linear, whose dimension is the rank of active units' input vectors. Under concavity, the maximal cone at a supporting price is generated by component-technology contact sets. Higher-dimensional cones exist exactly when the pointwise maximum of strictly concave component technologies is nonconcave on the unit simplex. As an application, coexistence of land-using and land-free activities implies infinite aggregate elasticity of substitution at sufficiently high nonland-to-land ratios.

econ.TH↗

arXiv2023

Haves and Have-Nots: A Theory of Economic Sufficientarianism

We introduce a generalization of the concept of sufficientarianism, intended to rank allocations involving multiple consumption goods. In ranking allocations of goods for a fixed society of agents, sufficientarianism posits that allocations are compared according to the number of individuals whose consumption is deemed sufficient. We base our analysis on a novel ethical concept, which we term sufficientarian judgment. Sufficientarian judgment asserts that if in starting from an allocation in which all agents have identical consumption, a change in one agent's consumption hurts society, then there is no change in any other agent's consumption which could subsequently benefit society. Sufficientarianism is shown to be equivalent to sufficientarian judgment, symmetry, and separability. We investigate our axioms in an abstract environment, and in specific economic environments. Finally, we argue formally that sufficientarian judgment is closely related to the leximin principle.

econ.TH↗

arXiv2023

Multiple Adjusted Quantiles

We cardinally and ordinally rank distribution functions (CDFs). We present a new class of statistics, maximal adjusted quantiles, and show that a statistic is invariant with respect to cardinal shifts, preserves least upper bounds with respect to the first order stochastic dominance relation, and is lower semicontinuous if and only if it is a maximal adjusted quantile. A dual result is provided, as are ordinal results. Preservation of least upper bounds is given several interpretations, including one that relates to changes in tax brackets, and one that relates to valuing options composed of two assets.

econ.TH↗

arXiv2023

Non-diversified portfolios with subjective expected utility

Diversification is the typical investment strategy of risk-averse agents. However, non-diversified positions that allocate all resources to a single asset, state of the world or revenue stream are common too. We show that whenever finitely many non-diversified demands under uncertainty are compatible with risk-averse subjective expected utility maximization under strictly positive beliefs, they are also rationalizable under the same beliefs by many qualitatively distinct risk-averse as well as risk-neutral and risk-seeking preferences.

econ.TH↗

arXiv2023

A Note on Invariant Extensions of Preorders

We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant binary relation extends. We find that, in general, the set of extensions agree on the ranking of many pairs that (i) are unranked by the original relation, and (ii) cannot be ranked by invariance or transitivity considerations alone. We interpret these additional implications as the out-of-sample predictions generated by invariance, and study their structure.

econ.TH↗

arXiv2023

Correlated Choice

We study random joint choice rules, allowing for interdependence of choice across agents. These capture random choice by multiple agents, or a single agent across goods or time periods. Our interest is in separable choice rules, where each agent can be thought of as acting independently of the other. A random joint choice rule satisfies marginality if for every individual choice set, we can determine the individual's choice probabilities over alternatives independently of the other individual's choice set. We offer two characterizations of random joint choice rules satisfying marginality in terms of separable choice rules. While marginality is a necessary condition for separability, we show that it fails to be sufficient. We provide an additional condition on the marginal choice rules which, along with marginality, is sufficient for separability.

econ.TH↗