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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:50:36 +0000Merging and testing opinions
https://resolver.caltech.edu/CaltechAUTHORS:20190405-094754350
Authors: {'items': [{'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Al-Najjar-N-I', 'name': {'family': 'Al-Najjar', 'given': 'Nabil'}}, {'id': 'Sandroni-A', 'name': {'family': 'Sandroni', 'given': 'Alvaro'}}]}
Year: 2014
DOI: 10.1214/14-AOS1212
We study the merging and the testing of opinions in the context of a prediction model. In the absence of incentive problems, opinions can be tested and rejected, regardless of whether or not data produces consensus among Bayesian agents. In contrast, in the presence of incentive problems, opinions can only be tested and rejected when data produces consensus among Bayesian agents. These results show a strong connection between the testing and the merging of opinions. They also relate the literature on Bayesian learning and the literature on testing strategic experts.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nsqtz-rwj14Claim Validation
https://resolver.caltech.edu/CaltechAUTHORS:20190405-093152329
Authors: {'items': [{'id': 'Al-Najjar-N-I', 'name': {'family': 'Al-Najjar', 'given': 'Nabil'}}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Sandroni-A', 'name': {'family': 'Sandroni', 'given': 'Alvaro'}}]}
Year: 2014
DOI: 10.1257/aer.104.11.3725
Hume (1748) challenged the idea that a general claim (e.g. "all swans are white") can be validated by empirical evidence, no matter how compelling. We examine this issue from the perspective of a tester who must accept or reject the forecasts of a potential expert. If experts can be skeptical about the validity of claims then they can strategically evade rejection. In contrast, if experts are required to conclude that claims backed by sufficient evidence are likely to be true, then they can be tested and rejected. These results provide an economic rationale for claim validation based on incentive problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tvyk6-c3t15Choice under aggregate uncertainty
https://resolver.caltech.edu/CaltechAUTHORS:20190405-093853327
Authors: {'items': [{'id': 'Al-Najjar-N-I', 'name': {'family': 'Al-Najjar', 'given': 'Nabil I.'}}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}]}
Year: 2016
DOI: 10.1007/s11238-015-9504-1
We provide a simple model to measure the impact of aggregate risks. We consider agents whose rankings of lotteries over vectors of outcomes satisfy expected utility and separability. Such rankings are characterized in terms of aggregative utilities that measure sensitivity to aggregate uncertainty in a straightforward way. We consider applications to models of product variety, portfolio choice, and public attitudes towards catastrophic risks. The framework lends support to precautionary measures that penalize policies for exposure to correlation. The model rationalizes a number of behavioral and policy patterns as attempts to hedge against aggregate uncertainty.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pac9m-xgk62An Axiomatic Theory of Inductive Inference
https://resolver.caltech.edu/CaltechAUTHORS:20180425-110409545
Authors: {'items': [{'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Sandroni-A', 'name': {'family': 'Sandroni', 'given': 'Alvaro'}}]}
Year: 2018
DOI: 10.1086/696386
This article develops an axiomatic theory of induction that speaks to the recent debate on Bayesian orgulity. It shows the exact principles associated with the belief that data can corroborate universal laws. We identify two types of disbelief about induction: skepticism that the existence of universal laws of nature can be determined empirically, and skepticism that the true law of nature, if it exists, can be successfully identified. We formalize and characterize these two dispositions toward induction by introducing novel axioms for subjective probabilities. We also relate these dispositions to the (controversial) axiom of σ-additivity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5hsqe-rnp86The cost of information
https://resolver.caltech.edu/CaltechAUTHORS:20190404-161816718
Authors: {'items': [{'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Strack-P', 'name': {'family': 'Strack', 'given': 'Philipp'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2019
DOI: 10.48550/arXiv.1812.04211
We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with probability half costs half its original cost. Together with a monotonicity and a continuity conditions, these axioms determine the cost of a signal up to a vector of parameters. These parameters have a clear economic interpretation and determine the difficulty of distinguishing states. We argue that this cost function is a versatile modeling tool that leads to more realistic predictions than mutual information.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yrhbn-2yz42Stable Matching under Forward-Induction Reasoning
https://resolver.caltech.edu/CaltechAUTHORS:20190405-110407806
Authors: {'items': [{'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}]}
Year: 2019
A standing question in the theory of matching markets is how to define stability under incomplete information. The crucial obstacle is that a notion of stability must include a theory of how beliefs are updated in a blocking pair. This paper proposes a novel epistemic approach. Agents negotiate through offers. Offers are interpreted according to the highest possible degree of rationality that can be ascribed to their proponents, in line with the principle of forward-induction reasoning. This approach leads to a new definition of stability. The main result shows an equivalence between this notion and "incomplete-information stability", a cooperative solution concept recently put forward by Liu, Mailath, Postlewaite and Samuelson (2014), for markets with one-sided incomplete information. The result implies that forward-induction reasoning leads to efficient matchings under standard supermodularity conditions. In addition, it provides an epistemic foundation for incomplete-information stability. The paper also shows new connections and distinctions between the cooperative and the epistemic approaches in matching markets.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b44hs-2yx73An Abstract Law of Large Numbers
https://resolver.caltech.edu/CaltechAUTHORS:20190404-160929922
Authors: {'items': [{'id': 'Al-Najjar-N-I', 'name': {'family': 'Al-Najjar', 'given': 'Nabil I.'}}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}]}
Year: 2020
DOI: 10.1007/s13171-018-00162-z
We study independent random variables (Z_i)_(i∈I) aggregated by integrating with respect to a nonatomic and finitely additive probability ν over the index set I. We analyze the behavior of the resulting random average ∫_IZ_idν(i). We establish that any ν that guarantees the measurability of ∫_IZ_idν(i) satisfies the following law of large numbers: for any collection (Zi)_(i∈I) of uniformly bounded and independent random variables, almost surely the realized average ∫_IZ_idν(i) equals the average expectation ∫_IE[Z_i]dν(i).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ep0zg-2rm74Stochastic Dominance Under Independent Noise
https://resolver.caltech.edu/CaltechAUTHORS:20190405-101226198
Authors: {'items': [{'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Strack-P', 'name': {'family': 'Strack', 'given': 'Philipp'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2020
DOI: 10.1086/705555
Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g., uninsurable labor risk, house price risk) can affect the ordering of gambles. We show that, perhaps surprisingly, background risk can be strong enough to render lotteries that are ranked by their expectation ranked in terms of first-order stochastic dominance. We extend our results to second-order stochastic dominance and show how they lead to a novel and elementary axiomatization of mean-variance preferences.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/m9xak-tca52Aggregate Risk and the Pareto Principle
https://resolver.caltech.edu/CaltechAUTHORS:20190405-092508707
Authors: {'items': [{'id': 'Al-Najjar-N-I', 'name': {'family': 'Al-Najjar', 'given': 'Nabil I.'}}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}]}
Year: 2020
DOI: 10.1016/j.jet.2020.105084
In the evaluation of public policies, a crucial distinction is between plans that involve purely idiosyncratic risk and those that generate correlated, or aggregate, risk. While natural, this distinction is not captured by standard utilitarian aggregators.
In this paper we revisit Harsanyi's (1955) celebrated theory of preferences aggregation and develop a parsimonious generalization of utilitarianism. The theory we propose captures sensitivity to aggregate risk in large populations and can be characterized by two simple axioms of preferences aggregation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9c60h-sc585Testable Forecasts
https://resolver.caltech.edu/CaltechAUTHORS:20190405-094352848
Authors: {'items': [{'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}]}
Year: 2021
DOI: 10.3982/TE3767
Predictions about the future are commonly evaluated through statistical tests. As shown by recent literature, many known tests are subject to adverse selection problems and cannot discriminate between forecasters who are competent and forecasters who are uninformed but predict strategically. We consider a framework where forecasters' predictions must be consistent with a paradigm, a set of candidate probability laws for the stochastic process of interest. The paper presents necessary and sufficient conditions on the paradigm under which it is possible to discriminate between informed and uninformed forecasters. We show that optimal tests take the form of likelihood-ratio tests comparing forecasters' predictions against the predictions of a hypothetical Bayesian outside observer. In addition, the paper illustrates a new connection between the problem of testing strategic forecasters and the classical Neyman-Pearson paradigm of hypothesis testing.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wcv7e-qnv41From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again
https://resolver.caltech.edu/CaltechAUTHORS:20200124-080643011
Authors: {'items': [{'id': 'Mu-Xiaosheng', 'name': {'family': 'Mu', 'given': 'Xiaosheng'}, 'orcid': '0000-0002-2868-5182'}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Strack-Philipp', 'name': {'family': 'Strack', 'given': 'Philipp'}}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2021
DOI: 10.3982/ECTA17548
We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Rényi divergences.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x70d0-23195Background Risk and Small-Stakes Risk Aversion
https://resolver.caltech.edu/CaltechAUTHORS:20210303-154333226
Authors: {'items': [{'id': 'Mu-Xiaosheng', 'name': {'family': 'Mu', 'given': 'Xiaosheng'}, 'orcid': '0000-0002-2868-5182'}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Strack-Philipp', 'name': {'family': 'Strack', 'given': 'Philipp'}, 'orcid': '0000-0002-7960-9243'}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2021
DOI: 10.48550/arXiv.2010.08033
We show that under plausible levels of background risk, no theory of choice under risk---such as expected utility theory, prospect theory, or rank dependent utility---can simultaneously satisfy the following three economic postulates: (i) Decision makers are risk-averse over small gambles, (ii) they respect stochastic dominance, and (iii) they account for background risk.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2wy8c-yg798Model and Predictive Uncertainty: A Foundation for Smooth Ambiguity Preferences
https://resolver.caltech.edu/CaltechAUTHORS:20220503-901748200
Authors: {'items': [{'id': 'Denti-Tommaso', 'name': {'family': 'Denti', 'given': 'Tommaso'}}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}]}
Year: 2022
DOI: 10.3982/ecta18009
Smooth ambiguity preferences (Klibanoff, Marinacci, and Mukerji (2005)) describe a decision maker who evaluates each act f according to the twofold expectation,
V(f) = ∫_p Φ(∫_Ω u(f)dp)dµ(p), defined by a utility function u, an ambiguity index ϕ, and a belief μ over a set of probabilities. We provide an axiomatic foundation for the representation, taking as a primitive a preference over Anscombe–Aumann acts. We study a special case where P is a subjective statistical model that is point identified, that is, the decision maker believes that the true law p ϵ P can be recovered empirically. Our main axiom is a joint weakening of Savage's sure-thing principle and Anscombe–Aumann's mixture independence. In addition, we show that the parameters of the representation can be uniquely recovered from preferences, thereby making operational the separation between ambiguity attitude and perception, a hallmark feature of the smooth ambiguity representation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6cg67-pe386Twofold multiprior preferences and failures of contingent reasoning
https://resolver.caltech.edu/CaltechAUTHORS:20210303-133740093
Authors: {'items': [{'id': 'Echenique-F', 'name': {'family': 'Echenique', 'given': 'Federico'}, 'orcid': '0000-0002-1567-6770'}, {'id': 'Miyashita-Masaki', 'name': {'family': 'Miyashita', 'given': 'Masaki'}, 'orcid': '0000-0002-9812-4225'}, {'id': 'Nakamura-Yuta', 'name': {'family': 'Nakamura', 'given': 'Yuta'}, 'orcid': '0000-0001-9725-3159'}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Vinson-Jamie', 'name': {'family': 'Vinson', 'given': 'Jamie'}, 'orcid': '0000-0002-0267-0396'}]}
Year: 2022
DOI: 10.1016/j.jet.2022.105448
We propose a model of incomplete twofold multiprior preferences, in which an act f is ranked above an act g only when f provides higher utility in a worst-case scenario than what g provides in a best-case scenario. The model explains failures of contingent reasoning, captured through a weakening of the state-by-state monotonicity (or dominance) axiom. Our model gives rise to rich comparative statics results, as well as extension exercises, and connections to choice theory. We present an application to second-price auctions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e641v-w8t25Monotone Additive Statistics
https://resolver.caltech.edu/CaltechAUTHORS:20210303-154811036
Authors: {'items': [{'id': 'Mu-Xiaosheng', 'name': {'family': 'Mu', 'given': 'Xiaosheng'}, 'orcid': '0000-0002-2868-5182'}, {'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}, {'id': 'Strack-Philipp', 'name': {'family': 'Strack', 'given': 'Philipp'}, 'orcid': '0000-0002-7960-9243'}, {'id': 'Tamuz-O', 'name': {'family': 'Tamuz', 'given': 'Omer'}, 'orcid': '0000-0002-0111-0418'}]}
Year: 2022
DOI: 10.1145/3490486.3538318
The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary, monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries, as well as a characterization of risk-averse preferences over monetary gambles that are invariant to mean-zero background risks.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qks6c-x6q46Stable matching under forward-induction reasoning
https://resolver.caltech.edu/CaltechAUTHORS:20221219-416589000.7
Authors: {'items': [{'id': 'Pomatto-L', 'name': {'family': 'Pomatto', 'given': 'Luciano'}, 'orcid': '0000-0002-4331-8436'}]}
Year: 2022
DOI: 10.3982/te3867
A standing question in the theory of matching markets is how to define stability under incomplete information. This paper proposes an epistemic approach. Agents negotiate through offers, and offers are interpreted according to the highest possible degree of rationality that can be ascribed to their proponents. A matching is deemed "stable" if maintaining the current allocation is a rationalizable action for each agent. The main result shows an equivalence between this notion and "incomplete‐information stability," a cooperative solution concept put forward by Liu, Mailath, Postlewaite, and Samuelson (2014) for markets with incomplete information.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ta5ep-kdj44