A note on rational inattention and rate distortion theory

Denti, Tommaso; Marinacci, Mássimo; Montrucchio, Luigi

doi:10.1007/s10203-019-00243-0

Cited by 13 publications

(8 citation statements)

References 12 publications

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“…Rate-distortion theory offers us a principled way to study the optimal precision of internal representations, formalized using information theory. As such, it has been fruitfully applied to human cognition in domains such as perceptual judgment and working memory 20 , and its close relative, rational inattention 11,21 , has been used to analyze a variety of economic problems 12,13 . In this framework, the agent is modeled as a communication channel that takes as input the signal and outputs an estimate of the value.…”

Section: Resultsmentioning

confidence: 99%

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Rationally inattentive intertemporal choice

Gershman

Bhui

2020

Nat Commun

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Discounting of future rewards is traditionally interpreted as evidence for an intrinsic preference in favor of sooner rewards. However, temporal discounting can also arise from internal uncertainty in value representations of future events, if one assumes that noisy mental simulations of the future are rationally combined with prior beliefs. Here, we further develop this idea by considering how simulation noise may be adaptively modulated by task demands, based on principles of rational inattention. We show how the optimal allocation of mental effort can give rise to the magnitude effect in intertemporal choice. In a re-analysis of two prior data sets, and in another experiment, we reveal several behavioral signatures of this theoretical account, tying choice stochasticity to the magnitude effect. We conclude that some aspects of temporal discounting may result from a cognitively plausible adaptive response to the costs of information processing.

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Section: Resultsmentioning

confidence: 99%

“…This model uses the same formulation as R1, but sets α using Eq. (21). The model has two free parameters: β and ω.…”

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confidence: 99%

Rationally inattentive intertemporal choice

Gershman

Bhui

2020

Nat Commun

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“…Rate-distortion theory offers us a principled way to study the optimal precision of internal representations, formalized using information theory. As such it has been fruitfully applied to human cognition in domains such as perceptual judgment and working memory [19], and its close relative, rational inattention [6,20], has been used to analyze a variety of economic problems [7,8]. In this framework, the agent is modeled as a communication channel that takes as input the signal and outputs an estimate of the value.…”

Section: Rational Inattentionmentioning

confidence: 99%

Rationally inattentive intertemporal choice

Gershman

Bhui

2019

Preprint

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Discounting of future rewards is traditionally interpreted as evidence for an intrinsic preference in favor of sooner rewards. However, temporal discounting can also arise from internal uncertainty in value representations of future events, if one assumes that noisy mental simulations of the future are rationally combined with prior beliefs. Here, we further develop this idea by considering how simulation noise may be adaptively modulated by task demands, based on principles of rational inattention. We show how the optimal allocation of mental effort can give rise to well-known phenomena in intertemporal choice, such as the magnitude effect and the interaction between sign and magnitude effects. In a re-analysis of two prior data sets, and in a new experiment, we reveal several behavioral signatures of this novel theoretical account, tying choice stochasticity to the magnitude effect. We conclude that some aspects of temporal discounting may result from a cognitively plausible adaptive response to the costs of information processing.

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“…We will refer to those situations characterizing economic science, statistics and other related fields of interest in which such a difference has no reason to exist because it is evident that an event cannot naturally be meant as a measurable set [3]. We have elsewhere shown that the subjective approach to decisions under uncertainty, as we propose it, has innovative contributions to offer because the probability is basically viewed as the solution to a specific decision problem rather than an opening assumption [4].…”

Section: Introductionmentioning

confidence: 99%

Non-Parametric Probability Distributions Embedded Inside of a Linear Space Provided with a Quadratic Metric

Angelini

Maturo

2020

Mathematics

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There exist uncertain situations in which a random event is not a measurable set, but it is a point of a linear space inside of which it is possible to study different random quantities characterized by non-parametric probability distributions. We show that if an event is not a measurable set then it is contained in a closed structure which is not a σ-algebra but a linear space over R. We think of probability as being a mass. It is really a mass with respect to problems of statistical sampling. It is a mass with respect to problems of social sciences. In particular, it is a mass with regard to economic situations studied by means of the subjective notion of utility. We are able to decompose a random quantity meant as a geometric entity inside of a metric space. It is also possible to decompose its prevision and variance inside of it. We show a quadratic metric in order to obtain the variance of a random quantity. The origin of the notion of variability is not standardized within this context. It always depends on the state of information and knowledge of an individual. We study different intrinsic properties of non-parametric probability distributions as well as of probabilistic indices summarizing them. We define the notion of α-distance between two non-parametric probability distributions.

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A note on rational inattention and rate distortion theory

Cited by 13 publications

References 12 publications

Rationally inattentive intertemporal choice

Rationally inattentive intertemporal choice

Rationally inattentive intertemporal choice

Non-Parametric Probability Distributions Embedded Inside of a Linear Space Provided with a Quadratic Metric

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