# Papers of Kota Saito

## Published/ Forthcoming Papers

2018 Mathematical Social Sciences 93(1):  67–76 [pdf]

We develop an axiomatic model that builds on Luce's (1959) model to incorporate a role for perception. We identify agents perception priorities from their violations of Luce's axiom of independence from irrelevant alternatives. Using such perception priorities, we adjust choice probabilities to account for the effects of perception. Our axiomatization requires that the agents' adjusted random choice conforms to Luce's model. Our model can explain the attraction, compromise, and similarity effects, which are well-documented behavioral phenomena in individual choice.

On path independent stochastic choice (Previous Title: Average Choice), 2017 Theoretical Econoics 13(1):  61–85 joint with David Ahn (UC Berkeley) and Federico Echenique. [pdf]

We investigate stochastic choice when only the average and not the entire distribution of choices is observable, focusing attention to the popular Luce model. Choice is path independent if it is recursive, in the sense that choosing from a menu can be broken up into choosing from smaller submenus. While an important property, path independence is known to be incompatible with continuous choice. The main result of our paper is that a natural modification of path independence, that we call {\em partial path independence}, is not only compatible with continuity but ends up characterizing the ubiquitous Luce (or Logit) rule.

Response Time and Utility, 2017 Journal of Economic Behavior and Organization 139(15):  49–59 joint with Federico Echenique. [pdf]

Response time is the time an agent needs to make a decision. One fundamental finding in psychology and neuroscience is that, in a binary choice, the response time is shorter as the difference between the utilities of the two options becomes larger. We consider situations in which utilities are not observed, but rather inferred from revealed preferences: meaning they are inferred from subjects' choices. Given data on subjects' choices, and the time to make those choices, we give conditions on the data that characterize the property that response time is decreasing in utility differences.

Testing theories of financial decision making (Previous title: Testable Implications of Translation Invariance and Homotheticity: Variational, Maximin, CARA AND CRRA Preferences), 2016
Proceedings of the National Academy of Sciences 113(15):  4003–370 [pdf] [submitted version] [online appendix (Proof of Theorem 4)]
joint with Federico Echenique and Chris Chambers (UC San Diego).

We provide revealed preference axioms that charac- terize models of translation invariant preferences. In particular, we characterize the models of variational, maxmin, CARA and CRRA utilities. In each case we present a revealed preference axiom that is satis ed by a dataset if and only if the dataset is consistent from the corresponding utility representation. Our results comple- ment traditional exercises in decision theory that take preferences as primitive.

Impure Altruism and Impure Selfishness, 2015 Journal of Economic Theory  158:  336–370.[pdf]

Altruism refers to a willingness to benefit others, even at one's own expense. In contrast, selfishness refers to prioritizing one's own interests with no consideration for others. However, even if an agent is selfish, he might nevertheless act as if he were altruistic out of selfish concerns triggered when his action is observed; that is, he might seek to feel pride in acting altruistically and to avoid the shame of acting selfishly. We call such behavior impurely altruistic . Alternatively, even if an agent is altruistic, he might nevertheless give in to the temptation to act selfishly. We call such behavior impurely selfish . This paper axiomatizes a model that distinguishes altruism from impure altruism and selfishness from impure selfishness. In the model, unique real numbers separately capture altruism and the other forces of pride, shame, and the temptation to act selfishly. We show that the model can describe recent experiments on dictator games with an exit option. In addition, we describe an empirical puzzle that government spending only partially crowds out consumers' donations, contrary to the prediction based on standard consumer theory.

Savage in the Market, 2015 Econometrica   83:  1457–1495. [pdf] [online appendix] joint with Federico Echenique

We develop a behavioral axiomatic characterization of Subjective Expected Utility (SEU) under risk aversion. Given is an individual agent's behavior in the market: assume a finite collection of asset purchases with corresponding prices. We show that such behavior satisfies a revealed preference axiom'' if and only if there exists a SEU model (a subjective probability over states and a concave utility function over money) that accounts for the given asset purchases.

Preferences for Flexibility and Randomization under Uncertainty, 2015. American Economic Review  1051246–1271. [pdf] [online appendix]

An uncertainty-averse agent prefers betting on an event whose probability is known, to betting on an event whose probability is unknown. Such an agent may randomize his choices to eliminate the effects of uncertainty. For what sort of preferences does a randomization eliminate the effects of uncertainty? To answer this question, we investigate an agent's preferences over sets of acts. We axiomatize a utility function, through which we can identify the agent's subjective belief that a randomization eliminates the effects of uncertainty.

Social Preferences under Risk: Equality of Opportunity vs. Equality of Outcome, 2013. American Economic Review 1033084–3101. [pdf]

This paper introduces a model of inequality aversion that captures a preference for equality of ex-ante expected payoff relative to a preference for equality of ex-post payoff by a single parameter. On deterministic allocations, the model reduces to the model of Fehr and Schmidt (1999). The model provides a unified explanation for recent experiments on probabilistic dictator games and dictator games under veil of ignorance. Moreover, the model can describe experiments on a preference for efficiency, which seem inconsistent with inequality aversion. We also apply the model to the optimal tournament. Finally, we provide a behavioral foundation of the model.

Strotz Meets Allais: Diminishing Impatience and the Certainty Effect: Comment, 2011. American Economic Review 1012271–2275. [pdf]

Halevy (2008) states the equivalence between diminishing impatience (i.e., quasi-hyperbolic discounting) and the common ratio effect. The present paper shows that one way of the equivalence is false and shows the correct and general relationships: diminishing impatience is equivalent to the certainty effect and that strong diminishing impatience (i.e., hyperbolic discounting) is equivalent to the common ratio effect.

## Working Papers

Axiomatizations of the Mixed Logit Model
First Draft: July 29, 2017, Current Version: June 17, 2018. [pdf]

A mixed logit function, also known as a random-coefficient logit function, is an integral of logit functions. Necessary and sufficient conditions are provided under which a random choice function can be represented as a mixed logit function. The axioms are based on the social surplus function proposed by McFadden (1978, 1981).

Approximate Expected Utility Rationalization
Current Version: June 17, 2018 joint with Federico Echenique and Taisuke Imai. [pdf][online appendix]

We propose a new measure of deviations from expected utility, given data on economic choices under risk and uncertainty. In a revealed preference setup, and given a positive number e, we provide a characterization of the datasets whose deviation (in beliefs, utility, or perceived prices) is within e of expected utility theory. The number e can then be used as a distance to the theory. We apply our methodology to three recent large-scale experiments. Many subjects in those experiments are consistent with utility maximization, but not expected utility maximization. The correlation of our measure with demographics is also interesting, and provides new and intuitive findings on expected utility.

General Luce Model
First Draft: June 17, 2015, Current Version: July 3, 2017, joint with Federico Echenique. [pdf]

We extend the Luce model of discrete choice theory to satisfactorily handle zero-probability choices. The Luce model (or the Logit model) is the most widely applied and used model in stochastic choice, but it struggles to explain choices that are not made. The Luce model requires that if an alternative $y$ is never chosen when $x$ is available, then there is no set of alternatives from which $y$ is chosen with positive probability: $y$ cannot be chosen, even from sets of alternatives that exclude $x$. We relax this assumption. In our model, if an alternative $y$ is never chosen when $x$ is available, then we infer that $y$ is dominated by $x$. While dominated by $x$, $y$ may still be chosen with positive probability---even with high probability---when grouped with a comparable set of alternatives.

Random Intertemporal Choice
Current Version: Feb 24, 2016, joint with Jay Lu (UCLA). [pdf]

We provide a theory of random intertemporal choice. Choice is random due to unobserved heterogeneity in discounting from the perspective of a modeler. First, we show that the modeler can identify the distribution of discount rates uniquely from random choice. We then provide axiomatic characterizations of random discounting utility models, including exponential and quasi-hyperbolic discounting as special cases. Finally, we test our axioms using recent experimental data. We find that random exponential discounting is not rejected and the distribution of discount rates is statistically indistinguishable across treatments.

A Relationship between Risk and Time
First Draft: February 10, 2011, Current Version: April 23, 2015. [pdf]

This paper investigates a general relationship between risk and time preferences. I consider a decision maker who chooses between consumption of a particular prize in one period and a different prize in another period. The individual believes that today's good is certain, and that, as the promised date for a future good becomes increasingly distant, the probability of his consuming the good decreases. Under these assumptions, this paper shows that the individuals exhibits the common ratio effect, the certainty effect, and the expected utility if and only if he discounts hyperbolically, quasi-hyperbolically and exponentially, respectively.

Testable Implications of Models of Intertemporal Choice: Exponential Discounting and Its Generalizations
First Draft: Nov 8, 2013 with the title Testable Implication of Exponential Discounting '', Current Version: April 12, 2015, joint with Federico Echenique and Taisuke Imai. Submitted [pdf]

We present the first revealed-preference characterizations of the most common models of intertemporal choice: the model of exponentially discounted concave utility, and some of its generalizations. Ours is the first axiomatization of these models taking consumption data as primitives. Our characterizations provide non-parametric revealed-preference tests. We apply our test to data from a recent experiment, and find that our axiomatization delivers new insights and perspectives on a dataset that had been analyzed by traditional parametric methods.