Search

This paper proposes a model of irresolute choice rationalizing random choice behavior and examines its applications to decision making under certainty, uncertainty, and risk. Depending on the context, the representations feature canonical signal spaces. Decisions are governed by random draws of signals generating stochastic choice functions. Application to portfolio selection and experimental testing are discussed. [ABSTRACT FROM AUTHOR]

We explore the ways that a reference point may direct attention. Utilizing a stochastic choice framework, we provide behavioral foundations for the Reference-Dependent Random Attention Model (RD-RAM). Our characterization result shows that preferences may be uniquely identified even when the attention process depends arbitrarily on both the menu and the reference point. We then analyze specific attention processes, characterizing reference-dependent versions of several prominent models of stochastic consideration. Our analysis illustrates which attention processes can accommodate behavioral patterns commonly observed in studies, such as frequency reversals among non-status quo alternatives and choice overload. [ABSTRACT FROM AUTHOR]

Summary: This paper is dedicated to a numerical method based on a random choice as proposed in Glimm's scheme. It is applied to the problem of advection of a scalar quantity. The numerical scheme proposed here relies on a fractional step approach for which: the first step is performed using any classical finite‐volume scheme, and the second step is a cell‐wise update. This second step is a projection based on a random choice. The resulting scheme possesses a very low level of numerical diffusion. In order to assess the capabilities of this approach, several test cases have been investigated including convergence studies with respect to the mesh‐size. The algorithm performs very well on one‐dimensional and multi‐dimensional problems. This algorithm is very easy to implement even for multi‐processor computations. [ABSTRACT FROM AUTHOR]

Dogan and Yildiz introduce and analyze the pro-con model that is inspired by Franklin's prudential algebra. Consider an agent who is endowed with two sets of orderings: pro- and con-orderings. For each choice set, if an alternative is the top-ranked by a pro-ordering (con-ordering), then this is a pro (con) for choosing that alternative. The alternative with more pros than cons is chosen from each choice set. Each ordering may have a weight reflecting its salience. In this case, the probability that an alternative is chosen equals the difference between the total weights of its pros and cons. Although, this is an additive model similar to the random utility model with structurally invariant primitives, authors show that every (random) choice function is (random) pro-con rational. Their technique requires a generalization of Ford-Fulkerson theorem. The connection between the random model and its deterministic counterpart demonstrates a fruitful use of classical integer programming techniques in choice theory. We consider an agent who is endowed with two sets of orderings: pro- and con-orderings. For each choice set, if an alternative is the top-ranked by a pro-ordering (con-ordering), then this is a pro (con) for choosing that alternative. The alternative with more pros than cons is chosen from each choice set. Each ordering may have a weight reflecting its salience. In this case, the probability that an alternative is chosen equals the difference between the total weights of its pros and cons. We show that every nuance of the rich human choice behavior can be captured via this structured model. Our technique requires a generalization of the Ford-Fulkerson theorem, which may be of independent interest. As an application of our results, we show that every choice rule is plurality-rationalizable. Funding: K. Yildiz is grateful for the hospitality of New York University, Department of Economics during his visit in the 2017–2018 academic year, and the support from the Scientific and Research Council of Turkey (TUBITAK) [Grant 1059B191601712]. [ABSTRACT FROM AUTHOR]

Consider an agent who decides whether to employ an information structure to learn about a payoff-relevant state of the world before making a decision. Information is costly either because (1) the agent has to wait some time until the information structure becomes available and is impatient, or because (2) she has to pay a fixed and menu-independent cost to use the information structure. For each menu of options the analyst observes random choice from the menu and whether the agent acquires the information. We give an axiomatic characterization of when this random choice is consistent with either of the cases (1) or (2). We identify the information structure the agent can employ, as well as its costs. We also discuss implications of our approach for sequential sampling. [ABSTRACT FROM AUTHOR]

In the presence of incomplete risk attitudes, choices between noncomparable risky prospects are random. A random choice model advanced by Karni (Incomplete preferences and random choice (unpublished manuscript), 2021) includes the hypothesis that choices among noncomparable risky prospects are prompted by signals drawn from personal distributions. This paper introduces a scheme designed to elicit subjects' assessments of their personal likelihoods of choices among noncomparable risky prospects and describes experiments designed to test the aforementioned hypothesis. [ABSTRACT FROM AUTHOR]

Consider an agent who faces choice problems and learns information about an objective state of the world through a technology of sequential experiments. We consider two cases of learning costs. In the first, the agent discounts future payoffs geometrically. In the second, she incurs a constant flow cost of time. If the observable data consist only of the joint distributions over chosen actions and decision times, an analyst can uniquely identify the discount factor in the first case and the flow cost of time in the second case. Moreover, we show how an analyst can recover the agent's ex ante welfare in both cases, besides identifying her prior belief. Our approach does not rely on any knowledge about the underlying sequential experiment. [ABSTRACT FROM AUTHOR]

I develop a simple axiomatic model that incorporates the order effect: the ordering of alternatives (e.g., ranking of universities, the location of products in a grocery store, the order of candidates on a ballot) affects choice frequencies. In my model, the probability of choosing an alternative is proportional to the utility of the alternative, similar to the Luce model. However, the utility of the alternative depends on the relative ordering of the alternative in the menu. I characterize this model by two weakenings of Luce's axiom of independence of irrelevant alternatives. I discuss how to identify the ordering of alternatives from choice data when it is not observed. Finally, I apply my model to an optimal ordering problem and to experimental data on intertemporal choice. This paper was accepted by Manel Baucells, decision analysis. [ABSTRACT FROM AUTHOR]

Random utility models are widely used to estimate preference parameters. In the case of intertemporal choice, the two most common models are the discounted logit and one we call the discounted Luce. Due to their apparent similarity, the choice to use one model or the other seems irrelevant. In this paper, we argue that the discounted Luce is superior to the discounted logit in two significant aspects. First, in relevant applications, the discounted Luce is monotone in the sense of Apesteguia and Ballester (2018), while the discounted logit is not. Second, we show that the discounted logit is incompatible with a property of choice probabilities we call "weak stationarity". The latter is compatible with common assumptions on the random nature of choices and is often not falsifiable with commonly available data. Fitting a logit model to weakly stationary choice probabilities biases the time-preference estimates. On the contrary, the discounted Luce can be safely used when choice probabilities are weakly stationary. An application to an existing dataset supports the theoretical results. [ABSTRACT FROM AUTHOR]

This article is dedicated to a numerical method based on Glimm's idea and applied to the specific problem of advection of an indicator function. The numerical scheme relies on a fractional step approach for which: the first step is performed using any classical finite‐volume scheme, and the second step sharpens the approximated solution issued from the first step. This second step is based on a random choice as proposed in the original idea of Glimm. In order to assess the capabilities of this approach, several test cases have been investigated including convergence studies with respect to the mesh‐size. The method proposed in this article is very easy to implement, even for multiprocessor computations, and it naturally extends to multidimensional domains. Several numerical test cases, including both one‐ and two‐dimensional domains, have been considered in order to examine its behavior in terms of robustness, accuracy, and convergence rate. [ABSTRACT FROM AUTHOR]

We present a characterization of the Luce rule in terms of positivity and a new choice axiom called odds supermodularity that strengthens the regularity axiom. This new characterization illuminates a connection that goes unnoticed, and sheds light on the behavioral underpinnings of the Luce rule and its extensions from a different perspective. We show that odds supermodularity per se characterizes a structured extension of the Luce rule that accommodates zero probability choices. We identify the random choice model characterized via a stochastic counterpart of Plott (1973) 's path independence axiom, which strengthens odds supermodularity. [ABSTRACT FROM AUTHOR]

We introduce the notion of perception complementarity in a representation for random choice rules, which we call Complemented Perception Categorical Consideration Representation. The model is similar in nature to the perception-adjusted Luce model of Echenique et al. (Math Soc Sci 93:67–76, 2018), but allows perception to be menu-dependent. We provide a representation theorem and an identification result. Furthermore, we consider special cases of the model, including the case when it reduces down to the Random Consideration Set Rule of Manzini and Mariotti (Econometrica 82(3):1153–1176, 2014). [ABSTRACT FROM AUTHOR]

The tropical fire ant Solenopsis geminata is an invasive ant species in Taiwan. In the present study, we investigated the turning behaviour of the tropical fire ant in the T-maze when external cues were shielded. In total, 1800 observations (600 workers × 3 choices) were conducted in the study. Workers presented eight types of left–right choice after three choices in the Tmaze experiment. We demonstrated that the turning behaviour of S. geminata workers was not significantly affected by the four cardinal directions. Moreover, eight types of left–right choice of workers were divided into four groups. The result shows that the ratio of the four groups is 1.33:3.27:3.25:1 (≈1:3:3:1). Notably, based on the binomial expansion, the left–right choice of workers is random. The workers’ choices did not exhibit a leftward or rightward turning bias after three choices in the experiment. Thus, we speculate that in the absence visual cues, S. geminata workers might navigate using random choice strategies when exploring the enclosed space. [ABSTRACT FROM AUTHOR]

Our study is devoted to a subject popular in the field of matrix population models, namely, estimating the stochastic growth rate, λS, a quantitative measure of long-term population viability, for a discrete-stage-structured population monitored during many years. “Reproductive uncertainty” refers to a feature inherent in the data and life cycle graph (LCG) when the LCG has more than one reproductive stage, but when the progeny cannot be associated to a parent stage in a unique way. Reproductive uncertainty complicates the procedure of λS estimation following the defining of λS from the limit of a sequence consisting of population projection matrices (PPMs) chosen randomly from a given set of annual PPMs. To construct a Markov chain that governs the choice of PPMs for a local population of Eritrichium caucasicum, an short-lived perennial alpine plant species, we have found a local weather index that is correlated with the variations in the annual PPMs, and we considered its long time series as a realization of the Markov chain that was to be constructed. Reproductive uncertainty has required a proper modification of how to restore the transition matrix from a long realization of the chain, and the restored matrix has been governing random choice in several series of Monte Carlo simulations of long-enough sequences. The resulting ranges of λS estimates turn out to be more narrow than those obtained by the popular i.i.d. methods of random choice (independent and identically distributed matrices); hence, we receive a more accurate and reliable forecast of population viability.

In applied sciences large-scale surveys are a popular means to acquire insights in the choices that people make in different contexts. In transportation research, for example, tens of thousands stated their choices between alternatives characterized by cost and time attributes. In this study I explore the extent to which the data acquired in such studies may exhibit the co-occurrence of different choice algorithms within such survey populations. For that purpose I propose a novel version of the outcome-oriented approach. It is applied to the outcomes of two Dutch value-of-time surveys. If the recorded choice patterns are viewed apart, most could be the result of several different algorithms, in line with the main criticism of the outcome-oriented approach. The novel version considers the causal relationships between an individual’s personal circumstances, his use of a particular algorithm and the resulting choice pattern. It employs inferential statistics for analyses of the frequencies of the expected and actually recorded choice patterns within groups of respondents. Applied to the Dutch survey results this allowed disentangling, at the aggregate level, the overlap in explaining compensatory and non-compensatory algorithms to a large extent. It revealed that weighted additive (WADD) algorithms incorporating different degrees of loss aversion could explain most recorded choice behaviour while none of the many non-compensatory algorithms that were considered yielded a more than marginal explanation. Replications of this study, preferably by re-analysing other large-scale surveys with more complicated choice sets, is recommended to find out whether or not these findings are incidental.

This note generalizes Gul and Pesendorfer’s random expected utility theory, a stochastic reformulation of von Neumann-Morgenstern expected utility theory for lotteries over a finite set of prizes, to the circumstances with a continuum of prizes. Let [0, M] denote this continuum of prizes; assume that each utility function is continuous, let C0[0,M] be the set of all utility functions which vanish at the origin, and define a random utility function to be a finitely additive probability measure on C0[0,M] (associated with an appropriate algebra). It is shown here that a random choice rule is mixture continuous, monotone, linear, and extreme if, and only if, the random choice rule maximizes some regular random utility function. To obtain countable additivity of the random utility function, we further restrict our consideration to those utility functions that are continuously differentiable on [0, M] and vanish at zero. With this restriction, it is shown that a random choice rule is continuous, monotone, linear, and extreme if, and only if, it maximizes some regular, countably additive random utility function. This generalization enables us to make a discussion of risk aversion in the framework of random expected utility theory. [ABSTRACT FROM AUTHOR]

In matrix population modeling the multi-year monitoring of a population structure results in a set of annual population projection matrices (PPMs), which gives rise to the stochastic growth rate λS, a quantitative measure of long-term population viability. This measure is usually found in the paradigm of population growth in a variable environment. The environment is represented by the set of PPMs, and λS ensues from a long sequence of PPMs chosen at random from the given set. because the known rules of random choice, such as the iid (independent and identically distributed) matrices, are generally artificial, the challenge is to find a more realistic rule. We achieve this with the a following a Markov chain that models, in a certain sense, the real variations in the environment. We develop a novel method to construct the ruling Markov chain from long-term weather data and to simulate, in a Monte Carlo mode, the long sequences of PPMs resulting in the estimates of λS. The stochastic nature of sequences causes the estimates to vary within some range, and we compare the range obtained by the “realistic choice” from 10 PPMs for a local population of a Red-Book species to those using the iid choice. As noted in the title of this paper, this realistic choice contracts the range of λS estimates, thus improving the estimation and confirming the Red-Book status of the species.