Choice probabilities and choice functions

Choice probabilities are basic to much of the theory of individual choice behavior in mathematical psychology. On the other hand, consumer economics has relied primarily on preference relations and choice functions for its theories of individual choice. Although there are sizable literatures on the connections between choice probabilities and preference relations, and between preference relations and choice functions, little has been done—apart from their common ties to preference relations—to connect choice probabilities and choice functions. The latter connection is studied in this paper. A family of choice functions that depends on a threshold parameter is defined from a choice probability function. It is then shown what must be true of the choice probability function so that the choice functions satisfy three traditional rationality conditions. Conversely, it is shown what must be true of the choice functions so that the choice probability function satisfies a version of Luce's axiom for individual choice probabilities.     

Discrete dynamic choice: An extension of the choice models of thurstone and luce

The present paper deals with the extension of two well-known static discrete choice theories to the dynamic situation in which individuals make choices at several points in (continuous) time. A dynamic version of Luce's Axiom, “independence from irrelevant alternatives”, is proposed and some of its implications are derived. In the static case Yellott (J. Math. Psych. 1977, 15, 109–146) and others have demonstrated that an independent random utility model generated from the extreme value distribution exp(?e^?ax?b) becomes equivalent to Luce's Axiom. Yellott also introduced an axiom called “invariance under uniform expansions of the choice set”, and he proved that within the class of random utility models with independent identically distributed utilities (apart from a location shift) this axiom is equivalent to Luce's Axiom. These results are extended to the dynamic situation and it is shown that if the utility processes are expressed by so-called extremal processes the corresponding choice model is Markovian. A nonstationary generalization is proposed which is a substantial interest in applications where the parameters of the choice process are influenced by previous choice experience or by time-varying exogenous variables. In particular, it is demonstrated that the nonstationary model is Markovian if and only if the joint choice probabilities at two points in time have a particular form. Thus, the paper provides a rationale for applying a specific class of Markov models as the point of departure when modelling mobility processes that involve individual discrete decisions over time.     

Implicit commitment in theory choice

The proper evaluation of a theory’s virtues seems to require taking into account what the theory is indirectly or implicitly committed to, in addition to what it explicitly says. Most extant proposals for criteria of theory choice in the literature spell out the relevant notion of implicit commitment via some notion of entailment. I show that such criteria behave implausibly in application to theories that differ over matters of entailment. A recent defence by Howard Peacock of such a criterion against this objection is examined and rejected. I go on to a develop a better proposal on which, roughly speaking, a theory is counted committed to a claim if and only if its best fully explicit extension is explicitly committed to the claim. Such extensions in turn are evaluated by ordinary standards of theory choice adapted to the case of theories assumed to articulate their intended content in a fully explicit fashion.     

Multiple identities and travel mode choice for regular journeys

Growing evidence supports a range of non-instrumental factors influencing travel mode. Amongst these, identity has been proposed. However, to date, the relationship has not been systematically investigated and few investigations have harnessed a theoretical framework for identity. Drawing on role theory (Stryker, 1980). Symbolic interactionism: A social structural version. CA: Benjamin Cummings, we hypothesised that multiple identities, of varying importance, are related to travel mode choice. The study of 248 UK urban/suburban, working, car-owning parents used survey-based data to test the influence of seven identities on travel mode choice in regular travel. Multiple and logistic regression analyses found multiple identities to be significantly related to travel mode to work, on escort education and on other regular journeys. The study demonstrated different patterns of relationship between identity on different types of journey and found evidence for travel mode choice as embedded within social identities. In addition to the study’s contribution of new empirical findings, its application of a theoretical focus on identity offers additional strategies in attempting to change travel behaviours towards sustainability.     

Multisensory processing of redundant information in go/no-go and choice responses

In multisensory research, faster responses are commonly observed when multimodal stimuli are presented, as compared to unimodal target presentations. This so-called redundant-signals effect can be explained by several frameworks, including separate-activation and coactivation models. The redundant-signals effect has been investigated in a large number of studies; however, most of those studies have been limited to the rejection of separate-activation models. Coactivation models have been analyzed in only a few studies, primarily using simple response tasks. Here, we investigated the mechanism of multisensory integration underlying go/no-go and choice responses to redundant auditory–visual stimuli. In the present study, the mean and variance of response times, as well as the accuracy rates of go/no-go and choice responses, were used to test a coactivation model based on the linear superposition of diffusion processes (Schwarz, 1994) within two absorbing barriers. The diffusion superposition model accurately describes the means and variances of response times as well as the proportions of correct responses observed in the two tasks. Linear superposition thus seems to be a general principle in the integration of redundant information provided by different sensory channels, and is not restricted to simple responses. The results connect existing theories of multisensory integration with theories on choice behavior.     

The probabilistic nature of preferential choice

Previous research has developed a variety of theories explaining when and why people's decisions under risk deviate from the standard economic view of expected utility maximization. These theories are limited in their predictive accuracy in that they do not explain the probabilistic nature of preferential choice, that is, why an individual makes different choices in nearly identical situations, or why the magnitude of these inconsistencies varies in different situations. To illustrate the advantage of probabilistic theories, three probabilistic theories of decision making under risk are compared with their deterministic counterparts. The probabilistic theories are (a) a probabilistic version of a simple choice heuristic, (b) a probabilistic version of cumulative prospect theory, and (c) decision field theory. By testing the theories with the data from three experimental studies, the superiority of the probabilistic models over their deterministic counterparts in predicting people's decisions under risk become evident. When testing the probabilistic theories against each other, decision field theory provides the best account of the observed behavior.     

社会困境问题的理论架构与实验研究

社会困境是指个体理性导致集体非理性这样的情境。社会困境研究的推进要求一个新的框架来理解已有理论, 这一框架将这些理论区分为宏观、中观和微观三个层面。实验研究依据这些不同层面的理论, 以实验游戏为工具来探讨人们在面临社会困境时做出选择的心理机制及其影响因素, 从而对社会困境问题发展出相应的问题解决路径。理论的发展、实验任务本身的改进以及研究的外在效度预示了通过实验方法来研究社会困境问题有着广阔的前景。     

De se belief and rational choice

The Sleeping Beauty puzzle has dramatized the divisive question of how de se beliefs should be integrated into formal theories of rational belief change. In this paper, I look ahead to a related question: how should de se beliefs be integrated into formal theories of rational choice? I argue that standard decision theoretic frameworks fail in special cases of de se uncertainty, like Sleeping Beauty. The nature of the failure reveals that sometimes rational choices are determined independently of one’s credences in the kinds of ‘narrow’ de se propositions that Sleepy Beauty has set in relief. Consequently, in addition to pinpointing a failure of standard decision theoretic frameworks, this result casts doubt on a large class of strategies for determining principles for the rationally updating de se beliefs in cases like Sleeping Beauty, and also calls into question the importance of making such a determination at all.     

Decision speed and choice regret: When haste feels like waste

We test a metacognitive account of why larger choice sets often lead to greater regret, proposing that people apply the lay theory that “a quick choice is a bad choice” when evaluating how well they have chosen. Because people often operate under time pressure, larger sets are likely to entail a more cursory selection process than smaller sets, generating a feeling of having rushed the evaluation of the alternatives and heightened regret. Four studies show that choice-set size does not influence participants' regret when they believe that they had enough time to choose, that the subjective feeling of being rushed accounts for greater regret when choosing from larger sets, and that changing people's lay theories about choosing quickly eliminates regret.     

女性食物选择的演化视角：基于性选择过程的理论探讨

性选择在人类心理、行为等表型的演化过程中扮演了重要角色,但其对女性食物选择的影响却相对较少被关注。性选择塑造了男女不同的择偶策略,男性择偶时对女性外在吸引力的关注使得女性更加重视身材等外在吸引力信息。而女性身材与饮食的密切联系,进一步提示性选择过程应该会对女性的食物选择产生影响。以之为基础,梳理求偶动机激活可能引发的女性食物选择的变化,以及女性生理期不同阶段在食物选择上的变异,有助于了解性选择过程对女性食物选择的影响。未来研究中,进一步从行为、激素、脑等不同层面剖析对应影响及涉及机制,对该领域的长远发展有重要意义。     

Quasi-dynamic choice models: Melioration and ratio invariance

There is continuing controversy about the behavioral process or processes that underlie the major regularities of free-operant choice such as molar matching and systematic deviations therefrom. A recent interchange between Vaughan and Silberberg and Ziriax concerned the relative merits of melioration, and a computer simulation of molecular maximizing. There are difficulties in evaluating theories expressed as computer programs because many arbitrary decisions must often be made in order to get the programs to operate. I therefore propose an alternative form of model that I term quasi-dynamic as a useful intermediate form of theory appropriate to our current state of knowledge about free-operant choice. Quasi-dynamic models resemble the game-theoretic analyses now commonplace in biology in that they can predict stable and unstable equilibria but not dynamic properties such as learning curves. It is possible to interpret melioration as a quasi-dynamic model. An alternative quasi-dynamic model for probabilistic choice, ratio invariance, has been proposed by Horner and Staddon. The present paper compares the predictions of melioration and ratio invariance for five experimental situations: concurrent variable-interval variable-interval schedules, concurrent variable-interval variable-ratio schedules, the two-armed bandit (concurrent random-ratio schedules), and two types of frequency-dependent schedule. Neither approach easily explains all the data, but ratio invariance seems to provide a better picture of pigeons' response to probabilistic choice procedures. Ratio invariance is also more adaptive (less susceptible to “traps”) and closer to the original expression of the law of effect than pure hill-climbing processes such as momentary maximizing and melioration, although such processes may come in to play on more complex procedures that provide opportunities for temporal discrimination.     

Preference reversal in multiattribute choice

A central puzzle for theories of choice is that people's preferences between options can be reversed by the presence of decoy options (that are not chosen) or by the presence of other irrelevant options added to the choice set. Three types of reversal effect reported in the decision-making literature, the attraction, compromise, and similarity effects, have been explained by a number of theoretical proposals. Yet a major theoretical challenge is capturing all 3 effects simultaneously. We review the range of mechanisms that have been proposed to account for decoy effects and analyze in detail 2 computational models, decision field theory (Roe, Busemeyer, & Townsend, 2001) and leaky competing accumulators (Usher & McClelland, 2004), that aim to combine several such mechanisms into an integrated account. By simulating the models, we examine differences in the ways the decoy effects are predicted. We argue that the LCA framework, which follows on Tversky's relational evaluation with loss aversion (Tversky & Kahneman, 1991), provides a more robust account, suggesting that common mechanisms are involved in both high-level decision making and perceptual choice, for which LCA was originally developed.     

Quasi-truth,paraconsistency, and the foundations of science

In order to develop an account of scientific rationality, two problems need to be addressed: (i) how to make sense of episodes of theory change in science where the lack of a cumulative development is found, and (ii) how to accommodate cases of scientific change where lack of consistency is involved. In this paper, we sketch a model of scientific rationality that accommodates both problems. We first provide a framework within which it is possible to make sense of scientific revolutions, but which still preserves some (partial) relations between old and new theories. The existence of these relations help to explain why the break between different theories is never too radical as to make it impossible for one to interpret the process in perfectly rational terms. We then defend the view that if scientific theories are taken to be quasi-true, and if the underlying logic is paraconsistent, it’s perfectly rational for scientists and mathematicians to entertain inconsistent theories without triviality. As a result, as opposed to what is demanded by traditional approaches to rationality, it’s not irrational to entertain inconsistent theories. Finally, we conclude the paper by arguing that the view advanced here provides a new way of thinking about the foundations of science. In particular, it extends in important respects both coherentist and foundationalist approaches to knowledge, without the troubles that plague traditional views of scientific rationality.     

A response to the critique of rational choice theory: Lakatos' and Laudan's conceptions applied

This paper analyzes the main features of rational choice theory and evaluates it with respect to the conceptions of Lakatos' research program and Laudan's research tradition. The analysis reveals that the thin rationality assumption, the axiomatic method and the reduction to the micro level are the only features shared by all rational choice models. On these grounds, it is argued that rational choice theory cannot be characterized as a research program. This is due to the fact that the thin rationality assumption cannot be understood as a hard core in Lakatos' terms. It is argued that Laudan's conception of a research tradition better characterizes rational choice theory. On the basis of this conclusion, certain important criticisms of rational choice theory are answered. First, the criticisms concerning the core assumptions of rational choice theory are countered. It is argued that this critique is based on a misunderstanding of rational choice theory as a unified set of models, such as Lakatos' research program. Second, Green and Shapiro's rational choice ‘pathologies’ – inconsistent predictions, post hoc theory development and arbitrary domain restrictions – are evaluated. Contrary to Green and Shapiro, it is argued that post hoc theory development is a more preferable strategy for developing RCT than domain restrictions based on ex ante rules.     

A discounting framework for choice with delayed and probabilistic rewards

When choosing between delayed or uncertain outcomes, individuals discount the value of such outcomes on the basis of the expected time to or the likelihood of their occurrence. In an integrative review of the expanding experimental literature on discounting, the authors show that although the same form of hyperbola-like function describes discounting of both delayed and probabilistic outcomes, a variety of recent findings are inconsistent with a single-process account. The authors also review studies that compare discounting in different populations and discuss the theoretical and practical implications of the findings. The present effort illustrates the value of studying choice involving both delayed and probabilistic outcomes within a general discounting framework that uses similar experimental procedures and a common analytical approach.     

Social learning and collective choice

To be pertinent to democratic practice, collective choice functions need not apply to all possible constellations of individual preference, but only to those that are humanly possible in an appropriate sense. The present paper develops a theory of humanly possible preference within the context of the mathematical theory of learning. The theory of preference is then exploited in an attempt to resolve Arrow's voting paradox through restriction of the domain of majoritarian choice functions.     

Binary choice, subset choice, random utility, and ranking: A unified perspective using the permutahedron

The d-permutahedron Π_d−1⊂R^d is defined as the convex hull of all d-dimensional permutation vectors, namely, vectors whose components are distinct values of a d-element set of integers [d]≡{1,2,…,d}. By construction, Π_d−1 is a convex polytope with d! vertices, each representing a linear order (ranking) on [d], and has dimension dim(Π_d−1)=d−1. This paper provides a review of some well-known properties of a permutahedron, applies the geometric-combinatoric insights to the investigation of the various popular choice paradigms and models by emphasizing their inter-connections, and presents a few new results along this line.Permutahedron provides a natural representation of ranking probability; in fact it is shown here to be the space of all Borda scores on ranking probabilities (also called “voters profiles” in the social choice literature). The following relations are immediate consequences of this identification. First, as all d! vertices of Π_d−1 are equidistant to its barycenter, Π_d−1 is circumscribed by a sphere S^d−2 in a (d−1)-dimensional space, with each spherical point representing an equivalent class of vectors whose components are defined on an interval scale. This property provides a natural expression of the random utility model of ranking probabilities, including the condition of Block and Marschak. Second, Π_d−1 can be realized as the image of an affine projection from the unit cube of dimension d(d−1)/2. As the latter is the space of all binary choice vectors describing probabilities of pairwise comparisons within d objects, Borda scores can be defined on binary choice probabilities through this projective mapping. The result is the Young's formula, now applicable to any arbitrary binary choice vector. Third, Π_d−1 can be realized as a “monotone path polytope” as induced from the lift-up of the projection of the cube onto the line segment [0,d]⊂R¹. As the 2^d vertices of the d-cube are in one-to-one correspondence to all subsets of [d], a connection between the subset choice paradigm and ranking probability is established. Specifically, it is shown here that, in the case of approval voting (AV) with the standard tally procedure (Amer. Pol. Sci. Rev. 72 (1978) 831), under the assumption that the choice of a subset indicates an approval (with equal probability) of all linear orders consistent with that chosen subset, the Brams-Fishburn score is then equivalent to the Borda score on the induced profile. Requiring this induced profile (ranking probability) to be also consistent with the size-independent model of subset choice (J. Math. Psychol. 40 (1996) 15) defines the “core” of the AV Polytope. Finally, Π_d−1 can be realized as a canonical projection from the so-called Birkhoff polytope, the space of rank-position probabilities arising out of the rank-matching paradigm; thus Borda scores can be defined on rank-position probabilities. To summarize, the many realizations of a permutahedron afford a unified framework for describing and relating various ranking and choice paradigms.     

Social functionalist frameworks for judgment and choice: intuitive politicians,theologians, and prosecutors

Research on judgment and choice has been dominated by functionalist assumptions that depict people as either intuitive scientists animated by epistemic goals or intuitive economists animated by utilitarian ones. This article identifies 3 alternative social functionalist starting points for inquiry: people as pragmatic politicians trying to cope with accountability demands from key constituencies in their lives, principled theologians trying to protect sacred values from secular encroachments, and prudent prosecutors trying to enforce social norms. Each functionalist framework stimulates middle-range theories that specify (a) cognitive-affective-behavioral strategies of coping with adaptive challenges and (b) the implications of these coping strategies for identifying empirical and normative boundary conditions on judgmental tendencies classified as errors or biases within the dominant research programs.     

Irrational choice behavior in human and nonhuman primates

Choice behavior in humans has motivated a large body of research with a focus on whether decisions can be considered to be rational. In general, humans prefer having choice, as do a number of other species that have been tested, even though having increased choice does not necessarily yield a positive outcome. Humans have been found to choose an option more often only because the opportunity to select it was diminishing, an example of a deviation from economic rationality. Here we extend this paradigm to nonhuman primates in an effort to understand the mechanisms underlying this finding. In this study, we presented two groups of laboratory monkeys, capuchins (Cebus apella) and rhesus macaques (Macaca mulatta), as well as human subjects, with a computerized task in which subjects were presented with two differently colored icons. When the subject selected an icon, differing numbers of food pellets were dispensed (or points were assigned), making each icon correspond to a certain level of risk (one icon yielded 1 or 4 pellets/points and the other yielded 2 or 3). Initially, both options remained constantly available and we established choice preference scores for each subject. Then, we assessed preference patterns once the options were not continuously available. Specifically, choosing one icon would cause the other to shrink in size on the screen and eventually disappear if never selected. Selecting it would restore it to its full size. As predicted, humans shifted their risk preferences in the diminishing options phase, choosing to click on both icons more equally in order to keep both options available. At the group level, capuchin monkeys showed this pattern as well, but there was a great deal of individual variability in both capuchins and macaques. The present work suggests that there is some degree of continuity between human and nonhuman primates in the desire to have choice simply for the sake of having choice.