Short-term memory models for choice behavior

In this paper we consider the effect of imposing memory restrictions on the accumulator and random-walk models of choice behavior outlined by Audley (Psychological Review, 1960, 67, 1–15). Specifically, it is assumed that subjects apply criteria to the numbers of impulses received, and that if the criteria are not satisfied by the time w impulses have been received, then thereafter the criteria are only applied to w impulses, which could, for example, be the last w impulses received. Exact and approximate mathematical approaches and simulation techniques are presented in detail. The results obtained demonstrate that both the restricted accumulator and the restricted random-walk models can make qualitative predictions in line with much recent data.     

Rational choice and polynomial measurement models

Rational choice behavior is defined in a manner that subsumes rational choice theory as part of general measurement theory. The special class of polynomial measurement problems are defined, and their solutions are reduced to solving polynomial inequalities. An algebraic criterion is given for the solvability of arbitrary finite sets of polynomial inequalities, resolving a conjecture of Tversky.     

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.     

Micro-economic models of problem choice in basic science

This paper describes the way in which a certain representation of basic scientific knowledge can be coupled with traditional microeconomic analysis to provide an analysis of rational research planning or agenda setting in basic science. Research planning is conceived as a resource allocation decision in which resources are being allocated to activities directed towards the solution of basic scientific problems. A structuralist representation of scientific knowledge is employed to provide a relatively precise characterization of a basic scientific problem.The research reported here was partially supported by a grant from the EXXON Foundation.     

Goodness-of-fit tests for models of latency and choice

A goodness-of-fit test based on the maximum likelihood criterion is derived for use in evaluating models of choice reaction time that predict choice probabilities and means and variances of latency. Special cases of the test involving models that predict only one or two of these statistics are considered and shown to be asymptotically identical to the traditional goodness-of-fit tests appropriate for these special cases.     

Probabilistic models of set-dependent and attribute-level best-worst choice

We characterize a class of probabilistic choice models where the choice probabilities depend on two scales, one with a value for each available option and the other with a value for the set of available options. Then, we develop similar results for a task in which a person is presented with a profile of attributes, each at a pre-specified level, and chooses the best or the best and the worst of those attribute-levels. The latter design is an important variant on previous designs using best-worst choice to elicit preference information, and there is various evidence that it yields reliable interpretable data. Nonetheless, the data from a single such task cannot yield separate measures of the “importance” of an attribute and the “utility” of an attribute-level. We discuss various empirical designs, involving more than one task of the above general type, that may allow such separation of importance and utility.     

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.     

Hyperbolic value addition and general models of animal choice

Three mathematical models of choice--the contextual-choice model (R. Grace, 1994), delay-reduction theory (N. Squires & E. Fantino, 1971), and a new model called the hyperbolic value-added model--were compared in their ability to predict the results from a wide variety of experiments with animal subjects. When supplied with 2 or 3 free parameters, all 3 models made fairly accurate predictions for a large set of experiments that used concurrent-chain procedures. One advantage of the hyperbolic value-added model is that it is derived from a simpler model that makes accurate predictions for many experiments using discrete-trial adjusting-delay procedures. Some results favor the hyperbolic value-added model and delay-reduction theory over the contextual-choice model, but more data are needed from choice situations for which the models make distinctly different predictions.     

Classes of models for selected axiomatic theories of choice

Adding a reversibility axiom to the other axioms of Luce's (1959) probabilistic ranking theory results in an impossibility theorem—that all alternatives in an alternative set are equally likely to be chosen (i.e., that preferences are random). This impossibility theorem is generally avoided by removing the reversibility axiom. Using simple algebraic methods such a modified theory is shown to contain a theorem similiar to the impossibility result. These results are discussed within the framework of mathematical model theory (model theory deals with the relations between sets of sentences (theories) and the structures which satisfy these sentences (models)) to illustrate the applicability of model theory as an analytic tool in theory development.     

Unification of models for choice between delayed reinforcers.

Two models for choice between delayed reinforcers, Fantino's delay-reduction theory and Killeen's incentive theory, are reviewed. Incentive theory is amended to incorporate the effects of arousal on alternate types of behavior that might block the reinforcement of the target behavior. This amended version is shown to differ from the delay-reduction theory in a term that is an exponential in incentive theory and a difference in delay-reduction theory. A power series approximation to the exponential generates a model that is formally identical with delay-reduction theory. Correlations between delay-reduction theory and the amended incentive theory show excellent congruence over a range of experimental conditions. Although the assumptions that gave rise to delay-reduction theory and incentive theory remain different and testable, the models deriving from the theories are unlikely to be discriminable by parametric experimental tests. This congruence of the models is recognized by naming the common model the delayed reinforcement model, which is then compared with other models of choice such as Killeen and Fetterman's (1988) behavioral theory of timing, Mazur's (1984) equivalence rule, and Vaughan's (1985) melioration theory.     

Loss aversion and inhibition in dynamical models of multialternative choice

The roles of loss aversion and inhibition among alternatives are examined in models of the similarity, compromise, and attraction effects that arise in choices among 3 alternatives differing on 2 attributes. R. M. Roe, J. R. Busemeyer, and J. T. Townsend (2001) have proposed a linear model in which effects previously attributed to loss aversion (A. Tversky & D. Kahneman, 1991) arise from attention switching between attributes and similarity-dependent inhibitory interactions among alternatives. However, there are several reasons to maintain loss aversion in a theory of choice. In view of this, an alternative theory is proposed, integrating loss aversion and attention switching into a nonlinear model (M. Usher & J. L. McClelland, 2001) that relies on inhibition independent of similarity among alternatives. The model accounts for the 3 effects and makes testable predictions contrasting with those of the Roe et al. (2001) model.     

Social psychological models of choice behavior and drivers' left turns

ABSTRACT. The authors reanalyzed data from a simulated left-turn experiment (P. A. Hancock, J. K. Caird, S. Shekhar, & M. Vercruyssen, 1991) to test the adequacy of the nonlinear Gray-Tallman satisfaction balance model of choice behavior (L. N. Gray & I. Tallman, 1984) in predicting left turns. Participants (Hancock et al., 1991) were 40 experienced U.S. drivers who were exposed to simulated oncoming traffic; the size of the vehicle (motorcycle, compact vehicle, full-sized vehicle, delivery truck), its speed (10-70 mph, or 16-112 kmph), and the intervehicle time gap (3-9 s) varied. Hancock et al. (1991) measured (a) the likelihood of a left turn and (b) the occurrence of a collision. The probability of a left turn was greater for larger intervehicle time gaps and for oncoming smaller vehicles traveling at higher speeds. The Gray-Tallman (1984) model explained 69% of the variation in turning versus 57% for a linear regression model. In making decisions people tend to treat the values and costs affecting choices in a multiplicative, rather than linear, fashion. The Gray-Tallman model also has the potential for incorporating, both theoretically and mathematically, an unlimited range of potential values and costs that may influence left turn decisions.     

Why additive utility models fail as descriptions of choice behavior

This experiment sought to determine whether previously found metric violations of additive expectancy-value models C.F. J. C. Shanteau, Journal of Experimental Psychology, 1974, 103, 680–691; J. G. Lynch and J. L. Cohen, Journal of Personality and Social Psychology, 1978, 36, 1138–1151) were attributable to the inappropriateness of these models or to nonlinearities in the relationship between numerical ratings and underlying psychological impressions. Undergraduate participants performed two tasks employing the same experimental stimuli. In the first task, they rated the subjective values of hypothetical bets, judged separately and in combination. In the second task, they made pairwise comparisons of the same bets in terms of preference. The use of the same experimental stimuli in both tasks allowed a test of alternative models of utility judgment through application of the criterion of scale convergence (M. H. Birnbaum & C. T. Veit, Perception and Psychophysics, 1974, 15, 7–15). Results suggested that the additive expectancy-value model of judgments of the utilities of combinations of outcomes should be replaced by a weighted averaging rule in which the weight given to the value of each outcome in the averaging process is greater when this value is negative and extreme than when it is neutral.     

The effect of normative models on individual and group choice

Studied the effect of a normative model (maximization of expected value) upon group and individual choice. 109 MBA students in a Lain square research design chose between two alternatives differing in expected value and in range of outcomes. Group choices were significantly (p < .05) closer to those predicted by the normative model than were individual choices. This difference was not due only to information about the presence and applicability of the normative model but rather it was due to the persuasiveness of the model in a group as a cogent and correct solution to the choice dilemma. Task instructions emphasizing the rewards from risk taking produced significantly more choices (p < .05) of the riskier alternative, particularly by individuals as opposed to groups, than did instructions emphasizing the penalties of risk taking. ‘Risky’ and ‘conservative’ shifts in choice between groups and individuals were explicable through knowledge of the influence of the normative model in individual and group choice.     

Psychological cost-benefit as an intervening construct in career choice models

A causal model for career choice was outlined, encompassing psychological cost-benefit-profit as a central intervening construct. The model was applied to the career choice (education vs work) after high school graduation and tested on longitudinal data from 173 students. The main problem concerned the relationship among the components in the causal career choice model, using multiple correlation and path analysis as tools. The results showed clear sex differences. For boys, the model was a rather powerful predictor of career choice (R = 0.70), and Psychological profit with regard to continued education had a clear direct effect as well as an indirect effect on career choice. For girls, the predictive validity was low (R = 0.35) and Psychological profit affected career choice only indirectly via Educational aspiration.     

Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time

Diffusion processes (e.g., Wiener process, Ornstein-Uhlenbeck process) are powerful approaches to model human information processes in a variety of psychological tasks. Lack of mathematical tractability, however, has prevented broad applications of these models to empirical data. This tutorial explains step by step, using a matrix approach, how to construct these models, how to implement them on a computer, and how to calculate the predictions made by these models. In particular, we present models for binaries choices for unidimensional and multiattribute choice alternatives; for simple reaction time tasks; and for three alternatives choice problems.     

Person x situation interactions: choice of situations and congruence response models

Two models of Person x Situation interaction wee examined. The first model predicts that there is a relation between personality and the situations people naturally choose to be in; the second model predicts that when there is congruence between the situation and personality, a person will experience more positive and less negative affect. These models were investigated by using mood and activity reports gathered on 3,512 occasions sampled randomly from the everyday lives of 42 subjects. Situational dimensions were related to some but not all personality variables investigated. Need for order predicted choice of typical situations and extraversion correlated with time spent recreating socially. However, it was found that individuals did not spend more time in those settings where they experienced more positive emotions nor less time in those situations where they experienced more negative affect. In terms of the affect-congruence model, several predicted relations wee found, but several others did not reach significance. The failure of the affect-congruence model to be consistently supported was probably because the affect of individuals was relatively consistent across situations. The present results suggest that although some theoretically meaningful Person x Situation interactions do occur, they are not necessarily strong or easily predictable.