The Disjunction Effect in two-stage simulated gambles. An experimental study and comparison of a heuristic logistic, Markov and quantum-like model.

Savage's rational axiom of decision making under uncertainty, called the 'Sure Thing' principle, was purportedly falsified in a two-stage gamble paradigm by Tversky and Shafir (1992). This work revealed that participants would take a second-stage gamble for both possible outcomes of the initial-stage gamble, but would significantly depress this choice when no information was available on the outcome of the initial-stage gamble. Subsequent research has reported difficulty to replicate this Disjunction Effect in the two-stage gamble paradigm. We repeated this simulated two-stage gamble paradigm in an online study (N = 1119) but adapted the range of payoff amounts, and controlled the order of the blocks of two-stage gambles with, respectively without, information on the outcome of the first-stage gamble. The main empirical contributions of this study are that more risk averse participants produced (i) a reliable order effect in relation to the Disjunction Effect and the violation of the Law of Total Probability, and (ii) a novel inflation effect on gambling in the Unknown outcome condition analogous but opposite to the Disjunction Effect when Unknown outcome conditioned two-stage gambles precede the Known outcome conditioned ones. By contrast, we found that less risk averse participants produced neither of these effects. We discuss the underlying choice processes and compare the effectiveness of a logistic model, a Markov model and a quantum-like model. Our main theoretical findings are (i) a standard utility model and a Markov model using heuristic linear utility, contextual influence and carry-over effect cannot accommodate the present empirical results, and (ii) a model based on quantum dynamics, matched in form to the Markov model, can successfully describe all major aspects of our data.

Hilbert space multidimensional modelling of continuous measurements.

Data fusion problems arise when a researcher needs to analyse results obtained by measuring empirical variables under different measurement contexts. A context is defined by a subset of variables taken from a complete set of variables under investigation. Multiple contexts can be formed from different subsets, which produce a separate distribution of measurements associated with each context. A context effect occurs when the distributions produced by the different contexts cannot be reproduced by marginalizing over a complete joint distribution formed by all the variables. We propose a Hilbert space multidimensional theory that uses a state vector and measurement operators to account for multiple distributions produced by different contexts. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.

Comparing quantum versus Markov random walk models of judgements measured by rating scales.

Quantum and Markov random walk models are proposed for describing how people evaluate stimuli using rating scales. To empirically test these competing models, we conducted an experiment in which participants judged the effectiveness of public health service announcements from either their own personal perspective or from the perspective of another person. The order of the self versus other judgements was manipulated, which produced significant sequential effects. The quantum and Markov models were fitted to the data using the same number of parameters, and the model comparison strongly supported the quantum over the Markov model.

Multialternative decision field theory: a dynamic connectionist model of decision making.

The authors interpret decision field theory (J. R. Busemeyer & J. T. Townsend, 1993) as a connectionist network and extend it to accommodate multialternative preferential choice situations. This article shows that the classic weighted additive utility model (see R. L. Keeney & H. Raiffa, 1976) and the classic Thurstone preferential choice model (see L. L. Thurstone, 1959) are special cases of this new multialternative decision field theory (MDFT), which also can emulate the search process of the popular elimination by aspects (EBA) model (see A. Tversky, 1969). The new theory is unique in its ability to explain several central empirical results found in the multialternative preference literature with a common set of principles. These empirical results include the similarity effect, the attraction effect, and the compromise effect, and the complex interactions among these three effects. The dynamic nature of the model also implies strong testable predictions concerning the moderating effect of time pressure on these three effects.

Dynamic and consequential consistency of choices between paths of decision trees.

The generally prescribed procedure for choosing a decision strategy from a decision tree employs a backward induction analysis that entails 3 fundamental consistency principles: dynamic, consequential, and strategic. The first requires the decision maker to follow through on plans to the end, the second requires the decision maker to focus solely on future events and final consequences given the current state of events, and the third is the conjunction of the first 2. Five experiments were reported to test these principles using different subject populations, different procedures for estimating consistency, and different factors for manipulating the attractiveness of the gamble at the final stage of the tree. The main findings were that strategic and dynamic consistency principles were violated at rates that exceeded choice inconsistency.

Decision making under time pressure: an independent test of sequential sampling models.

Choice probability and choice response time data from a risk-taking decision-making task were compared with predictions made by a sequential sampling model. The behavioral data, consistent with the model, showed that participants were less likely to take an action as risk levels increased, and that time pressure did not have a uniform effect on choice probability. Under time pressure, participants were more conservative at the lower risk levels but were more prone to take risks at the higher levels of risk. This crossover interaction reflected a reduction of the threshold within a single decision strategy rather than a switching of decision strategies. Response time data, as predicted by the model, showed that participants took more time to make decisions at the moderate risk levels and that time pressure reduced response time across all risk levels, but particularly at the those risk levels that took longer time with no pressure. Finally, response time data were used to rule out the hypothesis that time pressure effects could be explained by a fast-guess strategy.

Changing plans: dynamic inconsistency and the effect of experience on the reference point.

This article presents a new test of a principle of decision making called dynamic consistency. This principle was tested in an experiment in which participants were asked to make decisions about a second gamble within a sequence of two gambles. Participants were first asked to make a planned choice about the second gamble. The planned choice was made before the first gamble was played and was conditioned on the anticipated outcomes of the first gamble. After the first gamble was played, the same participants were asked to make a final choice about the second gamble, conditioned on the experienced outcome of the first gamble. The results showed that participants' final choices were frequently inconsistent with their plans, even when the anticipated and experienced outcomes were identical. These inconsistencies occurred in a systematic direction. Experiencing an anticipated gain resulted with a change toward risk aversion, and experiencing an anticipated loss resulted in a change toward risk seeking. These results are explained in terms of the effect of actual experience on the reference point used for the evaluation of the decision problem.

Extrapolation: the sine qua non for abstraction in function learning.

Abstraction was investigated by examining extrapolation behavior in a function-learning task. During training, participants associated stimulus and response magnitudes (in the form of horizontal bar lengths) that covaried according to a linear, exponential, or quadratic function. After training, novel stimulus magnitudes were presented as tests of extrapolation and interpolation. Participants extrapolated well beyond the range of learned responses, and their responses captured the general shape of the assigned functions, with some systematic deviations. Notable individual differences were observed, particularly in the quadratic condition. The number of unique stimulus-response pairs given during training (i.e., density) was also manipulated but did not affect training or transfer performance. Two rule-learning models, an associative-learning model, and a new hybrid model with associative learning and rule-based responding (extrapolation-association model [EXAM]) were evaluated with respect to the transfer data. EXAM best approximated the overall pattern of extrapolation performance.

Decision field theory: a dynamic-cognitive approach to decision making in an uncertain environment.

Decision field theory provides for a mathematical foundation leading to a dynamic, stochastic theory of decision behavior in an uncertain environment. This theory is used to explain (a) violations of stochastic dominance, (b) violations of strong stochastic transitivity, (c) violations of independence between alternatives, (d) serial position effects on preference, (e) speed-accuracy trade-off effects in decision making, (f) the inverse relation between choice probability and decision time, (g) changes in the direction of preference under time pressure, (h) slower decision times for avoidance as compared with approach conflicts, and (i) preference reversals between choice and selling price measures of preference. The proposed theory is compared with 4 other theories of decision making under uncertainty.

Incorporating prior biases in network models of conceptual rule learning.

A series of simulations is reported in which extant formal categorization models are applied to human rule-learning data (Salatas & Bourne, 1974). These data show that there are clear differences in the ease with which humans learn rules, with the conjunctive the easiest and the biconditional the hardest. The original ALCOVE model (an exemplar-based model), a configural-cue model, and two-layer backpropagation models did not fit the rule-learning data. ALCOVE successfully fit the data, however, when prior biases observed in human rule learning were implemented into weights of the network. Thus, current empirical learning models may not fare well in situations in which learners enter the concept-formation situation with preconceived biases regarding the kinds of concepts that are possible, but such biases might nevertheless be captured within these models. By incorporating preexperimental biases, ALCOVE may hold promise as a comprehensive category-learning model.

Decision making under uncertainty: a comparison of simple scalability, fixed-sample, and sequential-sampling models.

The purpose of this article is to investigate the learning and memory processes involved in decision making under uncertainty. In two different experiments, subjects were given a choice between a certain alternative that produced a single known payoff and an uncertain alternative that produced a normal distribution of payoffs. Initially this distribution was unknown, and in the first experiment it was learned through feedback from past decisions, whereas in the second experiment it was learned by observing sample outcomes. In the first experiment, a response deadline was used to limit the amount of time available for making a decision. In the second experiment, an observation cost was used to limit the number of samples that could be purchased. The mean and variance of the uncertain alternative and the value of the certain alternative were factorially manipulated to study their joint effects on choice probability, choice response time (Experiment 1), and number of observations purchased (Experiment 2). Algebraic-deterministic theories developed for decision making with simple gambles fail to explain the present results. Two new models are developed and tested--fixed- and sequential-sampling models--that attempt to describe the learning and memory processes involved in decision making under uncertainty.

Evaluation of exemplar-based generalization and the abstraction of categorical information.

This article reformulates and reanalyzes a problem originally put forth by Homa, Sterling, and Trepel (1981). The question is whether a pure, exemplar-based abstraction process is an adequate model of category learning or whether it is necessary to postulate an additional prototype-abstraction process. Based on quantitative discrepancies from a pure, exemplar-based model, Homa et al. argued that it was necessary to recognize the operation of a prototype-abstraction process in order to fully explain their results. However, Homa et al. never actually fit the exemplar plus prototype model to the data to determine if indeed the additional prototype process could explain the deviations from the pure exemplar model. The present article compared the pure exemplar model with a mixed (exemplar plus prototype) model and did not find consistent evidence requiring the postulation of an additional prototype-abstraction process. These results point out the difficulty of distinguishing alternative classification models and underscore the need for careful analytic work in this area.

Age preferences for professional helpers.

Persons between the ages of 16 to 91 years (N = 621) were asked to indicate the age of the physician nurse, policeman, lawyer, clergyman, and teacher they prefer when they need a service. For all occupations except clergyman there was a relationship between the age of the respondent and preferred age of the professional. Older individuals preferred older service providers with one exception, their physician. Highly educated respondents preferred younger physicians. Implications for providing services to older individuals are discussed.