Luce's Choice Research Articles

Luce's Axiom and occupational prestige: Test of a measurement model†

This paper reports research using a psychological theory, R. D. Luce's (1959) individual choice theory, to provide a ratio‐level measurement basis for an important sociological variable, occupational prestige. It is shown that earlier measurement procedures to scale this sociological variable are essentially arbitrary, although heuristically useful. Luce's Axiom of Choice and his Ranking Postulate are then tested on choice sets of occupations where subjects are asked to pair‐compare or rank the occupations on the basis of their prestige. The Axiom receives qualified support, while the Ranking Postulate is not supported. It is concluded that Luce's choice theory can provide a ratio‐level measurement basis for occupational prestige, although a procedure using rankings must be appropriately structured in order to be an adequate instrument of measurement.

The separation of bias and sensitivity in multiple-choice tasks.

With the growing realisation by psychologists of the need to take account of response biases in perception and memory, the lack of a simple and realistic model to enable ‘sensitivity’ and ‘bias’ to be measured separately in complex tasks is becoming acute. Though signal-detection theory (TSD) has proved very useful in two-alternative tasks, it is virtually intractable in multiple-choice tasks; for this reason experimenters have tended to resort to Luce's Choice Model (LCM) as an approximation to it. The relationship between TSD and LCM, however, though close in the two-alternative case, becomes increasingly tenuous as the number of alternatives is increased. Nevertheless the substitution may still be made, provided certain cautions are observed: computer simulations have been used here to study both forced- and unforced-choice tasks, and establish guidelines for experimenters who wish to apply a two-factor analysis to data from complex tasks.

A model for analogical reasoning

A theory of analogical reasoning is proposed in which the elements of a set of concepts, e.g., animals, are represented as points in a multidimensional Euclidean space. Four elements A,B,C,D, are in an analogical relationship A:B::C:D if the vector distance from A to B is the same as that from C to D. Given three elements A,B,C, an ideal solution point I for A:B::C:? exists. In a problem A:B::C:D 1, …, D i , …, D n , the probability of choosing D i as the best solution is a monotonic decreasing function of the absolute distance of D i from I. A stronger decision rule incorporating a negative exponential function in Luce's choice rule is also proposed. Both the strong and weak versions of the theory were supported in two experiments where S s rank-ordered the alternatives in problems A:B::C:D 1,D 2, D 3D 4. In a third experiment the theory was applied and further tested in teaching new concepts by analogy.

Perceptual analysis from confusions between vowels

In an experiment on vowel identification confusions were obtained between 11 Dutch vowel sounds. To recover the perceptual configurations of the stimuli multidimensional scaling techniques were applied directly to the asymmetric confusion matrix, and to the symmetrized confusion matrix. In order to investigate the agreement between the different solutions, all the configurations were matched to a perceptual configuration obtained in a previous study on the perception of the same vowel sounds in which similarities were obtained by the method of triadic combinations. The different solutions turned out to be very similar and in close agreement with the perceptual structure from similarity judgements. The solutions obtained by discarding the asymmetries first, showed the best correspondence with the perceptual similarity structure. In particular the solution based on Luce's choice axiom to correct for response bias seemed to be the most attractive.

Preferences for Color, Form, Borders, Lines and Dots by Preschool Children and Adults

The research identified preference for color, form, borders, lines and dots for 25 preschool children and 25 adults under choice conditions. Both groups strongly preferred form over color and borders. In the presence of form, children preferred color over borders, while adults preferred the reverse. Some variations of form were significantly more preferred than others, but the order of these variations was constant across groups. Adults preferred borders and form similarly, but preschool children preferred form significantly more often than borders. Adults preferred lines and dots similarly, but preschool children preferred lines significantly more often than dots. The research illustrates the use of Luce's choice axiom in predicting form preference in the context of a larger number of dimensions.

ASYMMETRIC SYNTACTIC RECOGNITION MATRICES: A CHOICE ANALYSIS AS EVIDENCE FOR A HYPOTHETICAL STIMULUS‐SAMPLING PROCESS1,2

ABSTRACTAn extension of Luce's choice analysis of recognition experiments has been made so as to predict quantitatively the syntactic confusions that occur among simple syntactically related sentences which are heard at several times normal conversation rate (speeded speech). Two states are assumed to account for the pattern of asymmetric confusions: (a) a dimensional loss state wherein dimensional cues of the stimulus sentence are lost on a certain proportion of trials, and (b) a nonloss state wherein all relevant syntactic cues are assumed to be sampled but where confusions among stimuli are still assumed to occur in a predictable manner. Some relationships between the present model and Chomsky's distinction between competence and performance are discussed.

Stimulus Recognition Model

A mathematical model for stimulus recognition has been developed that incorporates two processes, and has been applied to the recognition of words in noise. The activation process uses the stimulus information to restrict the possible alternatives to a subset of the total stimulus set. This process employs concepts analogous to signal detection theory but generalized to handle recognition. The decision process assumes that a stimulus is selected from the subset with some biased sampling probability, and that the name of the selected stimulus is then emitted as the recognition response. This process assumes that Luce's choice axiom applies to the sampling probabilities. The model is capable of factoring a confusion matrix into two matrices of sensitivity and bias parameters corresponding to the two processes. Tests with word-recognition data suggest that the model offers a reasonable explanation for the improvement in recognition performance with reduction in stimulus set size and with increase in stimulus probability. The latter is closely related to the word-frequency effect. [Research supported in part by U. S. Public Health Service Grant. The author is a U. S. PHS Predoctoral Fellow.]

A general theory of polynomial conjoint measurement

The present theory generalizes conjoint measurement in five major respects. (a) It is formulated in terms of partially rather than fully ordered data. (b) It applies to both ordinal and numerical data. (c) It is applicable to finite as well as infinite data structures. (d) It provides a necessary and sufficient condition for measurement. (e) This condition applies to any polynomial measurement model; that is, any model where each data element is expressed as a specified real-valued, order-preserving polynomial function of its components. Examples of polynomial measurement models include Savage's subjective expected utility model, Hull's and Spence's performance models, Luce's choice model, and multidimensional scaling models. It is shown that a data structure D satisfies a given polynomial measurement M if and only if D satisfies an abstract irreflexivity axiom with respect to M. The interpretation of the result and its implications to measurement theory are discussed.