Pairs Of Gambles Research Articles

An eye fixation analysis of choice and judgment with multiattribute stimuli

The present paper examined the selection of processing heuristics for choice and judgment across a range of stimuli. Eye fixations were monitored while six subjects made choices or judgments of pairs of gambles, vacations, or gifts. Each stimulus was represented by three attributes that varied in the amount of dimensional interdependency. The two heuristics of interest were dimensional and holistic evaluation. Each manifested a characteristic pattern of eye fixations. Dimensional evaluation required alternating fixations from a single attribute of one stimulus to the same attribute of the other stimulus. Holistic evaluation was characterized by transitions from attribute to attribute within a single stimulus. The results demonstrated that when the stimulus attributes were either interdependent (gambles) or dissimilar (gifts), the processing heuristic was determined by stimulus characteristics. When the stimulus dimensions were neither interdependent nor dissimilar (vacations), the selection of a processing strategy was determined by the prescribed task. This study suggests that any global theory of choice or judgment must be validated over a wide range of stimuli.

An empirical test for Fishburn's additivity axiom

Three experiments were done to test the empirical relevance of Fishburn's (1967) additivity axiom, which says that people should be indifferent between pairs of gambles which satisfy certain conditions specified in the axiom. Each of the experiments consisted of two parts. In the first part, subjects had to evaluate consequences which were used in the second part as possible outcomes in a gamble. In the second part, subjects had to make choices among pairs of gambles. The experiments differed in respect to kinds of consequences and kinds of subjects used. Additivity analysis was applied to the data of the first part of each experiment, using a conjoint measurement model. A Monte Carlo study is included, which provides some hints for the evaluation of the stress coefficients obtained after applying additivity analysis to the empirical data matrices. The data of the second part of each experiment are discussed in respect to their relevance for Fishburn's (1967) additivity axiom. It was not strongly supported by the data, unless for a very restricted situation.

Independence in Utility Theory with Whole Product Sets

One of the most important concepts in value theory or utility theory is the notion of independence among variables or additivity of values. Its importance stems from numerous multiple-criteria procedures used for rating people, products, and other things. Most of these rating procedures rely on the notion of independence (often implicitly) for their validity. However, a satisfactory definition of independence (additivity), based on multi-dimensional consequences and hypothetical gambles composed of such consequences, has not appeared. This paper therefore presents a definition of independence for cases where the set of consequences X is a product set X1 × X2 × ⋯ × Xn, each element in X being an ordered n-tuple (x1, x2, …, xn). The definition is stated in terms of indifference between special pairs of gambles formed from X. It is then shown that if the condition of the definition holds, the utility of each (x1, x2, …, xn) in X can be written in the additive form φ(x1, x2, …, xn) = φ1(x1) + φ2(x2) + ⋯ + φn(xn), where φi is a real-valued function defined on the set Xi, i = 1, 2, …, n. The development is free of any specific assumptions about φ (e.g., continuity, differentiability) except that it be a von Neumann-Morgenstern utility function, and places no restrictions on the natures of the Xi.