Further tests of theories of decision in an "expanded judgment" situation.

Abstract

According to the theory of decision developed by Cartwright and Festinger (1, 2, 3), the presentation of two stimuli for a comparative judgment arouses within S tendencies to make each of the responses that are permitted. In a two-category situation, these might be, e.g., the tendencies to say "greater" and to say "less." The strength of these opposed tendencies and that of their algebraic sum, the resultant tendency, is supposed to vary randomly in a normal distribution with the passage of time. Opposed to this resultant is a certain restraint against making a decision. When in its fluctuation the strength of the resultant happens to be greater than the strength of the restraint, a decision takes place. The mean of the distribution of resultants depends upon the size and direction of the stimulus difference, but the determiners of the variability of this distribution have not been discussed by Cartwright and Festinger.

Overcoming indecision by changing the decision boundary.

“…In the ensuing decades, Cartwright and Festinger’s theory fell out of favor because several shortcomings (see Irwin, Smith, & Mayfield, 1956; Vickers, Nettelbeck, & Willson, 1972) and was superseded by the signal detection theory (Tanner & Swets, 1954) and sequential sampling models (LaBerge, 1962; Laming, 1968; Link & Heath, 1975; Ratcliff, 1978; Stone, 1960; Vickers, 1970). These models do not mention a restraining force explicitly, but this concept is implicit in a threshold, which must be crossed before the decision maker indicates their choice.…”

“…Some evidence of time-dependent boundaries was found early on in studies that compared participant behavior with Wald’s optimal procedure. These studies used an expanded-judgment paradigm in which the participant makes their decision based on a sequence of discrete samples or observations presented at discrete times—for example, deciding between two deck of cards with different means based on cards sampled sequentially from the two decks (see, e.g., Becker, 1958; Busemeyer, 1985; Irwin et al, 1956; Manz, 1970; Pleskac & Busemeyer, 2010; Smith & Vickers, 1989; Vickers, 1995). The advantage of this paradigm is that the experimenter can record not only the response time and accuracy of the participant, but also the exact sequence of samples on which they base their decisions.…”

“…Although it has been argued that the results from an expanded-judgment task can be generalized to signal detection paradigms, where sampling is implicit (Edwards, 1965; Irwin & Smith, 1956; Sanders & Linden, 1967; Pleskac & Busemeyer, 2010; Vickers, Burt, Smith, & Brown, 1985), these tasks usually use a slow presentation rate and elicit longer response latencies than those expected for perceptual decisions. It is possible that attention and memory play a different role in decision making at this speed than at faster speeds at which perceptual decisions occur.…”

Accuracy in the Judgment of Consistency1

“…In fact, it has been shown by Irwin and Smith (1956;1957) that people are fairly good in their ability to guess the mean value of a distribution on an "intuitive" (sic) basis, even if there is a response set for judging proportions and probabilities to be closer to 50i than is true (Edwards, 1963;Erhlich, 1961) when the events being observed are affectively neutral, and another response set for judging probabilities as higher than true when some positive value is attached to the events being observed (Crandall, Solomon, & Kellaway, 1955;Irwin, 1953;Marks, 1951). To the extent that a mathematical model only requires that the S be able to make some reasonably accurate estimate of central tendency, the model is clearly appropriate for the demonstrated data processing capabilities of people.…”

The effect of outcome desirability on information required for decisions

“…The procedure was adapted from Irwin and Smith (1956), who required subjects on several trials to decide whether the mean of all the numbers, printed one per card, on the cards of a large pack was positive or negative. The present subjects were required to decide whether large packs of marked and blank cards contained a predominance of marked or blank cards.…”