Single-peaked functions and the theory of preference.

Abstract

Dependent variables such as preference, hedonic tone, aesthetic appreciation, stimulus generalization, degree of interest or attention, exploratory behavior, developmental stages, and intensity of attitudes are frequently observed to be single-peaked functions of the independent variables. We address the problem of deriving, from more elementary underlying processes, a preference function that rises monotonically to a peak and then falls monotonically. We propose psychological principles for the perception and processing of good and bad attributes such as pleasure and pain and an elimination principle that affects the options that are available. We show that single-peakedness is inevitable if there is only one component, is quite likely if there are two, and must be contrived if there are three or more components. The results are generalized for approach-avoidance, approach-approach, and avoidance-avoidance conflict in individuals and bear upon the resolution of social choice problems of a particular class.

Price Competition in Markets with Consumer Variety Seeking

“…We find that the pricing implications obtained with the staying cost operationalization of §3 are consistent with the 4 This explanation is consistent with the boredom explanation espoused by Brickman and D'Amato (1975), Raju (1980), and others. 5 This explanation is consistent with single-peaked preference functions that have been uncovered in physiological psychology experiments; see Coombs and Avrunin (1977). 6 There are other explanations for observed variety-seeking behavior of consumers, as detailed in the taxonomies developed by McAlister and Pessemier (1982) and Kahn (1995).…”

Preference and the contextual basis of ideals in judgment and choice.

“…In the present framework, this result is interpreted in terms of basic judgmental processes that are sensitive to the contextual distribution. Values near the average of the contextual distribution tend to be judged more moderately and, in accordance with ideal-point theory, moderate values are most preferable (Coombs & Avrunin, 1977). The contextual dependence of ideals found for the simple schematic faces used in Experiment 1 suggests a mechanism for explaining possible individual and cultural differences in judgments of attractiveness.…”

“…Such single-peaked preference curves are described by Coombs's (1964) ideal-point theory of preference, in which preference is determined by the similarity of the stimulus to an ideal. Monotonic preference curves occur when the ideal is at one extreme or the other, and single-peaked curves occur when the ideal is located at an intermediate value (Coombs, 1964;Coombs & Avrunin, 1977).…”

Size, entropy, and density: What is the difference that makes the difference between small and large real‐world assortments?

“…Of course, many other profiles are possible-in terms of either other choice strategies or other preference functions (e.g., a single peaked preference function; Coombs & Avrunin, 1977). These 20 types are, however, deemed to be sufficient to test for the difference between choice in a small and large store.…”