A quantitative theory of preferences: Some results on transition functions

We investigate a general theory of combining individual preferences into collective choice. The preferences are treated quantitatively, by means of preference functions (a,b), where 0(a,b) expresses the degree of preference of a to b. A transition function is a function (x,y) which computes (a,c) from (a,b) and (b,c), namely (a,c)=((a,b),(b,c)). We prove that given certain (reasonable) conditions on how individual preferences are aggregated, there is only one transition function that satisfies these conditions, namely the function (x,y)=x·y (multiplication of odds). We also formulate a property of transition functions called invariance, and prove that there is no invariant transition function; this impossibility theorem shows limitations of the quantitative method.Research supported in part by the National Science Foundation.     

Enrich marital inventory: a discriminant validity and cross-validation assessment

To assess the validity and clinical utility of the marital inventory ENRICH, a discriminant validity study was conducted using a national sample of 5039 married couples. The sample was randomly split in order to form a cross-validation group. ENRICH is a multidimensional scale and two types of analysis were conducted to assess the value of these various scales. Results from discriminant analysis indicated that using either the individual scores or couples' scores, happily married couples could be discriminated from unhappily married couples with 85–95% accuracy. These results were cross-validated with a second sample. Using regression analysis, it was clearly demonstrated that background factors account for little of the variance in discriminating happy from unhappily married couples compared to their relationship dynamics, i.e., scale scores. All ENRICH scales except equalitarian roles proved significant, indicating the validity of a multidimensional inventory.     

Therapeutic compliments: setting the stage for successful therapy

Compliments are often viewed primarily as a linear event in which one person expresses approval or admiration of another. Far less attention has been given to the circular nature of compliments and the manner in which they enhance the positions of both the giver and the receiver of the compliment. Therapeutic compliments have proven to be highly effective means of motivating clients, while at the same time increasing therapeutic leverage. This article proposes that compliments should be purposefully given, and that the type of compliment should vary with the stage of therapy and the intended response of the client to the compliment.     

Dimensions of occupational inequality and Duncan's socioeconomic index

Using the original 1962 Blau and Duncan data for white males, I compare relative amounts of inequality in the distributions of occupational prestige, earnings, autonomy, and job skills. Also assessed are the degree of status rigidity (or intercorrelations) among these four dimensions of occupational inequality and the simultaneous relations among these four dimensions in a father-to-son occupational mobility model. These findings are compared to those obtained with Duncan's socioeconomic index to determine whether additional information can be obtained when using independent measures representing the multiple dimensions of occupational inequality versus using the SEI alone. Only minor discrepancies are found, and these relate to autonomy and earnings.An earlier version of this paper was presented at the 1985 Pacific Sociological Association meetings.     

The employment contract: A test of the transaction cost theory

This paper tests some predictions derived from Williamson's transaction cost theory of the organization of work, which holds that the form of the employment relationship is determined largely by the idiosyncrasy of work—that is, the nature of skills and knowledge used in production. It examines the occurrence of theoretically relevant provisions in collective bargaining agreements in the United States and finds they are related to a contract-level proxy for idiosyncrasy (based on bargaining structure) as predicted by the theory. An analysis of an individual-level variable, the difficulty of finding a comparable job, provides some additional support. Finally, several alternative explanations of the results are considered, and it is argued that none are consistent with the evidence. The analysis thus finds strong, if necessarily provisional, support for the theory.     

The prevalence rates of pathological gambling: A look at methods

Planning the gambling environment requires protection of the public's health, safety and welfare. Whereas most public gaming provisions and statutes address the public's fears of organized crime as well as some welfare needs, rarely do they safeguard the public's health regarding the spread of the mental disease known as pathological gambling. Measurement of the prevalence and incidence of this disease would enable policy planners to evaluate both the state's responsibility for an epidemic and the adequacy of publicly funded treatment programs. The purpose of this paper is to examine the methods which underlie three different estimates of the prevalence rate of pathological gambling and to critique them in the light of sound epidemiological procedure. In 1975, the Institute for Social Research (ISR) of the University of Michigan conducted a national survey and a survey of the state of Nevada on behalf of the U.S. Commission on a National Policy Toward Gambling. Using discriminant function analysis coupled with subjective inspection of cases in the at-risk pool, the researchers estimated rates of probable and potential pathological gamblers. In 1984 and 1985, this author surveyed residents in the Delaware Valley and the state of Ohio using the cumulative clinical signs method which also posited rates of probable and potential pathological gamblers. In 1986, researchers at the Office of Mental Health for the State of New York employed a formal screening device to survey residents and proposed a rate of probable pathological gamblers and a rate of problem — although not pathological — gamblers. All three approaches produced different estimates. The utility of prevalence and incidence rate research in this field is threatened by a lack of consensus about the proper epidemiological procedure to be employed in arriving at these estimates. There is also confusion about the distinction between a probable and a potential pathological gambler. The planning purpose, method, validity and reliability of prevalence rate research about pathological gambling are addressed in this paper.     

A relation for the covariances of order statistics from n independent and non-identically distributed random variables

We derive a simple relation satisfied by the covariances of order statistics in the i.i.d. case and then generalize it to the case when the variables are independent and non-identically distributed. This relation could be employed successfully either to check the calculations or to reduce the amount of direct computations involved in evaluating the covariances of order statistics from an outlier model.     

Some quantitative concepts of value and utility from a utilitarian point of view

This paper clarifies and interprets some basic quantitative concepts of value, utility and utility function from a utilitarian point of view. First, I discuss the question as to whether value is objective or subjective. I hold that value is subjective and statistical in nature (although from the various subjective values of a certain object a norm can usually be obtained). Second, I emphasize the distinction between use value and exchange value in relation to utility. Third, I propose a law of diminishing incremental interest, which refers to the incremental (marginal) utility of money. Fourth, I identify the utility of money with the von Neumann-Morgenstern utility. Fifth, I question the necessity of the usual normalization of utility functions and the restricted linear transformation (and the consequent concept of strategic equivalence). Sixth, I discuss in detail the terminal values and utilities of a utility function from a philosophical rather than mathematical point of view, particularly the boundedness of a utility function and the magnitudes of V ₀ and U ₀. Finally, I conclude that, in order to be able to have interpersonal comparisons of utility, utility should have the same dimension as value rather than no dimension, and the normalization problem should be reconsidered in the light of terminal values and utilities.     

Retrospective on the utility theory of von Neumann and Morgenstern

This article offers an exegesis of the passages in von Neumann and Morgenstern (1944, 1947, 1953) that discuss their conception of utility. It is occasioned by two factors. First, as we approach the semicentennial of the publication of Theory of Games and Economic Behavior, its immense impact on economic thought in the intervening years encourages serious reflection on its authors' ideas. Second, misleading statements about the theory continue to appear. The article will have accomplished its purpose if it helps others appreciate the genius and spirit of the theory of utility fashioned by John von Neumann and Oskar Morgenstern.