Axiomatizations of the normalized Banzhaf value and the Shapley value

A cooperative game with transferable utilities– or simply a TU-game – describes a situation in which players can obtain certain payoffs by cooperation. A solution concept for these games is a function which assigns to every such a game a distribution of payoffs over the players in the game. Famous solution concepts for TU-games are the Shapley value and the Banzhaf value. Both solution concepts have been axiomatized in various ways. An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the `grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient. In this paper we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the `grand coalition' proportional to the Banzhaf values of the players. This value does not satisfy certain axioms underlying the Banzhaf value. In this paper we introduce some new axioms that characterize the normalized Banzhaf value. We also provide an axiomatization of the Shapley value using similar axioms. Received: 10 April 1996 / Accepted: 2 June 1997     

On the shrinkage of local linear curve estimators

Local linear curve estimators are typically constructed using a compactly supported kernel, which minimizes edge effects and (in the case of the Epanechnikov kernel) optimizes asymptotic performance in a mean square sense. The use of compactly supported kernels can produce numerical problems, however. A common remedy is ridging, which may be viewed as shrinkage of the local linear estimator towards the origin. In this paper we propose a general form of shrinkage, and suggest that, in practice, shrinkage be towards a proper curve estimator. For the latter we propose a local linear estimator based on an infinitely supported kernel. This approach is resistant against selection of too large a shrinkage parameter, which can impair performance when shrinkage is towards the origin. It also removes problems of numerical instability resulting from using a compactly supported kernel, and enjoys very good mean squared error properties.     

Reading,writing and word processing: Toward a phenomenology of the computer age

Ethnographers read cultures and in writing inscribe memory into texts; in literature, a reading is a dialogue with a writer through the medium the text, and writing translates text into action. In a study of humanists using the microcomputer as a writing technology, changes were perceived in the phenomenology of writing, the writer's relation to the text, and the relation to the reader. Typists remarked that the computer enabled them to recover a spoken voice because the screen gave the text a processual and temporal form which replaced the inflexible typed page. Handwriters often remarked that the computer changed humanistic craft labor into industrial production: the screen gave privilege to the lexical in place of the graphic; the sentence replaced the paragraph as a unit of meaning; writing became a medium for transmitting information rather than an artistic performance. Humanists perceived that technical norms were embedded in technical culture and software, and that the computer marked a shift in the reward structure of their professions toward productivity and efficiency. This suggests three issues for the writing crafts of ethnographers. Electronic memory may replace the interpretive text, making fieldnotes public and treating them as information. The technical capacity to organize fieldnotes in data bases may shift the fieldworker's conception of knowledge from interpretation to information. And consuming the norms and concepts of technical culture may shift the craftlike norms of the field worker's culture.

—Mallarme

     

Scientific management and class relations

Conclusion It has been the contention of this article that the true significance of the scientific management movement lies in what it can tell us about the engineering profession. Scientific management was not simply capitalist ideology, nor were the engineers who developed it simply the prisoners of capitalist ideology. Instead, scientific management was the product of the insertion of once-independent engineers into the complex, collective labor process in large corporations. It reflects both their inability to break loose fully from the dominant ideology and the fact that their interests as engineers were in conflict with the interests of their capitalist employers.The significance of this point, however, lies beyond the experience of turn-of-the-century shop culture engineers. For, if even as unpromising a group as the scientific managers could develop a program with implications inimical to the interests of capital, what of other, less commercialized groups? We have already seen that the early school-based engineers initiated a professionalizing project that included a claim to autonomy that was incompatible with the needs of their employers. It seems clear that the engineer's status as an employee, albeit an employee in an ambiguous position in the labor process, constitutes a basis for the development of conflicts with capitalist employers. This has been the thrust of our earlier discussion of the process of class formation. Gramsci's analysis of the situation of engineers in capitalist class relations, then, may not be without foundation:With the urban intellectuals it is another matter. Factory technicians do not exercise any political function over the instrumental masses, or at least this is a phase that has been superseded. Sometimes, rather, the contrary takes place, and the instrumental masses, at least in the person of their own organic intellectuals, exercise a political influence on the technicians.It may very well be that engineers, given a more militant labor movement, a more penetrating ideology, or a weaker capitalist class, could find themselves on the same side as more subordinate employees in conflicts with their employers.It is all the more important, then, that we understand the process by which American engineers have been domesticated. This has not happened automatically; far from it. Although there are ambiguities in the engineer's situation that make this process easier, the rapprochement of engineers with capital has had to be made. In this regard, the active intervention of business interests has been of particular importance, especially their efforts in fostering among engineers a safe variant of professionalism.Nor does this historical lesson apply only to engineers. For, there are other professional occupations that, increasingly, find themselves in situations comparable to engineers. Accountants, nurses, teachers, even certain kinds of lawyers have long been employed in large numbers by complex organizations. More recently, even doctors have begun to experience the condition of being an employee. For each of these occupations, we must avoid the easy assumption that there is something inherent in their social structural position that leads them into an accommodation with capital. On the contrary, as with engineers, we must stress the existence of real conflicts generated by capitalist relations of production, and then examine each occupation historically, asking what specific circumstances explain why its members do or do not enter into explicit conflict with their employers. However, while we must be aware of the possibility that professionals can (and sometimes do) enter into conflict with their employers, we also need to be sensitive to the complexity of the structural position of many professionals. Many professionals find themselves in positions of authority of some kind - either over subordinate workers in the case of engineers, or over clients in the case of doctors. This can be conducive to the attitude that the professionals' interests are different from those of the groups over which they have authority, or that their interests are the same as their employers'. Alternatively, as we saw in the case of engineers, this structural ambiguity may promote the formation of narrow occupational ideologies among professionals - i.e., the idea that their interests differ from those of both employers and subordinates. Therefore, while we need to be aware of the existence of employer/ professional conflict, we also need to recognize the existence of barriers to, and complexities within, the evolution of such conflicts.It is with this in mind that this article has stressed the importance of developing an adequate approach to the process of class formation. To restate briefly some of the arguments made earlier, the process of class formation in capitalist society is set in motion by the antagonisms inherent in capitalist relations of production. This is not, however, all that we need to know about the process of class formation - we also need to recognize the existence of both objective and historical barriers to this process. Nevertheless, one must be clear about what exactly these barriers are. There is, for example, an important difference between the relations of production that constitute class in the first place and workers' functions in the labor process. Similarly, one should not confuse barriers to the process of class formation with full-fledged class divisions. If we fail to distinguish among these various factors, we will be in danger of artificially placing a class barrier between engineers and other forms of wage-labor. If, on the other hand, we do make these distinctions, we will be able to account for both engineers' opposition to their employers and their domestication.

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An analysis of simple counting methods for ordering incomplete ordinal data

Measurement in the social sciences often involves an attempt to completely order a set of entities on the basis of an underlying attribute. However, limitations of the measurement process often prevent complete empirical determination of the desired ordering. Nevertheless, the ordinal data obtained from the measurement process can be used in attempting to recover or construct more of the underlying order than is provided by the data. Previous research (Fishburn and Gehrlein, 1974a) has shown that a simple one-stage construction method, referred to as the cardinal rule, is fairly effective in correctly identifying ordered pairs in the underlying linear order that are not identified by the measurement process. The present paper re-examines the cardinal rule from the perspective of construction methods based on simple counting measures derived from the data, and argues that it is the best one-stage method in this class when a natural monotonicity assumption holds for the measurement process. The paper then examines two-stage construction rules that are based on the cardinal rule and the simple counting measures. It is shown that one of the two-stage rules gives better overall results than does the cardinal rule by itself.     

Specification of nonverbal behaviors for clinical assessment

Nine categories of nonverbal behavior (extremity movements, self-manipulations, facial expression, posture, orienting, gestures, voice quality/tone, speech rate/pressure, and sense of timing) were tested in a standardized role play situation of social skills. Each category was judged using a new midi-level system of assessment which permitted specification of component behaviors but allowed observers to make single ratings at the ends of videotaped episodes. The midi-level measurements were as reliable and practical as more traditional global measures of social skill and social anxiety. Midis were superior to globals (i.e., single overall ratings of skill and anxiety) in terms of predicting physiological indices of social anxiety. Voice quality/tone and sense of timing appeared to be the best predictors of criterion social skill measures and self-manipulations, extremity movements, and gestures had the highest weights in predicting criterion measures of social anxiety.     

Ethnomethodology and Marxism: Their use for critical theorizing

Conclusion Each theory and, ultimately, school of theorizing exposes and criticizes the theorizing of others, and at the same time contains false or misleading statements. Theory as it is must rest on some presuppositions. Thus, Marxism exposes the flaws and lies of capitalism while positing another world view-Marxism—which it does not treat critically. Marxism also provides a critique of positivistic thinking. In The Grundrisse, Marx engages in a dialogue with economists and philosophers of his day. His theory emerges out of the rejection of their theory. Ethnomethodology can be seen as critique of positivism, too. It can also tell us something about Marxism, as some of its concerns are similar, although the methods are dissimilar. At the same time, ethnomethodology denies us certain information about itself. Theorists, then, question others and not themselves. Theory can be seen as a product of inquiry; the theorist shows only the product and hides what made the product. Indeed, just as the statistician reveals a correlation between two variables and omits all the common sense reasoning that went into the process (a method of theorizing ethnomethodologists criticize), so does the ethnomethodologist or Marxist omit, to a great extent, the process of theorizing involved.Thus, while neither form of theorizing, taken literally, can be critical (for to be critical, one must sometimes suspend belief in one's own theory, bracket it, or see it as strange), either form, if taken metaphorically (and in a way that is unfaithful to Marxism and ethnomethodology), can be used for critique.The ethnomethodological and Marxist critiques of social information, as in their processual framework and their emphasis on the thinking individual, provide critiques of contemporary society and an impetus to try to change it. Links between the two schools of theorizing would perhaps help overcome the deficiencies of each mode of theorizing. Taylor, Walton, and Young advocated (although they never carried it out) building a bridge in criminology so to speak, between ethnomethodology and Marxism. The advantage would be to enable us to escape from the straitjacket of an economic determinism and the relativism of some subjective approaches to a theory of contradiction in a social structure which recognizes in deviance the acts of men (men and women) in the process of actively making, rather than passively taking, the external world.Our special thanks to Ishna Abrams, Igor Freund, and Peter Schwarzburg for their tireless assistance.     

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