Skip to main content

Über dieses Buch

In the history of science "paradoxes" are not only amusing puzzles and chal­ lenges to the human mind but also driving forces of scientific development. The notion of "paradox" is intimately related to the notion of "contradiction". Logi­ cal paradoxes allow for the derivation of contradictory propositions (e.g. "Rus­ sell's set of all sets not being members of themselves" or the ancient problem with propositions like "I am lying" 1), normative paradoxes deal with contradic­ tions among equally well accepted normative postulates (Arrow's "impossibility theorem", Sen's "Impossibility of a Paretian Liberal") and "factual" paradoxes refer to conflicts between conventional opinion based on an accepted empirical theory and contradictory empirical evidence (e.g. the "St. Petersburg paradox" or the "Allais paradox" in decision theory2). Paradoxes, either logical, normative or factual, also contradict our intui­ tions. The counter-intuitive property which seems to be a common feature of all paradoxes plays an important part in the empirical social sciences, particularly in the old research tradition of scrutinizing the unintended consequences of pur­ posive actions. Expectations based on naive theories ignoring interdependencies between individual actions are very often in conflict with "surprising" empirical evidence on collective results of social behavior. Examples are numerous reach­ ing from panic situations, the individual struggle for status gains resulting in collective deprivation, the less than optimal supply of collective goods etc. to global problems of the armament race and mismanagement of common resources.



Individual Utilities and Utilitarian Ethics

The fundamental assumption of utilitarian theory is that we ought to choose our moral standards by rational criteria, more particularly, that we ought to choose the moral standards of the highest expected social utility.1 Here “expected” stands for “the expected value of ”, while “social utility” refers to the arithmetic mean (or possibly the sum) of all individuals’ utility levels. (Except in discussing the problem of optimum population, we can regard the number of individuals in society as given so that maximizing the arithmetic mean and maximizing the sum of individual utilities will be mathematically equivalent.) Of course, either definition of social utility assumes that individual utilities are cardinal quantities measurable on an interval scale and are interpersonally comparable in a meaningful manner. For convenience, I will sometimes use the term “social-utility function” instead of “social utility”. Note that many economists would employ the term “social welfare function” to describe what I will call “social utility” or the “social-utility function”.
John C. Harsanyi

Some Paradoxes in Economics

Just to make sure that we know what we are talking about, I have consulted (1) Encyclopedia Britannica, (2) The Concise Oxford Dictionary, and (3) Colin’s National Dictionary. The result of my research is that we don’t know. In (1) there is no explicit definition of “paradox”, but it is said to be approximately the same as antinomy, which is a pair of (seemingly) correct but contradictory implications from the same base. In (2) we find a similar definition, but also: “statement contrary to received opinion”. In (3) less neutrally: “statement seemingly absurd or self-contradictory, but really founded on truth”.
Ole Hagen

Pragmatic Intuitions and Rational Choice

The literature of rational choice is pervaded with apparent paradoxes. Often the paradoxes are contrived in the following sense. We consider a problem as though it were a realistic or typical choice problem similar to the kinds of problems we normally face in everyday life. Yet the conditions of the problem as specified defy normal experience. Reasoning through the problem under the specified conditions yields one result while baldly attacking the problem from the intuitions developed from our normal experience yields a contrary result. Hence we think there is a paradox.
Russell Hardin

Guidelines for Solving Sen’s Paradox

Judged in terms of social policy, Sen’s Paradox is perhaps more striking than its cousin, Arrow’s Paradox, although the latter might be intellectually more difficult and hence more intriguing. Perhaps this is because Sen’s Paradox is actually a special case of the Prisoner’s Dilemma: in the context of committees, it is equivalent to logrolling, whereby the (logrolling) side-payments are traded off directly with votes on issues; the point being that Sen’s Paradox, like other cases of the Prisoner’s Dilemma, represents a conflict between ‘selfish’ and ‘moral’ ends. The Prisoner’s-Dilemma-formulation of Sen’s Paradox is described in Bernholz (1976), Fine (1975) and Breyer (1978: 136ff.). These are the sources for the presentation 1 give below in §II. Nevertheless, these paradoxes, together with “Gibbard’s Paradox”,1 not to mention Newcomb’s Paradox, appear to be tough and obtuse in the following sense: even though interesting and clearly important analyses have clarified the mutual relations among the principles involved, no intuitively clear, universally acceptable and generally applicable ‘solutions’ to any of the well-known paradoxes have appeared.
Eckehart Köhler

System Breaks and Positive Feedback as Sources of Catastrophe

In the course of a friendship with Anatol Rapoport that has now lasted over thirty years, I have learned a great many things from him, more, indeed, than I could possibly acknowledge. One remark of his stands out vividly in my memory, in which he said in effect that the most careful empirical study of the path of falling leaves would never have revealed to us the law of gravity, even though this is certainly one of the principles that underlies and helps to explain their behavior. This was a dramatic illustration of the epistemological difficulties that we run into when we study complex systems. The human race, in its endless pursuit of knowledge, has run into a curious paradox. What we are most immediately aware of is ourselves through consciousness and the ability to penetrate the consciousness of other human beings through language and other forms of communication.
Kenneth E. Boulding

Social Structure and the Emergence of Norms among Rational Actors

Anatol Rapoport has been a major contributor to the application of game theory to problems in the social sciences. One of his lesser-heralded accomplishments is his submitting the winning entries for two tournaments based on an iterated prisoner’s dilemma game, organized by Robert Axelrod (1984). This work led Axelrod into the study of how cooperative strategies might evolve in populations of interacting individuals in an incentive structure that allowed exploitation of the other, and the strategy employed by Rapoport in his winning entries played an important role in Axelrod’s development of these ideas.
James S. Coleman

Conditions for Cooperation in Problematic Social Situations

The Prisoner’s Dilemma has intrigued Anatol Rapoport as a model of real life conflict situations — the arms race and price reductions by competing firms being his favorite examples — in which individual rationality and collective rationality are at cross purposes (e.g. Rapoport, 1974: 17–18,24). In the social sciences and particularly in social psychology, the game has attracted above all an impressive array of experimental investigations (cf. the now classic study by Rapoport and Chammah, 1965 and the survey in Rapoport, 1974: 19–29). In contrast to such a micro-approach we will try to sketch some implications of Prisoner’s Dilemmas and related situations of strategic interdependence for a more macrosociological problem. Our analysis refers to conditions of cooperation of (individually rational) actors in situations where cooperation generates efficiency, i.e. collective rationality, but is beset by incentive problems. Section II of this paper contains an explication in terms of game theory of such “problematic social situations”, the classical Prisoner’s Dilemma being a paradigmatic example. In Section III some results of the game theoretical analysis of these situations are outlined. In Section IV, we deal with implications of these results for conditions which are conducive to cooperation.
Werner Raub, Thomas Voss

The Evolution of Reciprocal Cooperation

It is the aim of this paper to develop a new way to model reciprocal cooperation. Hitherto reciprocity has counted merely as a form of cooperation, which has mainly been treated in the context of the well-known Prisoner’s Dilemma (PD) game. I will try to show that it is necessary to turn to a different game structure for a satisfactory account of reciprocal cooperation, involving features of a number of cooperation forms that are out of reach of the old structure. In the end I hope to have introduced a tool for the structural analysis of real phenomena, which allows a better appreciation of its richness and complexity than the standard PD.
Rudolf A. Schüßler

Is it Always Efficient to be Nice? A Computer Simulation of Axelrod’s Computer Tournament

The simplest model of a conflict between two parties is a 2 × 2 game. Each player has two strategies, say c (to cooperate) and d (to defect). If one takes only the rank order of the payoffs into account there are 78 nonequivalent 2 × 2 games (Rapoport, Guyer, Gordon 1976). The most extensively analysed of these 78 is Prisoner’s Dilemma (see Table I). Following the taxonomy of Rapoport (Rapoport et al. 1976) we define a 2 × 2 game as Prisoner’s Dilemma, whenever
$$T > R > P > S$$
The paradox of Prisoner’s Dilemma is that each player gets — independent from what the other plays — a higher payoff when playing D. To defect is a so called dominant strategy. But when both players act individually rational and chose D both suffer from their individual rationality. Mutual cooperation would be collectively rational. The most outstanding situation which has (on an abstract level) such a structure is the arms race between the two superpowers.
Christian Donninger

The Prisoner’s Dilemma and its Evolutionary Iteration

The logicians of the Middle Ages called paradoxes “insolubilia” — unsolvable problems for rational logicians —, and for some paradoxes they were right. If, for example, we define an egoist as being a non-altruist and an altruist as being a non-egoist, we run into a paradoxical situation when we have to explain how egoists (non-altruists) can behave altruistically. This is in nuce the paradox of the Prisoner’s Dilemma. But what happens if we repeat or ‘iterate’ such a paradoxical situation? Jourdain’s iterated card paradox is an illustrative example. “On the face side of a card there is written a true statement.” However, if you turn the card over there will appear the words: “On the other side of this card is written a false statement”. If we rely on common sense or on our logic and suppose that the statement on the front side is true, then the statement on the back side must be true, too; but, as a rational consequence of supposing the later statement to be true — which the logicians call proof by reductio ad absurdum —, the statement on the front must now be false! If we now assume that the statement on the front of the card is false, then the statement on the back must be false, too, and hence the statement on the front must now be true! Thus it is our logic which rationally connects the statements on both sides of the card and makes truth dependent on falsehood and falsehood on truth etc., ad infinitum. As Hofstadter (1978: 78) would say, we are trapped on a Moebius strip or an Escher staircase (Kreuzer, 1986).
Werner Leinfellner

The Evolution of a Prisoner’s Dilemma in the Market

The old issue whether cooperation evolves in a world of egoists and, if so, in what way has recently attracted attention by social scientists focussing on situations corresponding to game-theoretical models like the prisoner’s dilemma or coordination games (see particularly Axelrod, 1984; Lewis, 1969; Orbell et al., 1984; Schotter, 1981; Taylor, 1976, 1981; Ullmann-Margalit, 1977; see also Kliemt and Schauenberg, 1984; Voss, 1985). From the point of view of scholars interested in explaining various types of cooperation in real-life situations, this rapidly growing literature exhibits three major weaknesses.
Karl-Dieter Opp

On Explaining the Rise of the New Social Movements in Germany

Anatol Rapoport was among the first to recognize the great potential of the non-constant-sum game, called the “Prisoner’s Dilemma”, in shedding light on the interrelation of social conflict and social cooperation. He was also one of the first to initiate experimental research in the early sixties on the intriguing questions posed by the Dilemma (Rapoport, 1974).
Lucian Kern, Hans-Georg Räder

Volunteer’s Dilemma. A Social Trap without a Dominant Strategy and some Empirical Results

Conflicts between individual and collective interests are usually discussed in a prisoner’s dilemma context. Panic situations, the armaments race of the superpowers, exploitation of resources (“tragedy of the commons”), Hobbe’s problem of cooperation in anarchic societies and the evolution of cooperation (Axelrod, 1984), as well as numerous other examples of “social traps” (Platt, 1973) were described in the game theoretical language of prisoner’s dilemma. Increasing interest in N-person-prisoner’s dilemma (N-PD) stems also from the fact that there is a structural equality between Olson’s (1965) “Logic of Collective Action” and N-PD as was shown by Hardin (1971). The generalized PD-game seems to serve as a paradigm for social dilemmas, where interdependent individual actions cause paradoxical results. Dawes (1975) defines social dilemmas by two characteristics: the existence of a dominant strategy and the Pareto-inferior intersection of dominant strategies. Both characteristics in a broad sense also define generalized PD-games.
Andreas Diekmann

Take-Some Games: The Commons Dilemma and a Land of Cockaigne

Platt (1973) introduced the term social traps as a designation of situations where men or organizations or whole societies get themselves started in some direction or some set of relationships that later prove to be unpleasant or lethal and that they see no easy way to back out of or to avoid. The two preliminary examples given by him concern the two types of social traps which are probably the most relevant ones: conflicts of conservation and conflicts of contribution (Platt as well as other authors seem to prefer the term social fence for the second type). Platt’s conservation conflict example is Garrett Hardin’s seminal article “The Tragedy of the Commons” (1968). This title refers to public greens in traditional communities where anyone could graze his cattle freely. As cattle owners can increase their profit by driving more and more cattle to the commons, there are good chances that the pasture becomes overgrazed and finally destroyed. Thus the continued pursuit of individual advantage has exactly the contrary effect of severe disadvantages both for each individual and for the whole community. The harder they try, the less they (finally) get.
Peter Mitter

Games with Perceptive Commanders but with Indoctrinated or Less Perceptive Subordinates

The perceptive work of Kissinger (1958), Wohlstetter (1975), Kahn (1960) and many others was devoted to helping to provide advice and guidance for operational problems set in the context of differing cultures, political systems and technological reality. In all instances the argument was strategic but heavily context constrained. In contrast much of the work in formal game theory has been more or less free from context. In between these two considerably different approaches there has been some work which has posed problems with the difficulties of theory without context and context without sufficient theory. In particular various paradoxes have been raised by Ellsberg (1961) concerning risk and uncertainty; Schelling (1960, 1978) on precommitment, threat communication and mass behavior; Shubik (1954, 1971) on “truels” or three way fights and escalation and Raiffa (1982) on bargaining.
Martin Shubik

Moral Sentiments and Self-Interest Reconsidered

In this paper, the concepts of moral sentiments and self-interest, as conceptualized by Adam Smith, will be reconsidered with respect to their capacity to bring about “fair and reasonable” social decisions. The well-known Prisoner’s Dilemma and a “new” variable-sum game called Volunteer’s Dilemma are chosen to illustrate the problem and to discuss solutions. The results are presented in Sections 3 and 4 of this paper. In the concluding section, the problematique of symmetry, inherent to the analysed decision situations and proposed solution concepts, will be reconsidered. First, however, definitions of moral sentiments and self- interest seem to be in place.
Manfred J. Holler

On the Economic Virtues of Incompetency and Dishonesty

Most people would agree with the statement that if incompetency and dishonesty were costless to eliminate their optimal level would be zero. The reasoning would be that incompetency is wasteful since it leads to mistakes while dishonesty is wasteful because if faulty information is relied on it can lead to suboptimal decisions. But the existence of dishonesty and incompetency can also have secondary effects which may be beneficial. In fact, in this paper I will present a simple example of a market with asymmetric information in which these second order effects dominate and present a clear case in which positive levels of incompetency and dishonesty are socially beneficial.
Andrew Schotter

New Chairman Paradoxes

Power is one of the most alluring but also one of the most intractable concepts in political science. It leads to a number of paradoxes (Brams, 1976, ch. 7), which continue to manifest themselves in real-life voting bodies like the European Community Council of Ministers (Brams and Affuso, 1985; Brams, 1985: 101–104). For example, one implication of some definitions of power is that the greater proportion of resources (such as votes) that an actor controls, the greater is his power. In this paper, we shall show that this implication in a certain context may be false.
Steven J. Brams, Dan S. Felsenthal, Zeev Maoz

Cumulative Effects of Sequential Decisions in Organizations

With the recent revival of the individualistic approach in sociology, the study of nonobvious consequences of well understood actions, which, by their surprise aspect, create the impression of a paradox, has become increasingly important. People react with surprise when confronted with events the appearance of which is forbidden by the beliefs they are holding. Because surprise, like beauty, is in the eye of the beholder, the paradoxical character of these phenomena vanishes as soon as it is explicated how they are produced by well understood actions.
Jeroen Weesie, Reinhard Wippler

Ethnic Segmentation as the Unintended Result of Intentional Action

The substantive object of this contribution and the definition of the collective characteristic to be studied here are simple to describe: the ethnic segmentation as a certain kind of selectivity of social relations. Ethnic segmentation is considered to be present where persons of differing ethnicity can be shown to choose, from among the various options open to them (for interaction, economic activity, identification etc.), that alternative which is orientated to ethnic criteria, and to do so more often than would be predicted given random choice. The methodological peculiarity is also quite clear: segmentation is undoubtably a collective phenomenon. In most cases segmentation occurs with such an inevitability (for example, race-relations cycles) that one really could speak of there being an ‘iron law’ at work i.e. the social process involved takes its course even if it runs contrary to the declared intentions of the individuals involved and is thus ‘inevitable’ and ‘irreversible’. The present contribution concerns itself with the individualistic reconstruction of ethnic segmentation as an — under certain conditions — ‘inevitable’ result of intentional actions of individuals.
Hartmut Esser

The Paradox of Privatization in Consumption

Most everyday goods can be more or less private in consumption. For example, a family may share one bathroom or may enjoy the luxury of one bathroom per person in which case the good has been completely privatized. Even such “personal” goods as haircuts may be shared in the sense that family members take turns getting a haircut rather than having their hair cut whenever they individually decide to do so. Thus, even haircuts may be privatized in consumption. There is a definite trend towards increasing privatization in consumption with increasing income. The paradox I would like to discuss in this paper can be summarized as follows: by increasing privacy in consumption, people seemingly also destroy something they cannot replace by their own efforts: certain forms of social approval. They seemingly act in such a way that they increase their own deprivation with regard to these forms of social approval.
Siegwart Lindenberg

Declining Life Expectancy in a Highly Developed Nation: Paradox or Statistical Artifact?

One of the most reliable indicators of a country’s socioeconomic development is the so-called life-expectancy at birth, a summary measure of mortality-rates from infant mortality to mortality at the most advanced ages. Since mortality is to reflect factors like nutrition, medical technology, prevention, or public health standards, it has been and still is a frequently used argument in ideological competition between East and West, too. Without doubt the Soviet Union was one of the most underdeveloped European countries at the time of the October Revolution. In terms of life-expectancy it lagged behind the other Industrialized countries of Europe by a gap of about 15 years (Pressat, 1985: 318). Even in the period between the two World Wars, the increases in Soviet life-expectancy were only relatively meager.
Reiner Dinkel

Fallacies and Paradoxes Caused by Heterogeneity

Sociological model building has made great advances during the last decades. Developing their own models as well as borrowing models from statistics, econometrics, psychometrics and biometry, sociological methodologists have been able to solve several long standing problems. Examples are:
  • the treatment of dichotomous, ordinal and unordered categorical dependent variables using threshold and random utility maximization models such as dichotomous, ordinal and multinomial logit and probit models (Daganzo, 1979; McFadden, 1981; Maddala, 1983). These may be extended to model event histories with transition probabilities in discrete time (Allison, 1982; Arminger, 1984; Hamerle, 1985).
  • the analysis of count data using loglinear models, which is especially useful for the analysis of contingency tables (McCullagh and Nelder, 1983).
  • more generally, the analysis of dependent variables belonging to the exponential family using generalized linear models (McCullagh and Nelder, 1983).
  • the treatment of event histories in continuous time and discrete state space with transition rate models (Tuma and Hannan, 1984; Heckman and Singer, 1984a, 1984b).
  • the simultaneous estimation of factor analytic and structural equation models for metric observed variables, often carried out with the LISREL program (Jøreskog and Sørbom 1984), which has been extended by Muthén (1984) using normal distribution theory to include dichotomous and ordinal observed variables.
Gerhard Arminger


Weitere Informationen