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advancing a theoretical alternative to escape from the non-cooperation trap. ..... model to analyze how adapting actors might find the way out of social traps as ...
Institutional Change, Collective Action and Cooperation Presented by

Fernando Buendía Business Administration Department and Center for Socioeconomic and Political Studies University of the Américas, Puebla Santa Catarina Mártir, Cholula, Puebla, 72820 Mexico Phone: +52 (222) 229-24-54 Fax: +52 (222) 229-27-26 E-mail: [email protected] for Th

The 7 Annual Meeting of the International Society for New Institutional Economics September 11-13, 2003 Prague, Budapest, Hungary Abstract Institutional change, collective action, and cooperation are closely related. The connection between institutional change and collective action comes from the fact that both democratic political institutions and norms of behavior are collectively chosen: they are the result of a collective action process. Collective action, however, requires a solution to the cooperation problem, for it is usually associated to the Prisoner’s Dilemma, which provides a formal representation of a ubiquitous type of situations that arises when individual interests undermine the collective welfare of the group. Essentially, the pessimistic result of this game is due to the fact that the players, who have a choice between cooperation and defection, prefer to defect, so the “cooperative” strategy equilibrium (P,P) for the one-shot game is Pareto-dominated by (R, R) where the payoffs obey T>R>P>S. This paper suggests a theory of institutional change by advancing a theoretical alternative to escape from the non-cooperation trap. Keyword: Institutional Change, Collective action, Prisoner’s Dilemma, Cooperation.

1. Introduction North (1990) has advanced a solution to the cooperation problem —the cooperation that permits economies to capture the gains from trade that were the key to Smith’s Wealth of Nations— which has earned a prominent place in the new institutional economics. He sees modern economic growth as inherently connected to the institutional framework of well developed coercive polities. This leads to the following question: Why is it that some polities provide an institutional environment that promotes trade and economic growth, while other perpetuate underdevelopment? North’s arguments on path-dependence, the inventive capacity of entrepreneurs to develop new technologies and detect new opportunities, and the relevance of ideas, dogmas, fads, and ideology as sources of institutional change are of obvious importance. And so is his observation that political institutions, like electoral procedures, often offer the possibility to transform institutional structures by expressing one’s ideas at practically no cost. However, what creates norms of behaviors and efficient political institutions? His answer is that “[w]e need to know much more about culturally derived norms of behavior and how they interact with formal rules to get better answer to such issues” (North, 1990: 140). North, therefore, states that institutions create the hospitable environment to solve the problem of human cooperation which makes the gains from trade possible, but he does not give a complete explanation of how cooperation emerges among economic agents to provide themselves with public goods such as, norms of conduct and democratic political institutions. North, in other words, provides a complete theory of institutions and a partial explanation of institutional change.

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This paper suggests a theory of institutional change where collective action and cooperation play a prominent role. The relationship between institutional change and collective action stems from the fact that both democratic political institutions and norms of behavior are the result of a collective action process. Collective action, in turn, is usually associated to the Prisoner’s Dilemma which is the most accepted formal representation of the kind of situations that arises when individual interests undermine the collective welfare of the group. If in a world of rational, perfectly-informed individuals, defection instead of cooperation is the dominant strategy in any social interaction, then it is not farfetched to conclude that in that world there is no institutional change at all. In order to escape from the non-cooperation trap of the Prisoner Dilemma, this article models the influence of heterogeneous individuals on the emergence of cooperation. In this model a population of individuals with different levels of preferences for different kinds of public goods is assumed. If in this population there are some individuals with a strong preference for a specific public good (the pioneers), they might act and start a collective action to obtain that good. Followers (those individuals with weaker preferences for the public good) may jump on the “bandwagon” when they see the pioneers’ behavior. In the model, then, collective action evolves in a kind of “domino” effect, but it is argued that such an effect comes about only under certain conditions. Specifically, it is suggested that if a certain level of critical mass, interdependence of decision, geographical proximity among individual, social ties among individuals, progressive learning and other conditions are reached, full cooperation is obtained and collective action takes place, which in turns leads to the acquisition of a specific public

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good. This paper proceeds as follows: section two reviews the literature on the theoretical problem of collective action to identify its present state. In section three Olson’s original formulation and its criticisms are analyzed. The fourth section studies the ideas that have been suggested to solve the cooperation problem and their weaknesses. Section five outlines a solution to the collective action problem. Specifically, it proposes a way to escape from the noncooperation trap by establishing a one-shot game where heterogeneous learning individuals are assumed. Last section sketches some ideas to formalize this dynamics as a self-organizing process.

2. Olson’s Original Formulation of Collective Action and its Weaknesses Collective action has long attracted the interest of sociologists, economists, political scientists because it is central to understand the way social and political change occurs. Collective action is extremely useful to explain issues that range from transition from centrally controlled economies to market economies and the possibility to have many societies under one general government to the cooperation in volunteer organizations to give charity, eliminate pollution or eradicate diseases. Since Olson (1965) wrote his controversial The Logic of Collective Action and identified the collective action problem1, some sociologist and economists have suggested some

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Mcphail (1991) offers a review of the radical different explanations of collective behavior that have been advanced since the introduction of LeBon’s Psychologie des Foules in 1895. LeBon’s explanation is that people are transformed by a maddening crowd that makes them lose control over their own behavior, and engage in behaviors quite different from those in which they ordinarily engage. Another classical explanation of collective behavior is that people flock together because of similar psychological or ideological predispositions, which also compel them 3

ideas to explain why people cooperate to collectively act and obtain public goods by criticizing Olson’s pioneering analysis on collective action. So to assess the present state of collective action theory, it seems convenient to study at this point how he diagnosed and suggested solving this problem. According to Olson (1965)2, the theory of collective action started with the idea that groups of individuals with common interests behave as single individuals in search for their personal interests: if the members of a group are better off when they achieve a common interest or objective, then it follows that their rational behavior is to act to attain their aim. In his The Logic of Collective Action, Olson challenged this conventional approach by arguing that the purpose of organizations is to achieve the interests of their members, when they cannot do it by themselves or when unorganized actions cannot serve certain of their goals. The members of large organizations, however, face the predicament of choosing between their individual interests and the common interests of the organization. This situation is analogous to the one of a perfectly competitive industry whose firms have a common interest in a higher price, but they also have an interest in selling as much as they can (until the cost of producing another unit exceeds the price of that unit). Thus, profit-maximizing firms in a perfectly competitive industry end up worse off as a group, even though they are maximizing their individual utility function.

to engage in behaviors within the crowd that correspond to their madness-in-common. Norms are other classical explanation of the cause of what two or more persons do together. A last account of collective action is the sociocybernetic model of collective action, whose basic idea is that individuals are purposive actors and that they control their own behavior by means of self-instructions which are ruled by their own goals and objectives. Although Mcphail provides an excellent overlook of the earliest interpretations of the collective problem, at the end of his book he reduces it to the behavior of the crowd. This is unfortunate, because most interesting collective phenomena are those which arise in different places, during different periods of time and include different level of institutional complexity, such as revolutions, woman liberation movements or workers union struggles. 2 In this article, each time that Olson’s work is mentioned it should be referred to Olson (1965). 4

Furthermore, just as it was not rational for a particular producer to constrain his output to keep a higher price for the product of his industry, so it would not rational for him to sacrifice his time and money to support a lobbying organization to obtain government assistance for the industry. In other words, the provision of public goods —the achievement of any common goal or the satisfaction of any common interest— is the fundamental function of organizations. But given that they trade in public goods, little or none cooperation can be expected from their rational members. To solve the dilemma between private and common interests, Olson develops his well-known argument on group size. He suggests that, while large groups may fail in providing public goods, small ones may succeed in achieving this goal, although their quantity may not be the optimal one3 and there may be a surprising tendency for the ‘exploitation’ of the great by the small4. However, Olson’s central conclusion that big groups are much less likely to provide themselves with a collective good than small ones is seriously flawed by his fail to consider jointness of supply. To explain why this is so, it is necessary to give a brief on the theory of public good. As any other public good, the one provided by the achievement of a group has the characteristics of non-excludability, non-rivalry, and jointness of supply. Non-excludability 3

This tendency toward sub-optimality —Olson explains— is due to the fact that a collective good is, by definition, such that other individuals in the group cannot be kept from consuming it once any individual in the group provided it for himself. Since an individual member thus gets only part of the benefit of any expenditure he makes to obtain more of the collective good, he will discontinue his purchase of the collective good before the optimal amount for the group as a whole has been obtained. In addition, the amount of the collective good that a member of the group receives free from other members will further reduce his incentives to provide more of that good at his own expense (p.35)”. 4 Once a smaller member has the amount of the collective good he gets free from the largest member, he has more than he would have purchased for himself, and has no incentive to obtain any of the collective good at his own

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means that if a member of the group consumes or demands a public good, it is neither feasibly nor efficient to withhold it from the other group members. Given that it is not possible to exclude anyone from sharing in the public good once it has been demanded, the most rational behavior of a self-interested individual is to free-ride; that is to say, to avoid rivaling for the good in the market. This characteristic of public goods is called non-rivalry. Private goods, in contrast, can be enjoyed exclusively by the individual who demands them. This, in turn, implies that he or she has to rival for them. Another characteristic that distinguishes a public good from a private one is its jointness of supply. In one hand, when the costs of providing a good is proportional to the number of individuals who enjoy it, then that good has zero jointness of supply: it is a private good. On the other hand, a good with pure jointness of supply costs the same no matter the number of individuals enjoying it5. It has “fixed costs” but no proportional costs. There are many kinds of collective goods, but the kind Olson had in mind in his analysis are clearly that with zero jointness of supply. In assuming zero jointness of supply, Olson views individual benefits as a decreasing function of group size and collective action as the result of conventional market behavior where rational individuals invest in private goods. Nevertheless, the real collective action problem involves pure public goods —i.e., those with non-excludability and pure jointness of supply. Therefore, the dilemma between common and individual interest in organizations remains in Olson’s logic. Olson’s argument on group size in some way forces him to develop his “by-product theory”. If the provision of the public good is not enough to overcome the free-rider problem and expense.

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motivate people to join an organization, then they must also be organized for some other purpose or motivated by additional benefits, such as union pension plans, or social approval in the same way as lobbying for collective goods is a by-product of organizations that receive their strength from selective incentives. Olson argues that “selective incentives” are needed to overcome the free-rider problem by providing additional benefits that depend on individual contributions, so those who do not work for the group interest and those who contribute can be treated differently. Olson’s solution to the collective action problem also relies heavily on social references, which includes formal organization and leadership, political entrepreneurs —who are an important element to explain the emergence and existence of interest group—, selective incentives —such as prestige, social pressure, and so on—, and moral incentives, which inspire “mass movements” and non-economic lobbies with social, political, religious or philanthropic interest.

3. Alternatives to Olson’s Logic In his analysis of Olson’s logic —which was of considerable importance for the subsequent treatment of the cooperation problem— Hardin (1982) suggest that one-shot, N-person Prisoner’s Dilemma game is a rather accurate representation of the collective action problem. The result of this game is that for each of the N persons, defection dominates cooperation, independently of the others’ choice. That universal defection is Pareto-inferior vis-à-vis universal cooperation becomes extremely relevant for economic analysis, because it correspond to exactly the opposite outcome of Adam Smith’s invisible hand. Here individual rational behavior leads to collective irrationality, instead of common good.

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There are, of course, cases that lie between these two extremes. 7

Given the definition of collective action as a Prisoner’s Dilemma, it seems that an adequate means of going out from the non-cooperation trap depends, to a great extent, on the solution to the free rider problem contained in the Prisoner’s Dilemma game. Perhaps the most well known solution to generate cooperation among individual is repeated games. In an infinitely repeated game, rational individuals will find worthwhile to adopt trigger strategies, so called because player i cooperates until someone fails to cooperate, which triggers a switch to noncooperation forever after. This is, however, very unrealistic because such indefinite interactions are not very common in the real world. Infinite interactions may be replaced by finitely repeated games. These games depend on the Folk Theorem, which requires of a discount rate close to one to obtain a sub-game-perfect Nash equilibrium. The higher the discount rate, the less the expect value of future payoffs, and the higher the probability of leaving the game very soon. Hence the discount rate may be interpreted as a stop probability or a measure of impatience. Yet the assumption of any specific, positive discount rate is alarmingly ad hoc for a model that is supposed to provide an endogenous explanation. Then, the internal solution to the collective action in this approaches rely upon a gratuitously exogenous assumption which foreordain the desired outcome. Besides, this game is the antithesis of the most common real-world cases of collective action in which there are no repetitive interactions. Robert Axelrod (1984)’s computer tournament is another well-known use of iterated games. Axelrod found that the strategy that emerges victorious was tit-for-tat: the strategy of always to cooperate in the first round and to defect when the others players defect. In a static one-shot Prisoner’s Dilemma people meet once, so contractarianism is not possible, but in

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dynamic games, contracts may solve the cooperative problem. The flaw of this approach is that, to get universal cooperation, the game must be repeated and with small number of players, and wealth-maximizing individuals must be non-myopic, confident that other individuals are rational and fully informed about the situation, the gain from universal cooperation must be substantial, the gain from unilateral non-cooperation not large, and the loss from unilateral cooperation small. In large groups, with people who do not know each other very well the adoption of strategies as tit-for-tat is unlikely to be realized. Besides, if many people cooperate, they do so because others cooperated many times in the past, but this is more likely to reflect a norm of fairness created through repeated interactions than reaction of rational, self-interested behavior. The main point here is that this rule of fairness solves the first cooperation problem, but gives rise to second-order cooperation problem. Taylor (1976) was the first in applying Prisoner’s Dilemma supergames to collective action. His conclusions is similar to that of Axerlrod: in two-person supergames cooperation is possible among rational egoists, if they use conditional cooperative strategies (tit-for-tat) if the number of two-person Prisoner’s Dilemma games is indefinite and if the players do not discount in future too much, relative to the immediate. Taylor (1990) also suggests a wider definition of the collective problem. He thinks that public goods interactions are not necessarily those of a Prisoner’s Dilemma but in many cases are those of a Chicken game. In the N-person Chicken, as in the N-person Prisoner’s Dilemmas, rational action can lead to Pareto-inferior outcome, but in the one-shot, N-person, two-strategy Chicken game there are some conditions to assume that some cooperation is more likely possible than in the cases in which the one-shot Prisoner’s

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Dilemma is the appropriate model. For this to be so there must be stable profitable subgroup (at least one corresponding to each player) whose members find it in their interests to cooperate when individuals outside the group do not. Aware of the weaknesses of game theory to solve the cooperation problem, Hechter (1990) considers the merits of his joint-good approach as an explanation of how cooperation can emerges. There are two types of solidaristic explanations: imposed and voluntary solidarity. In the former, institutions emergence is explained by significant power differential among individuals. Individuals with roughly equal power can create institution voluntarily. The driving force in this explanation of the origin of cooperation institutions is the rational egoist’s desire to consume a small number of private goods —security, insurance, and credit—, which can only produced jointly and therefore induce these individuals to enter into voluntary cooperative social relations. In fact, the demand for these joint goods serves as a series of “Schelling point” that enable otherwise unconnected individuals to coordinate predictions, to read the same message in the common situation, to identify the one course of action that their expectations of each other can converge on. Linked by their common interest in consuming some joint good, these individuals are reluctant to invest their own time and other assets in cooperative effort in the absence of thirdparty enforcement; for they want to be assured that their investment will yield a positive return. This assurance can only be provided if it is expected that free riding can be deterred, hence, in order to consume these joint goods, individuals must create their own controls. The determinant of the rise of control lies in the conditions allowing for visibility in both the production and

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consumption of joint goods. In the state of nature, this visibility will be at maximum when joint goods are collected and disbursed from some central place. Visibility, in turn, is necessary condition for the development of control. From these controls, cooperative institutions are born. Recent contributions within the sociological school of collective action (Oliver et al., 1985; Oliver et al. 1988, and Marwell et al., 1988) have challenged the rational-choice explanation of collective action and proposed a solution to the efficacy problem: the “critical mass” theory, which makes the free-rider problem less severe. They found that in large groups there is higher probability to find a small group of highly resourceful and interested individuals willing to support collective action. They argue that when this core of “irrational” individuals are selected by organizers (who are assumed to have the larger personal networks), contributions tend to explode and draw in the other less interested or less resourceful members of the population and to carry the event toward its maximum potential. Taking in account the fact that public goods are not only non-excludable but they also have jointness of supply, they generate an important result: when free-riders are not a burden on those who contribute, it is not necessary to organize every member of a large interest group. A small subset or “critical mass” of highly resourceful and interested member can patronize a much larger group without concern that the benefit to others will diminish their own. The problem of universal cooperation is reduced only to those who form the critical mass. This has sense, since it is not necessary that every individual enjoying, for instance, political stability stemming from revolutions, participates in such revolutions.

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Another contribution of the sociological school of collective action is Macy (1990, 1991). Macy’s argument is that, if in a collectivity there are a group of people willing to provide a public good, it is because these people have learned to cooperate through precedent interactions or because they have participated in other collective actions. Actors learn through experience, adapting their decision rules in response to social feedback. Macy uses a stochastic learning model to analyze how adapting actors might find the way out of social traps as they respond to the social signals and cues generated by the action of others. However, his stochastic learning model, as Macy (1990) himself recognizes, imposes two new constraints: first, decisions must be repeated so repetition may cause reinforcement. Second, effective learning requires accurate and immediate feedback. Macy (1990) tries to surmount these difficulties assuming instead that actors acquire experience through what others have done before. That is to say, instead of assuming N social interactions that explain how actors might develop habits of compliance and internalize norms of cooperation, he assumes only one collective action in which actors learn to cooperate from the previous behavior of others individuals participating in the same collective action. Altruism, solidarity, sanctions, values and other selective incentives have been the typical solution to the problem of collective action6. Rationality means that each individual takes the 6

These selective incentives have been identified as solution to collective action problem (cf. Margolis, 1982 and Udéhn, 1993). But if selective incentives are necessary, why bother with collective goods at all? And since selective incentives are private goods, how come they are not provided by firms on the market? Since firms can produce these goods without the detour of collective goods, they must be able to produce them at much lower cost. Is not there something slightly absurd about a theory of interest groups, or collective goods, as by-products of organization providing private goods, in the form of selective incentives, at an enormous competitive disadvantage? Also, if people join social movements mainly for the social selective incentives involved why do they need a cause? Wouldn’t a club be better alternative? Do people need an excuse for sociability? These arguments, as Udéhn (1993) says, are devastating to the selective incentives argument. 12

place of the other and sees the world from his point of view. If each individual does the same, the result is infinitely reflection (or common knowledge). But this infinitely reflection has to stop somewhere, otherwise individuals would continue reflecting indefinitely and they would never make a decision. To stop reflecting and being capable to coordinate their decisions —as convention economics (Schelling, 1960; Orléan, 1994) has suggested— individuals need a common social reference or focal point. An interesting aspect of convention economics is that it enhances the paradigm of rationality by the introduction of external social reference, so that it makes the homo economicus depend on the homo sociologicus. Now the former has at hand all the social resources of the homo sociologicus to solve uncertainty: conventions, trust, and norms. Nevertheless, the homo sociologicus has the problem to be based on a sociological determinism, to the blind obedience of conventions and norms. Although convention economics has underlined the role of conventions and other of non-market processes in the functioning of the economy, it is necessary to go beyond; it is indispensable to explain how norms and similar social structures emerge, which is the fundamental problem of collective action theory. In other words, sanctions are an effective solution to the first collective action problem, but it gives rise to a second-order problem for they are themselves collective goods that beg for an explanation.

5. Escaping from the Non-cooperation Trap: A Model The analysis in the previous sections on the contributions to the collective action literature shows that they are elaborations upon themes already analyzed in Olson’s The Logic of Collective Action. In this section we suggest a framework to escape from the non-cooperation trap by

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accommodating and extending the ideas on the emergence of collective action so far analyzed and adding others. Oliver et al. (1985)’s critical mass theory is perhaps one of the main, though not completely radical, corrections to Olson’s analysis. Critical mass is simply a number of heterogeneous individual that makes collective action possible. The novelty of this idea is that heterogeneity of preferences opens a new avenue to further developments on collective action, because it can be used as a foundation to understand why an individual’s decision to join a collective action is sequential and conditional of others’ decision. Of all the members of a heterogeneous group that eventually will share in a public good, there is a subset that has more interest in obtaining it. This subgroup is the critical mass. It is natural, therefore, to assume that each member of this subgroup has stronger preferences for the public good. But, even though this is so, do not they find in their interest to free-ride? The answer, according to Elster (1989a), is no. He argues that, although some economists claim that individuals have the same preferences and desires, the fact is that people differ in their preferences. This is so evident that it does not require any proof. This idea of Elster can be supplemented introducing “bandwagon” preferences. When individuals have bandwagon preferences their motivations interact and reinforce one another, so the result is more than the sum of their isolated effects. Central to the understanding of this dynamic is the answer to the question: why do people imitate? Schelling (1978) had already pointed out that people’s behavior influence others’, but he does not explain the reason for such influence. An alternative explanation of the causes of imitation is considering the fact that an individual’s actions influence others’ behavior, because the first’s action alters the second’s

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utility function. If the individual B imitates the behavior of the individual A is because A’s behavior reduces significantly his uncertainty, risk, information costs, etcetera. On the other hand, individual B’s behavior enhances the value of the action of the individual A. With the interdependent and self-reinforcing character of decisions it is possible, in turns, to explain the form of the group’s preference function, which determine the emergence, the continuing and outcome of a collective action. Bandwagon preferences are a simple idea that provides a theoretical element to explain how collective action is started and continued. But heterogeneity of resources is also central to convince other individual to join the bandwagon. The actions of resourceful individuals, if they spend large resources to get the public good, are quite conspicuous and might trigger the cooperation of less resourceful agents. Sequential decision making, therefore, is important, so they must be introduced in the model. Individuals’ preferences for public good, depending of their strength, have different effectiveness at different stages in the cumulative development of collective action. If the individuals with stronger public-good preferences act in the first phase of the cooperation process, their actions will be imitated by the less interested individuals with a higher probability. On the other hand, if less interested individuals act in the early phases of the collective action process, there is highly probable that collective action never began. In sum, when people have a common reference or focal point it is not necessary to assume that they make their decisions in a sequence. Sequential decision-making, however, is important in those cases in which members of a group have different preferences concerning the public good and possess different resources to acquire it. To introduce sequential decision 15

making in our model, we assume a society of I individuals with different preferences for G different common goods. Thus, the level of interest of individual i for the public good g can be represented with the expression

β



( 0 ,1 ] .

However, the level of preference for a public good is not enough to determine whether the individual i will act to obtain the public good g. Thus, the conditions under which he will be willing to participate in a collective action have to be established. This can be done through the binary acting function 1;η i ≥ α i ζ (η ig ) =  gi 0,η g < α i

; with i = 1,2,3,..., I ,

which implies that if the level of preference of individual i exceeds a threshold αi, he will participate in the collective action to get good g. ξ = 1, therefore, indicates that he is acting, while ξ = 0 implies that he defects. Given that the set of preferences of the individuals who want the public good g is given i

by {η g ; i = 1,2,3,..., I } , then the set of preferences of the individuals who want a specific good i = 1,2,3,..., I is defined by the sets {η1i}, {η i2},...,{η iG}; i = 1,2,..., I . The elements of these sets must

satisfy the following condition η 1g > η 2g > ... > η ig−1 > η ig > η ig+1 > ... > η Ig−1 >η Ig .

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This implies that in our model all preferences for all goods follow an order, such that stronger ones precede weaker preferences. For instance, individual i has a higher level of interest for the good g than individuals i + 1, i + 2, i + 3, …, I. Therefore, the maximum level of interest for the i public good g within the set {η g} is possessed by the first individual. Therefore, the maximum of i

1

interest can be defined as η g ,max = max[{η g}] = η g .

In the model, it is assumed that there is not only a maximum interest for a given good, but also that there is a global maximum level of interest for all possible goods, which can be described using the following expression: η max = max[{η1i}, {η i2},..., {η iG}; i = 1,2,..., I ] = max[η11 ,η12 ,...,η1G ] .

That is to say, in the model it is assumed that the level of interest of the individual i for the public good 1 is the largest. Figure 1 shows the level of preferences for all public goods a given society wants to obtain.

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Level of preference

ηg max

ηg1 ηg2

ηg3 ηg4 ηgi-1

ηgi

………. 1

2

3

4

ηgi+1

ηgI-1 ηgI

………. i-1

i

i+1

I-1

I

Individual

Figure 1. A Society’s Level of Preferences for Public Goods

As we said before, in our model there are bandwagon preferences. This implies that the level of preference for a given public good of a specific individual may be affected by other considerations. In the first place, it is influenced by the level of preferences of the other individuals wanting to obtain the same public good. This means that if one individual sees individual i to act to obtain the public good he desires, there is a probability that the former individual gets his own level of preference increased. This could be expressed as η ig = F (η1g , η 2g ,...,η ig−1 , η ig+1 ,..., η Ig−1 , η Ig )

In the model, the level of preference of individual i for the public good g is supposed to be increased when this individual sees other to follow him and foresees that in the future other individual will join the collective action bandwagon. This mutual influence makes the addition of the levels of preferences of the individuals participating in the collective action larger than the addition of the levels of preference of the same individuals before their participation in that

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p

collective. That is to say, the level of preference of individual p, η g , is influenced by the level of q preference of individual q, η g , and the other way around. The mutual influence between

η gp and η qg can be expressed by

η gp = F (η1g , η 2g ,...,η gp −1 , η qg ,...,η Ig−1 , η Ig )

η qg = F (η1g , η 2g ,...,η gp , η qg+1 ,..., η Ig−1 , η Ig )

j i We assume that the higher the difference η g − η g (j < i) is, the higher the change

∆η ig

will

j i i be. We also assume that the difference η g − η g (j < i) has more influence on η g than the i k difference η g − η g (i < k). In other words, the preference of individual i is affected more by the

preferences of those individuals who precede him than by the preferences of those who follow j

i

i

k

him. If the difference η g − η g is expressed with the coefficients γ i and the difference η g − η g is expressed with the coefficient λ i , then the fact that the first difference has more weight on ∆η ig

than the second one, can be expressed by γ i > λ i . Thus the change on the level of preference

due to can be expressed with the following function: ∆η ig = F [γ i (η 1g − η ig ), γ i (η 2g − η ig ),..., γ i (η ig−1 − η ig ), λ i (η ig − η ig+1),..., λ i (η ig −η

I −1

I

g

g

), λ i (η ig −η )] .

i The preference of individual i for a good g, η g , is assumed to be also influenced by the

physical distance among individuals interested in the same public good. Then the physical distance between individual i and individual j is r i, j . The set of distances between the individuals

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in a society is given by {r i,1 , r i ,2 ,..., r i ,i −1 , r i,i +1 ,..., r i, I −1 , r i, I } . The last consideration influencing the i level of preference η g is the strength of social ties. For each pair of persons (i, j) there is a social

tie factor si, j which denotes how strong is the relationship between those persons. The set of factors symbolizing the social ties among the individual of a society is given by {si ,1 , si ,2 ,..., si ,i −1 , si ,i+1 ,..., si , I −1 , si , I} . For a pair of individuals i and j, the physical distance is quantitatively defined as 0 ≤ r i , j ≤ R;

i = 1,2,3,..., I ; j = 1,2,3,..., I ; i ≠ j ,

with R being the maximum distance separating a pair

of individuals in the group. The social tie factor gives a quantitative measure of the affinity between two individuals. Such affinity is related to kin, common interests, friendship, social status, etc; and it is quantitatively defined as 0 ≤ si, j ≤ 1;

i = 1,2,3,..., I ; j = 1,2,3,..., I ; i ≠ j .

For instance,

if two individuals, k and l, have no affinity, then sk,l = 0. In the other hand, if individuals m and n are closed friends or relatives, their level of affinity is sm,n = 1. The total influence of all these i factors on η g can be denoted as

η ig = F (η1g , η 2g ,...,η ig−1 , η ig+1 ,...,η Ig−1 , η Ig , r i ,1 , r i , 2 ,..., r i ,i −1 , r i ,i +1 ,..., r i , I , s i ,1 , s i , 2 ,..., s i ,i −1 , s i ,i +1 ,..., s i , I ) .

Then the total change of preference of individual i for good g, ∆ η ig , depends on the preferences of individuals who are already participating in the collective action

{η 1g ,η 2g ,...,η ig−1} ,

on

the preferences of the individuals who will follow individual i, { η ig+1,...,η Ig−1,η Ig }, on the sets of physical

distances

{r i ,1 , r i , 2 ,..., r i ,i −1 , r i ,i +1 ,..., r i , I −1 , r i , I } ,

20

and

on

the

set

of

social

ties,

{si ,1 , si ,2 ,..., si ,i −1 , si ,i +1 ,..., si , I −1 , si , I } .

The change of preference of the individual i can be expressed

with the following function: ∆η ig = F (η1g − η ig ,η 2g − η ig ,...,η ig−1 − η ig , η ig − η ig+1 ,...,η ig −η

I −1 g

I

,η ig −η , s i ,1, s i , 2 ,..., s i ,i −1, s i ,i +1,..., s i , I , s i ,1 , s i ,2 ,..., s i ,i −1, s i ,i +1,..., s i , I ) g

To express the dependence of

∆η ig

on the preference differences, physical distances and

social ties among individuals, the previous function can take the following form: r i ,1 r i,2 r i, I ) si ,1 , γ i (η 2g − η ig )(1 − ) si , 2 ,..., γ i (η ig−1 − η ig )(1 − ) si , I , R R R I I −1 r i ,i +1 r i , I −1 ri,I i i +1 ) si ,i +1 ,..., λ i (η ig −η )(1 − ) si , I −1 , λ i (η ig −η )(1 − ) si , I ] λ i (η g − η g )(1 − g g R R R

∆η ig = F [γ i (η1g − η ig )(1 −

The conditional probability for an individual to participate in the collective action, taking into consideration the mutual influence of preferences, η gj , is given Pr ob ( ∆η ig ≥ ρ | η gj ) = F (∆η ig = ρ | η gj )

where F(x, y) is the conditional probability distribution of x given y. If ∆η ig is bigger than or equal to ρ, then individual i participates in the collective action, given the influence from η gj (with j > i). If we assume that this probability distribution function is linear, then the probability follows the dynamics shown in figure 2

21

F ( ∆η ig = ρ | η gj )

Figure 2. Collective Action Probability Distribution Function

If each distribution is weighted by the coefficient coefficient

λ i (1 −

r i, j ) si, j R

r i, j ) si, j R

when j > i and by the

∆η ig

is bigger than ρ becomes a linear

F ( ∆η ig = ρ | η gj ) ,

as the following function shows:

when j < i, then the probability that

combination of the density distribution functions

γ i (1 −

r i ,1 r r ) s i ,1 + γ i F ( ρ ,η 2g )(1 − i , 2 ) s i , 2 + ... + γ i F ( ρ ,η ig−1)(1 − i , I ) s i , I + R R R r r r ..... + λ i F ( ρ | η ig+1)(1 − i ,i +1 ) s i ,i +1 + ... + λ i F ( ρ | η Ig−1)(1 − i , I −1 ) s i , I −1 + λ i F ( ρ | η Ig )(1 − i , I ) s i , I R R R

P(∆η ig ≥ ρ ) = γ i F ( ρ | η 1g )(1 −

With this function is possible to measure the probability that an individual participates in a collective action. Therefore, the social probability or what can be referred to as the collective action function, I

P(collective action) = ∑ P(∆η ig ≥ ρ i ) , i =1

is just the addition of individual probability functions which are subject to the acting function defined above. Economic agent, under the conditions established in this model, instead of 22

prisoner confined in the non-cooperation trap, are free cooperative agents joining together to assure the provision of public goods. These agents, therefore, instead of facing a Prisoner’s Dilemma they enjoy of what we can call a free man’s opportunity. Economies, therefore, benefit from that kind of cooperation that allows the trade of private, but from that type of cooperation that permits the transactions of public good.

References Axelrod, R., 1984, The Evolution of Cooperation, New York: Basic Books. Cook, K. S. & Levi, M., eds., The Limits of Rationality, University of Chicago Press. Elster, J. 1989a, The Cement of Society, Cambridge: Cambridge University Press. Elster, J. 1989b, Nuts and Bolts for the Social Sciences, Cambridge: Cambridge University Press. Elster, J., 1989c, “Rationality and Social Norms”, in J. E. Fenstad, I. T. Frolov and R. Hilpinen (eds), Logic, Methodology and Philosophy of Science VIII, Amsterdam: North Holland. Hardin, R., 1982, Collective Action, Baltimore: The Johns Hopkins University Press. Hechter, M., 1990, “Comment: On the Inadequacy of Game Theory for the Solution of RealWorld Collective Action”, in K. S. & M. Levi, (eds.). Margolis, H, 1982, Selfishness, Altruism, and Rationality: A Theory of Social Choice, Chicago University Press. Marwell, G., Oliver, P. E. and R. Prahl, 1988, “Social Networks and Collective Action: A

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Theory of the Critical Mass. III” American Journal of Sociology, 94, 502-534. Macy, M. C, 1990, “Learning Theory and the Logic of Critical Mass”, American Sociological Review, 55, 809-826. Macy, M. C., 1991, “Chains of Cooperation: Threshold Effects in Collective Action” American Sociological Review, 56, 730-740. McPhail, C., 1991, The Myth of the Maddening Crowd, New York: Aldine De Gruyter. North, D., 1990, Institutions, Institutional Change and Economic Performance, Cambridge, MA: Cambridge University Press. Oliver, P. E., 1980, “Rewards and Punishments as Selective Incentives for Collective Action”, American Journal of Sociology, 85, 1356-1375. Oliver, P. E., Marwell, G. & Texeira, R., 1985, “A Theory of the Critical Mass I: Interdependence, Group Heterogeneity, and the Production of Collective Action”, American journal of Sociology, 91, 522-556. Oliver, P. E. and Marwell, G., 1988, “The Paradox of Group Size in Collective Action: A Theory of the Critical Mass. II”, American Sociological Review, 53, 1-8. Olson, M., 1965, The Logic of Collective Action and the Theory of Groups, Cambridge, MA: Harvard University Press. Orléan, A., 1994, Analyse Economique des Conventions, France : Presse Universitaires de France. Schelling, T., 1960, The Strategy of Conflict, Cambridge, MA: Harvard University Press. Schelling, T. C. 1978. Micromotives and Macrobehaviour, New York: W. Norton. 24

Taylor, M., 1976, Anarchy and Cooperation, London: John Wiley. Taylor, M. 1990, “Cooperation and Rationality: Notes on the Collective Action Problem and Its Solution”, in K. S. Cook & M. Levi, (eds.). Udéhn, L, 1993, “Twenty-five Years with The Logic of Collective Action, The Scandinavian Journal of Management, 239-261. Vanberg, V, 1992, “Institution, Institutional Change and Economic Performance: Book Review, Public Choice, 74, 379-382. Williamson, O. E., 1975, Markets and Hierarchies: Analysis and Antitrust Implications, New York: Free Press.

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