Olson’s Logic of Collective Action at fifty

The exploitation of the great by the small result is the basis for the literature on burden-sharing in international alliances (Olson and Zeckhauser 1966). I will not be discussing this literature in this paper. See Sandler and Hartley (2001) for a survey.

A major exception to this is the literature on rent seeking in groups in which two or more groups seek a rent. This literature is discussed in Sect. 2.4.

If a good is excludable, then there is a presumption that it can be provided privately. If it is excludable, but has some degree of nonrivalry, then it may be a club good, as in Buchanan (1965). Olson (1965, p. 14, footnote 21) and Ostrom (2003) both argue that nonexcludablilty is an essential aspect of the collective action problem, but that nonrivalry is not an essential aspect of the problem.

One weakness of the book is that the discussion shifts between continuous and discrete public goods without warning. This hurts the clarity of the exposition.

Some alternatives to the summation technology include best-shot and weakest link (Hirshleifer 1983). Cornes (1993) provides a model in which best shot, weakest link and summation are all special cases.

The modern literature on public goods derives from Lindahl (1967) and Samuelson (1954). In addition to the work of Chamberlin (1974) and McGuire (1974), which is discussed below, other key works contributing to the development of the standard model of public good provision include Sugden (1982), Warr (1983), Cornes and Sandler (1984, 1985), Bergstrom, Blume and Varian (1986) and Andreoni (1988). An extended analysis of public goods may be found in Cornes and Sandler (1996).

It should be noted, however, that the widening gap between the equilibrium level of provision and the optimal level of provision might not be observed for alternative aggregation technologies. See, for example, Sandler’s (1992, pp. 52–54) discussion of this relationship for the weakest link technology.

The marginal utility of income is the opportunity cost of contributing towards the public good. Assume for simplicity that group members are identical. The per-person contribution goes to 0 as group size increases, so that asymptotically all spending is on the private good. This sets the lower bound on the marginal utility of income and, in turn, determines the level of the public good’s provision as group size grows large.

An absence of income effects is associated with quasi-linear preferences or situations in which the contribution towards the public good affects profits. Examples of the latter would include a common-pool resource, such as a fishery (Sandler 1992, pp. 117–123), and tariff lobbying.

When two groups are included in the model, a natural interpretation is a political example wherein one group lobbies in favor of and one lobbies against a particular policy.

Esteban and Ray (2001, p. 663) cite a passage from Pareto that gives an example along the lines presented here.

Olson uses the example of firms in an industry attempting to raise the price of the good they produce by restricting supply. If the group contains all of an industry’s firms, then clearly each firm would like the group to be smaller. If the group comprises a set of firms colluding to reduce output, then (conditional on the size of the industry) each firm would like the group to be larger. In Olson’s discussion, the group is defined as the number of firms in the industry. For a recent treatment of this issue, see Van Essen (2013), who analyzes Cournot oligopoly from the perspective of the theory of public goods. He considers both firms that produce substitute goods and firms that produce perfect complements.

In footnote 61 on page 40, Olson argues that if the good is not a pure public good, but nevertheless is sufficiently non-rival, the group in question would welcome new members. As discussed later, however, even a small degree of rivalry can make a significant difference in the ability of a large group to provide itself with a public good.

This is true in the sense that the benefit received by each individual from the contribution is independent of how many others belong to the group, if the good is a pure public good. Also, it does no good to appeal to the idea that if many others are contributing, a single individual’s contribution would appear to make only a trivial difference and therefore will not be made. This presumes that many others are contributing and, if this is so, the group has, to some degree, overcome the free-rider problem. It is self-contradictory to argue that a single individual will not contribute because so many others already are contributing, and then conclude that the group will be unable to provide itself with any of the public good.

Olson does not use the term nonrival. Rather he states that the large group could provide the good if the cost of doing so did not change even as millions entered the group. If the cost of providing members a given amount of the good does not change when millions enter the group, the good must be nonrival.

Utility is assumed to be increasing in both arguments. It is also assumed that the marginal rate of substitution between x and g is finite when x is finite and g > 0.

Chamberlin (1974) uses reaction functions to show that rivalry can lead to a strong from of the group-size paradox. This occurs when the reaction function converges toward the origin, as group size grows large. He does not provide a measure of the degree of rivalry in his analysis, but the discussion above suggests that the reaction functions converge towards the origin for all β > 0. It will prove useful for later discussions in the paper to be able to use β as a measure of the degree of rivalry.

Pecorino (2009a) also shows that above some critical value of n, dg/dn < 0. Based on his simulations with a CES utility function, the critical value of n does not appear to be very large even for values of β close to 0.

For example, in the Grossman and Helpman (1994) model of tariff lobbying, when all sectors are politically organized, the outcome is free trade. .

They consider both Cobb-Douglas and quasi-linear utility functions.

Other recent work is also supportive of Olson. Konishi and Shinohara (2014) consider voluntary participation in a process that will provide a public good. They find that public good provision goes to 0 as group size grows large.

This might not be true if there are fairness concerns. If the five feel exploited by the non-contributors, then they might not be willing to reach the same agreement in the presence of other members of the group. Fairness concerns might be thought of as a way in which groups could at least partially overcome the free-rider problem if they lead individuals to contribute when they are otherwise predicted to free ride. As the example presented here suggests, however, this could cut the other way and lead to a failure to provide goods that might otherwise have been predicted to be provided. .

An exception is Pecorino (2009b), but the model in that paper is not relevant to the political application of the group-size paradox; also see Mondal (2013).

Kolmar and Wagener (2012) extend Morgan’s work by considering a more general class of contests of which the lottery is a special case.

A noncooperative outcome is always a possible equilibrium of the model regardless of the value of the discount parameter.

This contrasts with earlier work by Lambson (1984, 1987), who analyzes cooperation in a repeated game between oligopolists. He found that unless certain stringent conditions are met, cooperation would break-down, as the number of firms in the industry grows large. This occurs because the critical value of the discount parameter generally approaches 1 as the number of firms in the industry approaches infinity. Also see the discussion in Shapiro (1989). For more recent work on public good provision in a repeated game setting, see Haag and Lagunoff (2007) and Cheikbossian (2012).

Ostrom’s (1990, 1998) work suggests that repeated interactions are important if a group is to effectively manage a common-pool resource.

The work of Borcherding and Deacon (1972) and Bergstrom and Goodman (1973) indicates that many publically provided goods exhibit a high degree of rivalry consistent with values of β near 1.

Esteban and Ray also assume that an agent currently making a zero contribution (s _i  = 0) has a zero marginal cost of making a contribution.

Also see McGinty (2014), who shows that the free-rider problem in team production depends on the relationship between returns to scale and the substitution elasticity between effort levels of team members.

Even making a contribution online requires incurring some fixed costs of participation.

Pecorino and Temimi (2008) model rivalry by defining g = S/n ^β , as in our discussion here. This differs from the approach of Esteban and Ray (2001), and this difference plays a key role in the result they find. Also, while Esteban and Ray analyze a rent-seeking contest, Pecorino and Temimi apply the Esteban and Ray technology to a traditional public goods problem. However, Pecorino and Temimi show that their argument also applies to the rent-seeking contest analyzed Esteban and Ray.

Of the papers discussed so far, Esteban and Ray (2001) is an exception. In their model two groups compete for a rent.

If individual valuations of the rent are drawn from a distribution, larger groups will have an advantage. The larger the group, the larger is the expected value of highest valuation of the rent.

Other papers of note on the topic of rent seeking in groups include Cheikbossian (2008), Gradstein (1993), Baik and Lee (2007), Nitzan and Ueda (2009, 2011) and Kolmar and Rommeswinkel (2013).

Olson talks a fair bit about non-economic motives and social pressures that might lead someone to contribute to a public good (e.g., pp. 60–61). He argues that these motives are less likely to apply to political lobbying and that they are more likely to apply in a small group rather than in a large group. These motives thus serve as another source of advantage for small groups over large groups.

Stigler is referring to a situation in which the public good and private good are not technologically linked, as in the joint products model of Cornes and Sandler (1984).

An alternative approach is taken by Bagnoli and Watts (2003) who model consumers as experiencing a warm glow when they make purchases from byproduct firms.

See, among others, Teisl et al. (2002), Landry and Price (2007), Casadesus-Masanell et al. (2009), Elfenbein and McManus (2010) and Hiscox and Smyth (2011).

See Mayer (2002) for an analysis of the pricing problem faced by a byproduct firm when it acts as a monopolist.

See Okrent’s (2010) discussion of the success of the Anti-Saloon League in getting “dry” candidates elected even though the overall public sentiment in favor of Prohibition was not very strong.