Ullmann-Margalit’s Game-Theoretic Account of Social Norms


Game theory is now a fairly standard tool in the study of social norms and institutions. Among the pioneering game-theoretic accounts of norms figures Edna Ullmann-Margalit’s book The Emergence of Norms. Originally published in 1977, it has been recently reedited by Oxford University Press. This offers an opportunity to rediscover an interesting study which anticipates several developments in the analysis of social norms.

The title of the book seems to indicate that Ullmann-Margalit is interested in the way norms have appeared and evolved, i.e. what today we would rather call the evolution of norms. Her approach is “structural” rather than “historical”: types of norms and their emergence are related to their functions in different kinds of strategic interactions which differ in their properties. This gives Ulmann-Margalit’s account a strong functionalist stance which she explicitly recognizes: the existence of norms is explained by their functions. I will return at the end of this post on this point but it can be already noted that this makes the title of the book slightly misleading. Ullmann-Margalit’s account is far more convincing if viewed as an account of the way norms work (i.e. determine individual’s behaviors) than an account of the mechanisms by which norms evolve.

The book distinguishes between three kinds of strategic interactions with specific features which give rise to three kinds of social norms: prisoner’s dilemma (PD) norms, coordination norms and norms of partiality. Ullmann-Margalit’s analysis of coordination norms partially builds on Schelling’s and Lewis’ game-theoretic accounts. Coordination norms are defined as solutions to coordination problems, i.e. interactions where the players’ interests are perfectly aligned and where at least two profiles of actions fully satisfy them. Like Schelling and Lewis, she points out that salience is the most general way through which a recurrent coordination problem is solved. Once a solution has been singled out by the participants, the repetition of the interactions gives rise to a social norm. For novel coordination problems however, or at least some of them, she argues that it is most likely that the solution comes from a norm dictated and enforced by some external authority. Moreover, contrary to Schelling and Lewis, Ullmann-Margalit suggests that coordination norms are “real” norms and not simply conventions. That means that coordination norms have a normative force: social pressure and/or moral obligation rather than simply convergent expectations contribute to explain why people conform to some specific norm.

As their name suggests, PD norms are solutions to prisoner’s dilemma type of interactions. Basically, PD norms help to foster cooperation in strategic interactions where defection is the dominant strategy. Ullmann-Margalit’s account can be seen as one of the numerous attempts made by social scientists and philosophers to show that it can be rational to cooperate in a PD. However, contrary to other philosophers (for instance, David Gauthier’s theory of constrained maximization), Ullmann-Margalit does not attempt to argue that playing dominated strategies is rational. Rather, she suggests that PD norms foster cooperation on the basis of several “payoff-transforming” mechanisms depending on external sanctions and/or moral commitments. The payoff-matrix then no longer corresponds to a PD but to a game where mutual cooperation is (possibly the only) an equilibrium. On this point, there is some similarity between Ullmann-Margalit’s account and the theory of social norms developed recently by Christina Bicchieri. Bicchieri’s suggests that social norms rely on a conditional preference for conformity which in some cases a PD into a coordination game.

Ullmann-Margalit’s study of the third kind of norms – norms of partiality, is the most original and intriguing. Norms of partiality stabilize situations where some parties are favored and other disfavored. More exactly, they legitimize a status quo of inequality. The analysis builds on an interesting (though not totally convincing) distinction between equilibrium and strategic stability. The former corresponds to the standard Nash equilibrium solution concept and follows from the fact that each player is rationally searching for improving his absolute position. An equilibrium is simply a state of affairs where no player can improve his absolute position by changing his behavior. Strategic stability matters as soon as we assume that the players are also concerned by their relative position (assuming of course that this concern is not already incorporated into the payoff matrix). In a situation of inequality, a disfavored party may seek to reduce the inequality level even if this leads to a worsening of her absolute position. The threat of such a move becomes credible once it is realized that in some cases, the favored party’s rational response to this move leads to an improvement in both the disfavored party’s relative and absolute position. In this case, a state of affairs may be an equilibrium but still be strategically unstable: one may want to change his behavior even though it worsens temporarily his absolute position. According to Ullmann-Margalit, norms of partiality’s function is to stabilize state of affairs which are strategically unstable through they correspond to a game-theoretic equilibrium. The matrix below corresponds to the paradigmatic illustration:


Assume that R1-C1 is the status quo. Though it is an equilibrium, it is not strategically stable since the column player may try to convince the row player that it will play C2 to improve his relative position. Then, row player’s best response will be to switch to R2, thus leading to R2-C2 with a reversal of fortune for the two parties. Norms of partiality prevent such kinds of strategic move by generating some kind of normatively binding constraint.

Though ingenious, this functional account of the role of norms in stabilizing situations of inequality is not totally convincing because of a lack of concrete examples (which the author herself points out). As noted by Cass Sunstein in his review of Ullmann Margalit’s book, the examples cited in the latter (property rights, rights inheritance) are not enforced by norms but rather by law (at least in developed countries). In other cases, obvious situations of inequality (for instance between men and women regarding wages) seem to lack any broad normative or moral support but still endure thanks to other social mechanisms. It is not clear therefore whether norms of partiality really have an empirical counterpart.

This leads me to the last point of this post. As I briefly note above, Ullmann-Margalit’s study is not really an account of the emergence of norms. Such an account would propose one or several causal mechanisms for the creation and the evolution of norms. Since the 1980’s, evolutionary game-theoretic accounts of norms have been developed. They remain largely unconvincing however because the emergence problem is fundamentally an empirical one. At the very first line of her book, Ullmann-Margalit states clearly that her essay belongs to “speculative sociology” (nowadays, we would rather call it “social ontology”). She claims that she is intending to propose a “rational reconstruction” of norms rather than an historical account. By this, she means that her goal is to provide a list of reasons or features that may explain why norms exist. As noted above, her approach is functionalist because she tries to relate the existence of norms to the functions they fulfill. But as argued by Jon Elster, functional explanations are no explanation at all; only causal explanations are. The title thus wrongly suggests that the book provides a causal explanation (either theoretical or historical) of the emergence of norms, which is not the case. However, Ullmann-Margalit’s work is highly valuable if it is taken to give an account of the way norms are working, i.e. how they actually affect people’s behavior. Because she insists on the functional stance of her approach, Ullmann-Margalit does not make this point clearly enough. However, for each kind of norms, one or several mechanisms are suggested to explain why people cooperate or succeed in coordinating: commitment (strategic or moral), framing effects, social pressure, and so on are all hinted as explanations for the working of norms. From this point of view, The Emergence of Norms anticipates many contemporary developments in social ontology, game theory and experimental economics and for this reason remains a valuable read.