do they owe us a living?

course they do

here's what i learned in school this year:

Why do we follow the rules?

"Rules govern all aspects of experience, what we are able to experience, and what not to experience, the operations we must and must not carry out, in order to arrive at a permitted picture of ourselves and others in the world. But a special situation exists if there is a rule against examining or questioning values: and beyond that, if there are rules against even being aware that such rules exist, including this last rule." R.D. Laing (1972)

The role of social norms and conventions has been a central area of study in sociology since the subject's beginnings, and in philosophy it goes back at least to David Hume (2000). The contribution of the game theory approach is more recent: the ground was laid by David Lewis in his Convention (1969), followed by Edna Ullman-Margalit's Emergence of Norms (1977). These game theory approaches can bring powerful analytic tools to work on old questions; but they also come with unhelpful baggage, carried over from the narrow use of rational choice theory associated with neoclassical economic theory. The essay begins by looking at some of the problems rational choice theory has faced in getting to grips with norms; it then moves to develop an alternative "context/heuristic" approach for looking at norms as decision rules within a framework of "procedural rationality".

norms and reasons

In a field where authors often reinvent the terminology as they go, one useful anchoring point is Max Weber's (2002) account of "conventions", equivalent to what theorists nowadays more usually call "social norms". Weber defined a convention as a "customary rule" supported by "sanctions" applied by a social group as a whole, distinguishing a custom from a "law" where sanctions are wielded by a "specialised staff". Many recent accounts still include the following key Weberian elements: a norm is, in some sense, a rule (we will discuss this point in much detail further on); norms are bound up with custom, tradition, habitual social practice; they are usually (if, at least for some writers, not necessarily) enforced with sanctions; some of the most forceful sanctions may be ones which are "internalised" or self-applied; norms are, for many writers, to be distinguished from formalised laws; and they carry some kind of "normative force" -- a perception of obligation, “oughtness”, or, perhaps, "rightness" or "legitimacy".

The first major work on social norms in the rational choice tradition is Ullman-Margalit's 1977 The Emergence of Norms. Adapting legal philosopher H.L.A. Hart's (1961) analysis of what he called "rules of obligations", Ullman-Margalit defined three characteristics for norms of obligation:

(i) "a significant social pressure for conformity to them and against deviation -- actual or potential -- from them";

(ii) "the belief by the people concerned in their indispensability for the proper functioning of society";

(iii) "expected clashes between their dictates on the one hand and personal desires on the other".

The first two characteristics are fully in step with sociological thinking about norms: we can relate condition (i) to Weber's "sanctions", and condition (ii) to his work on "legitimacy". But condition (iii) serves to highlight where sociological and rational choice theories typically part ways. In Weber's view people can be motivated by self-regarding desires and wishes, by altruistic desires, by emotions, by habits, by values, and more. Sometimes individuals will experience conflicts between different types of motivations; but it is not generally assumed that self-regarding wants stand in a particular relation of conflict with normative obligations.

On a broad interpretation, a rational choice explanation of a social action involves: an agent who performs the action; and reasons which explain the agent’s action. These reasons are the agent’s desires (or – preferences) and beliefs. Saying that an agent is rational here is to say two things: first, that she acts (as if) to achieve her preferences, given her beliefs; and, second, that her preferences form a coherent pattern specified by certain consistency requirements -- for example, Savage’s rationality axioms, though I won't go into the details here. Finally, explaining the actions of an agent within a broad framework of rationality does not need to imply anything about the cognitive states of agents: for example, whether or not they act consciously or deliberatively, or in what way (if any) their preferences and beliefs are “instantiated” in minds or brains.

"Broad" rational choice theory (RCT) thus says much about the "form" of agents' beliefs and desires, but is silent about their "content". On this line we can cite Geoffrey Brennan's suggestion that rational choice theory would be better thought of as a rational choice grammar (or – framework). As Brennan puts it: “the rational actor / rational choice approach is best interpreted expansively and better understood as a kind of grammar of argument than as a particular theory ... any particular application of rationality assumptions involves a specification of the content of utility functions that is not itself part of the theory ....” (2007: 112)

But in practice most rational choice theory does typically "narrow" in with specific assumptions, explicit or not, about the content of utility functions. Very commonly, given RCT's ties to economic theory, it is connected to a view of human behaviour as dominated by economic self-interest. Indeed, as Brennan puts it: “in some circles it seems to count as a professional accomplishment to show how phenomena most naturally explained by altruism (or commitment to norms) on the part of relevant agents can, with a measure of ingenuity, be explained as wealth-maximising.”

And so the recent engagement of rational choice theory with norms largely takes the form of a series of puzzles. Game theorists have been turning to this area to help "resolve" the apparent breakdowns of such narrowly self-regarding models, for example in situations where subjects are seen to act "fairly" against their economic self-interest.

the ultimatum game problem

One example much discussed in recent literature is the "ultimatum game" experiment. Two people divide a sum of money (say, $10) in the following way: first, the Proposer suggests a split of the money; then the Responder can either accept the offer or reject it. If she accepts, the money is divided as proposed; if she rejects, neither player receives anything. Under standard game theory assumptions, and if we assume that both players value only money, a rational Proposer will offer the minimum amount (say, one cent) to the Responder; and a rational Responder will accept, as anything is better than nothing. In reality, players in experiments from Slovenia to Tokyo do anything but this. The most common offer is a roughly equal split; and responders commonly "punish" low offers with refusal.

Most commentators conclude that the players, rather than pursuing economic self-interest, are instead following norms of "fair division". In principle, this should not be a problem for a broad rational choice theory. As Brian Skyrms (1996: 28) makes the point: “we have a clear violation of the rational choice paradigm here only on the assumption that, for these subjects, utility equals income. There is no principled reason why norms of fairness cannot be reflected in their utilities in such a way as to make their actions consistent with the theory of rational choice.”

More generally, a challenge for any theory of human action is how to explain not just the regularity but the diversity of social behaviour: as Dan Hausman (2007: 56) puts it, to help us understand “why people may be cut-throats at work, devoted parents at home, liberals at the voting booth, racists at the club, public spirited one moment, pious at another, principled before lunch, and utterly selfish afterwards.” There are some situations where some people pursue material self-interest above all, and RCT models have (arguably) done well in economics when confined to "market" interactions. But what if we recognise "the market" as just one limited sphere of social life which operates on quite specific rules? Can rational choice approaches work in non-market contexts, if broadened?

There are maybe two possible approaches open to broad rational choice theorists. The first, which we might read in Philip Pettit (1990), is to stick to the idea that agents have just one coherent set of preferences (utility function) which applies in all contexts, but make it one which encompasses a richer, more realistic, range of motivations and desires. This approach is still reductionist: it seeks to reduce or relate apparently conflicting "surface" motivations to an underlying basic ordering that holds throughout all the different situations in which individuals act. But it recognises that economic reductionism boils away too much. Thus, e.g., Pettit citing John Harsanyi (1969) proposes not one but "two dominant interests: economic gain, and social acceptance." The problem for this approach is to leave enough motivational variety to explain behavioural diversity; but not so much that the explanatory power of a simplifying theory is diluted away.

Alternatively, one might stay within the "grammar of rationality" but abandon the idea of a single preference set for an approach in which agents have a range of different, possibly conflicting, preferences operating in different contexts. This is the approach taken by Cristina Bicchieri (2006), and which we will develop further into this essay. Then, if rational choice explanation is to remain explanatory, the problem becomes to explain how or why these different preference sets come to obtain in given contexts.

regularities, rules, and reasons

Ullman-Margalit's book on norms followed a trail blazed by David Lewis' (1967) work on convention.¹ Lewis starts by looking at coordination problems. In Lewis' game theory approach, a coordination problem is an interaction where there are multiple combinations of actions which are proper coordination equilibria; and where "coincidence of interest predominates". Roughly speaking, the players are relatively unconcerned as to which of the coordination equilibria they arrive at, so long as they arrive at one or them. Thus, for example, while I may have some personal preference for driving on the left or on the right side of the road, what really matters to me is that everyone else drives on the same side as I do, whichever it may be.

Thomas Schelling (1960) had studied coordination problems experimentally and argued that, even for novel problems where players cannot communicate, players manage to coordinate on an equilibrium by taking advantage of "salient" features which mark out that combination of actions as somehow unique -- a "focal point". Following this lead, Lewis notes that one important type of salient feature is the existence of a precedent: if we have seen a certain coordination problem solved a certain way in the past, and a relevantly similar problem then occurs, we can coordinate by following the precedent.

This is then the root of Lewis' explanation² of the origins of the social regularities he calls conventions: groups are often faced by recurring coordination problems; it doesn't matter how a particular coordination equilibrium is settled on in the first instance, but once it is chosen it quickly becomes established as a "regularity"; the next time the situation occurs, we will turn to that action as "salient", and we expect that others in the group will do the same. "Once the process gets started we have a metastable self-perpetuating system of preferences, expectations, and actions capable of persisting indefinitely."

A key feature to note is that, as "coincidence of interest" already holds in a coordination equilibrium, there is no need to introduce any new incentives to motivate agents to follow a convention. If we suppose that the players start with certain personal preferences modelled by the coordination game, these preferences can stay fixed throughout the analysis. In a fuller analysis, we may see that new preferences grow up around a convention: e.g., it may (in a Weberian account) acquire the status of "tradition", and gain some "normativity" (Lewis argues that conventions are also norms). But these extra motivations are supplementary, not necessary.

Lewis' conventions are regularities: recurring actions which agents take in relevantly similar situations. Lewis also goes on to claim that they (or at least many of them) are rules. While, as Lewis notes, the word "rule" picks out "an especially messy cluster concept", here I will use it in the following sense: in a particular situation S, a rule R specifies a particular action (or a restricted set of actions) for actors to take. To say that actors "follow" or "conform to" the rule in this situation means that they perform the specified action. A rule in this sense is a purely descriptive term which says nothing about normativity -- about whether, and if so why, actors should, or believe they should, follow any rule.³

A rule can feature in a causal explanation of an observed regularity. We see agents acting in a certain regular pattern not just because they happen, for whatever reasons, to choose actions which fit the pattern -- but because they are choosing in accordance with the rule. We may then go on to ask: why do they choose following the rule? This is how we can schematise a central line in rational choice analysis of social regularities: first, identify a regularity; second, explain that regularity as a result of agents following a rule; third, identify the reasons why agents follow the rule.

rules and reasons

But here we get to a second kind of puzzle for rational choice theory. This is what Edward McClennen (2004: 224) calls the "fundamental dilemma" faced by all rational choice accounts of rule-following: "either the rule gives the wrong result, in which case it is irrational to follow it; or it gives the right result, in which case guidance by the rule is irrelevant."

Lewis' conventions appear to escape the dilemma: they deliver the best result, and are also relevant in identifying it. This is because the convention-rule is essentially just a tool for achieving the right result: that is, it is what Rawls (1955) would call a "rule of thumb", a heuristic instrument for arriving at a good decision. It plays no part in determining the "rightness" of the right result, which is defined by preferences which exist independently of the rule. So we can say, in the case of conventions: the reason agents follow the rule is because doing so best realises their pre-existing preferences -- it "gives the right result".

The situation is more difficult for norms. In particular, the norms that rational choice theorists have been most interested in are those which Ullman-Margalit identifies as "PD norms", Lewis as "social contracts", and for which other writers such as Bicchieri reserve the term "social norms" altogether. In the standard game theory analysis, while the role of conventions is to solve coordination problems, these norms are rules which enable groups to solve collective action problems.⁴ A collective action problem exists where there is an available combination of actions for the group which is collectively beneficial, but which rational individuals following their personal preferences do not take.⁵ Public goods problems (where individual freeriding leads to failure to provide a collectively desired public good) and commons problems (where individuals exhaust a common resource) are the classic cases. A relevant norm, here, is a rule that tells agents to take the collectively beneficial action.

Of course, for a norm to "solve" a collective action problem, there have to be reasons for agents to follow it. The basic framework of game theory approaches to norms is one in which norms "emerge" to solve problems: this provides a simple (or simplistic) schema for thinking about the role of norms and conditions in which they might develop. We can think here of two social situations: an initial state (a "state of nature") in which there is no norm in place, and a collective action problem exists; and a subsequent state after the norm has emerged and taken hold, in which the collective action problem is solved.

By way of example, we can skip through Hume's story of the origin of property norms, the venerated ancestor of game theory work on rules. "Emergence" kicks off when "I observe that it will be in my interest to leave another in the possession of his goods, provided he will act in the same manner with regard to me" (Treatise 3.2.2). If this were merely a coordination problem, mutually noticing common interest and a salient property convention would be enough. But in a "numerous society" "we may frequently lose sight of that interest that we have, in maintaining order, and may follow a lesser and more present interest": i.e., we face a collective action problem. Thus while "self-interest is the original motive to the establishment of justice" it only takes us the first step. Next we learn to associate principles of justice such as property norms with moral approval and disapproval; and so justice is created as an "artificial virtue". While Hume believes that this is a "natural" and "necessary" process, it is helped along by "private education and instruction" as well as by "the artifice of politicians, who, in order to govern men more easily and preserve peace in human society, have endeavour'd to produce an esteem for justice and an abhorrence of injustice." And once the norm has become "firmly established", it is bolstered by social sanctions in terms of "merits and demerits" to our reputation. Finally, formal property laws add legal sanctions backed by state power.

Without digging deeper into Hume's story, or other authors' versions, I will just use it to note a basic distinction between some types of reasons for following norms:

(1) where a norm is also a convention, it also fits the Lewisian analysis above: once it is noted as salient, agents may follow it because it achieves the "right result" given their existing preferences.

(2) if sanctions are put in place to uphold the norm, agents may follow it because they prefer to avoid those sanctions. Again, here the introduction of a norm need not involve changes to agents' preferences (e.g., suppose agents start out with purely economic preferences, and monetary sanctions are introduced).

(3) on the other hand, following the rule may become a good in itself: agents acquire a preference for following the rule. For example, they come to see it as "right" or "virtuous" to do so; or maybe they simply desire to follow it, without this preference being articulated in the language of morals. Unlike the other types, here the "emergence" of the norm is accompanied by a change in preferences.

I am not going to say any more in this essay about the analysis of norms in terms of collective action problems; or about the actual processes in which norms, and reasons for norm-following, develop. Here I just want to note one more formal point: all of the above types concern reasons for following a rule, rather than just reasons which independently lead agents to act in line with an observable regularity. In the first two cases, following the rule achieves a "right result" which can be defined without reference to the rule: but this does not make rule-following irrelevant. In the first case, I follow the rule in order to co-ordinate my behaviour with others; in the second, in order to avoid sanctions defined in reference to the rule. In both cases the regularity of my behaviour is not coincidental: I know that the rule exists, and choose to follow it.

The third type is different. Here the "right result" cannot be defined without reference to the rule: the result is right, at least in part, just because it results from the rule. Here we have indeed broken with what McClennen characterises as "a theory of rational deliberation in which personal, moral, social or legal rules are regarded as having an instrumental value"; we are saying that sometimes there can be a "special value" attached "to rule-following as such" (or rather, to the following of certain rules). We might want to say that it is in this case that a norm is truly normative.

substance and process

Herbert Simon (1986: 369) distinguishes two kinds of rational choice theories. On the one hand, he characterises the orthodox theory we have been looking at up until now as a theory of "substantive rationality": the idea is that an agent's choice is rational if she chooses the right result given her preferences; how she goes about making that decision is irrelevant, with decision-making procedures kept within a "black box". Simon himself proposes an alternative "procedural rationality" approach in which a rational agent "goes about making his or her decisions in a way that is procedurally reasonable in the light of the available knowledge and means of computation". What counts here for attributing rational is not the "substance" of decisions but the procedures used to arrive at them.

Specifically, the procedural approach I will explore here follows that of Gigerenzer, Todd et al. (1999), whose suggest that human individuals use an assortment of heuristic principles to choose actions. As with other forms of "bounded rationality", this approach incorporates the idea that human decision-making always faces constraints on time and other resources. Gigerenzer and Todd take on Simon's idea that decision-making is bounded in two ways: "the limitations of the human mind, and the structure of the environment in which the mind operates." The mind's limitation means that "optimal strategies are unknown or unknowable" -- there is no approaching, or recognising, a "right answer" -- and thus decision makers must always use "approximate methods". Secondly, Gigerenzer and Todd introduce a notion of "ecological rationality" to explore the interaction of mind with environment.

On the first point, Gigerenzer and Todd model heuristic principles in three stages: principles for searching for information to make a decision; principles for when to stop the search (given that searching is a costly activity); and principles for using the search results as input into a decision. Through the lens of a procedural rationality approach, orthodox RCT can be viewed as a model in which there are no constraints on search: an agent has omniscient power to identify the choice that maximises her utility function. (More exactly, if we accept the "black box" principle, orthodox RCT is a model in which agents can be understood as acting as if they had unlimited decision-making powers).

Taking bounded rationality to its fullest extent, a heuristics approach drops any idea of optimisation: there is no way of assessing a "best" solution to the decision problem faced at any of these stages. Instead, the idea of ecological rationality is meant to provide the criteria for "reasonableness" of a decision procedure. The "measure of success" of a heuristic is how well it serves the agent in a particular environment: "A heuristic is ecologically rational to the degree that it is adapted to the structure of an environment." (13).

Although this is perhaps a weak point for the model as it stands: if we are to have a standard of rationality, we still need some success criteria which cannot be read off environmental conditions -- what does it mean for an agent to succeed in an environment? Though I will leave this point alone for now: my interest is not so much in characterising the rationality (or otherwise) of decision-making than in pursuing the idea that people act by following procedures which they learn, pick up, adapt and develop in the course of repeated interactions.

Cristina Bicchieri applies such a heuristics approach to the analysis of social norms. Individuals use contextual stimuli to categorise a new situation, drawing on an existing "memory store" of past encounters. Categorisation activates a cognitive schema of "beliefs, expectations, and behavioural rules" associated with the context. Bicchieri proposes that these "schemata" often take the form of scripts in which we cast ourselves and others in set roles. The roles in which we cast others come with associated behavioural and normative expectations.⁶ The roles in which we cast ourselves come also with context-dependent preferences: including preferences to follow particular norms or other behavioural rule in certain contexts.

However, Bicchieri dilutes the procedural rationality approach in a dual theory of "deliberational" and "heuristic" decision-making. She identifies norms as "default rules" within heuristic decision-making processes; but she maintains that there is also a non-heuristic way in which people make decisions through a conscious "process of rational deliberation". Bicchieri thus maintains ties with standard RCT, arguing that expected utility maximisation approximates, albeit "somewhat ideally" (p4), this deliberational form of decision-making which we apply in certain types of decision situations.

A more fully "procedural" approach would make no such clear cut distinction between deliberational and heuristic decision "modes". Rather, we could think of a spectrum of more or less simple or intricate, quick or lengthy, rough or "careful" decision procedures. (Nor, I think, is conscious awareness a key distinguishing feature.) On this view, deliberational reasoning processes could be seen as schedules or programmes of linked or nested heuristics. For example, "take time to consider a range of options, and weigh up the pros and cons" is a heuristic decision principle.

Below I will explore such a "context/heuristic approach", and its differences from orthodox RCT, in more depth. First, though, we can get a better feel for this approach by applying it to the puzzle we started with.

the ultimatum game revisited

The ultimatum game becomes puzzling because there is a confusion between two different "scripts" -- though we may want to ask just who is getting confused. We can see narrow (economic) rational choice theory as a theory that explains, successfully or not, the decision-making of human beings when they are conforming to a particular script which mandates decision procedures aiming to maximise personal economic gain. We could call this a "market script". But in reality most people (even, it seems, economics students) do not categorise the ultimatum game situation as a market interaction. Many people seem to class it as the type of context that requires them to follow what we might call a "fair division" script; though the scripts people play also show some interesting cultural differences. For example, according to Joseph Henrich (2000), some indigenous Mapuche Proposers make big (more than 50%) offers, which are rejected by Mapuche Responders: they seem to be playing a script familiar from the kind of gift exchanges famously studied by Marcel Mauss (2002).

Some theorists might want to claim that ultimatum game players are acting irrationally. This might be understood as a case of misreading an unfamiliar situation: fair division scripts and Maussian gift exchange scripts are appropriate for situations where players can expect recurring, so potentially reciprocal, interactions; the ultimatum game presents some of the same cues as these familiar situations, and therefore players categorise it wrongly. Is it possible to frame such a claim in a contextualised approach? To do so, we would need a standard for assessing the correct categorisation of contexts. For example, the irrationality claim might come down to the view that players have a "real" basic preference for economic gain which underlies their behaviour in non-market situations.

I think this kind of reductionism is grounded more in ideology than evidence; but even supposing it were right, it does not sustain the idea of irrationality. If the ultimatum game results are systematic human error, that means that actual decision-making procedures are second-bests which people fall back on because, as cognitively limited creatures, we are unable to directly optimise our "basic" preferences. But then rationality becomes an impossible, and so unexplanatory, standard: or else we should move to an idea of bounded rationality. We might still want to pursue the interesting question: how far have some deep "self-aggrandizing" instincts shaped the way in which human decision-making scripts have developed, in different cultures? But this is a question of (evolutionary) history not rationality.

a context/heuristic approach

We looked above at two puzzles faced by rational choice theory when it engages with norms; and began to develop an alternative context/heuristic approach. However neither puzzle necessitates moving away from a broad enough version of orthodox RCT. There are two specific areas where the theory needs to become broad. First, it needs to allow contextualised preferences (or, alternatively, find a "richer" reductionism of basic preferences -- though I am not investigating that route here). Second, it needs to allow preferences for following rules. Neither of these seems, in principle, closed to orthodox RCT; and I am not here attempting a conclusive argument that a context/heuristic approach does better, only a suggestive outline of an alternative. Ultimately the question is likely to be: by accommodating these changes, so diluting the simplicity of standard RCT, does the theory lose much of its explanatory power and become just a (perhaps trivial) way of reading human behaviour as purposive?

A key feature of orthodox RCT here is that the fundamental level of explanations -- of giving reasons -- is always in terms of agents' preferences (and beliefs). We may explain regularities by pointing to rules, but we then have to show the reasons why agents follow those rules. The context/heuristic approach moves away from this. An explanation involves identifying and characterising the decision-making script or schema which operates in a given situation; decision rules, beliefs and desires can all be seem as component parts of the script, on the same level.

Suppose, for example, that an agent makes a decision following a normative decision rule. We might say that she believed or felt it to be right to follow the rule. These locutions point to the normative character of the rule she is following, but they do not uncover some more "fundamental" reason for following the norm in terms of preferences. We can say: she followed the rule because she had a preference for following this rule in that context; but this does not add to the explanation.

We can put a bit more shading on our sketch of the decision-making process. We can say that any script involves both beliefs (including expectations about others' -- and one's own -- behaviour) and desires; and decision rules. We might say: beliefs and desires give the background or depth of character to a role, and can be called on in the decision-making process; heuristic decision rules are the immediate prompts which steer the process.

We can start by thinking about an initial heuristic that kicks off the decision process; as the process continues, and further informational cues are received, new rules are triggered. For example, a heuristic may mandate a certain search procedure. This may involve searching information coming from the external environment; but it could also involve searching the "internal background" of the agent's own beliefs and desires: for example, weighing up one's preferences, comparing environmental information with expectations, etc. That is: a search can also involve "deliberational" procedures. On the other hand, we might come to what Bicchieri calls a "default rule". This is a rule which stops the search and commands an immediate action. A default rule can be triggered by a cue (from external or internal information) at the very beginning of the process, or at any later stage.

In fact there is no particular reason to associate norms particularly strongly with default rules. Normativity is by no means confined to more hasty less "deliberational" decision-making: we often reason, reflect, weigh up, ponder and anguish at length upon normative demands. And of course there are plenty of default rules that are not norms: e.g., urgent fight or flight responses; or, say, mechanical "buy/sell"calls of an experienced market trader. A norm might be a default rule or a factor in deliberation.

It could be interesting to look more at how (narrow) RCT developed as a theory in which normative behaviour is considered abnormal; but in fact is self-interested behaviour any less normative than fairness? We can find plenty of "oughtness" claims and sanctioning behaviour in market interactions: sharp dealers get approval and status rewards; the gullible get laughed at; risk-lovers are alternately admired and shunned, etc. Market scripts, like other scripts, mix deliberation, default rules, and rules with greater or lesser normative force.

Of course we may well want to explain how the actor came to operate with the norms, rules, schemas that she does. Just as in a preference-based account we may want to know how she came to have the preferences she does. These are the really interesting questions: but the answers go beyond what rational choice theory, orthodox or otherwise, can offer.

Bicchieri, Cristina. 2006. The Grammar of Society (Cambridge: Cambridge University Press)

Brennan, Geoffrey. 2007. "The Grammar of Rationality", in Rationality and Commitment, ed. by Fabienne Peter and Hans Bernhard Schmidt (Oxford: Oxford University Press)

Gigerenzer, Gerd, Peter M. Todd, and the ABC Research Group. 1999. Simple Heuristics That Make Us Smart (Oxford, Oxford University Press)

Harsanyi, John. 1969. "Rational Choice Models of Behaviour versus Functionalist and Conformist Theories", World Politics, 22: 513-38

Hausman, David. 2007. "Sympathy, Commitment and Preference", in Rationality and Commitment, ed. by Fabienne Peter and Hans Bernhard Schmidt (Oxford: Oxford University Press)

Henrich, Joseph. 2000. “Does culture matter in economic behaviour? Ultimatum game bargaining amongst the Machiguenga”, Journal of Experimental Social Psychology, 37: 316-324.

Hume, David. 2000. A Treatise of Human Nature, ed. by David Fate Norton and Mary J. Norton (Oxford: Clarendon Press)

Lewis, David. 1969. Convention. A Philosophical Study (Cambridge, MA: Harvard University Press)

Laing, Ronald David. 1972. "Rules and Metarules", in The Politics of the Family and Other Essays (New York: Vintage Books)

Mauss, Marcel. 2002 (1950). The Gift, trans. by W.D. Halls (London: Routledge Classics).

McClennen, Edward F. 2004. “The Rationality of Being Guided by Rules”, in The Oxford Handbook of Rationality (Oxford: Oxford University Press)

Parsons, Talcott. 1951. The Social System (London: Routledge & Kegan Paul)

Pettit, Philip. 2002. "Virtus Normativa: Rational Choice Perspectives", in Rules, Reasons, and Norms (Oxford: Oxford University Press)

Simon, Herbert A. 1986. "Rationality in Psychology and Economics", in Models of Bounded Rationality, volume 3 (Boston, MA: Massachusetts Institute of Technology Press)

Skyrms, Brian. 1996. The Evolution of the Social Contract (Cambridge: Cambridge University Press)

Weber, Max. 2002. Basic Concepts in Sociology, trans. by H.P. Secher (New York: Citadel Press)

Ullmann-Margalit, Edna. 1977. The Emergence of Norms (Oxford: Clarendon Press)

1Here I will follow the majority practice now and distinguish conventions (in Lewis' sense -- not Weber's) from social norms. Both are sub-classes of what in general (for both Weber and Lewis) are called "social regularities" -- or "social rules".

2I am reading Lewis' account here as an explanation of how actual conventions are generated. However this is not the way Lewis (mostly) presents his work. In the introduction he explains that his task, motivated originally by issues in the philosophy of language, is one of conceptual analysis rather than causal explanation of "convention". This approach leads to him actually defining -- rather than explaining -- conventions in terms of coordination problems. It may at least in part be Lewis' influence that leads to a tendency for subsequent game theorists working in this area to stipulatively define the regularities they are looking at (norms, conventions, etc.) in terms of game models.

3A rule in this basic sense doesn't carry the weight of some rules under some classifications: for example Rawls (1955) "rules of practices", Searle's (1995) "constitutive rules", or indeed Hart's "rules of obligation".

4It is usual in the game theory literature to define norms in terms of particular game structures: e.g., for Lewis, Ullman-Margalit, and many others, the prisoners' dilemma; for Bicchieri the broader class of "mixed motive games". I am trying here to avoid begging questions that might be raised by bringing game theory representations into definitions.

5I leave open how to define "collectively beneficial": one interpretation might be "Pareto optimal", but we don't need to commit to that.

6Here Bicchieri's rational choice theory comes close to Talcott Parsons' doctrine of "role-expectations" and values (1951) in the sociological tradition.