Social norms heavily influence human behaviour. In particular, social norms can play a key role when individuals make economic decisions. In some cases, this is rather evident. For example, think about the norms surrounding the phenomenon of gift making: the norm of reciprocity will influence whom should an individual buy gifts for; various cultural norms will influence the kind and value of each particular gift. Apart from trivial settings such as that of gift-making, social norms have influence on more economically relevant phenomena, such as contracting terms of employment, saving and consumption habits, retirement age [Young, 2003], decisions regarding education, investment strategies, and many others.
The aim of this dissertation is to show how stochastic evolutionary game theory (SEGT) can be used to model the evolution of social norms within a given society, and to assess the explanatory merits of such theoretical frameworks. Social norms are, ontologically speaking, a particular kind of belief, shared by humans living in societies, which contribute to cause behaviour. Therefore, the term ‘evolution' is to be intended here as in cultural evolution, i.e. change of belief over time [Alexander 2007, p. vii]. The models provided by SEGT can be used to refine orthodox economics models that aim to explain and predict the behaviour of (boundedly) rational agents, and make such models more consistent with the empirical findings. To better show this point, I will concentrate on a particular area as a case study, where the predictions of orthodox economic theory and the empirical evidence greatly differ: the question of tax compliance.
In Section 2, I will outline some of the general issues that orthodox economic faces as it models agents as perfectly rational utility maximisers. In particular, after defining them, I will argue that social norms, which are ignored in most economic models, can play a key causal role in the decision making process of human beings. More precisely, social norms become particularly important when the players of the ‘social games' are agents with limited rationality. More precisely, social norms seem to work in many cases as heuristics, rules of thumb to follow whenever what is at stake and/or the structure of the game is not clear.
Following this, in Section 3, I will present a general evolutionary model of norm dynamics in a population, using the formal and theoretical machinery provided by SEGT. In this section I will closely follow Young  for the formal representation. In describing the model I will assess the kind of an explanation that such framework offers, and argue that, as a type of explanation, it is superior to the ones provided by traditional orthodox economic theory for two main reasons: first, because it acknowledges the evidence that individuals do not always act as perfect rationality would require and hence provides a theory which can explain behaviour in a context of bounded rationality; second, because it recognises that the norms, culture and more generally the set of beliefs shared by the individuals in a society are constantly changing, and therefore we require a theory capable of explaining and describing such dynamics. In this respect SEGT is a step forward from classic game theory which is an inherently static theory.
In Section 4, I will first present the issues that the orthodox theory (which is mainly based on the highly influential paper published by Allingham and Sandmo ) faces in the topic of Tax Compliance. I will then show how the models discussed in the previous section can be applied in this context and used to refine our explanations and predictions, making them more consistent with the empirical findings. Moreover, I will argue that such evolutionary models can help explain why, within geographical areas with the same taxation law and similar demographic characteristics, one can observe very diverse levels of tax compliance. Finally, I will discuss the practical and theoretical benefits of employing these new models and theories.
Section 5 briefly concludes.
1. Rational agents and social norms.
In order to explain and predict economic behaviour, orthodox economic theory models individuals as agents that act according to the rational choice principle, i.e. as maximisers of their expected utility. In this section I will concentrate on the issues that arise when RCT is intended as a descriptive theory of real agents rather than just a normative theory which aims to answer the question of what ideal rational individuals should do in decision problems.
2.1. Some philosophical issues of standard Rational Choice explanations.
RCT falls under the broader class of rational choice explanations, which are themselves a subset of intentional explanations. The analytical structure of the latter is as follows [Elster 1988, p51]: an individual intentionally chooses to act, i.e. behaves in a certain way, whenever a) given her beliefs about the state of the world, such behaviour is the best way to realise her desires; b) beliefs and desires are the causes of behaviour and c) they are causes qua reasons, in order to avoid those cases in which behaviour, while being caused by beliefs and desires, is not actually realised following the agent decision to act in such way, but for some other contingent reason (a famous example of such an occurrence is provided by Davidson [1979, p.79]). Rationality then additionally requires the set of beliefs and the set of desires to be internally consistent, meaning that there must be a possible world in which all beliefs and desires are respectively true and satisfied.
This theoretical framework is better understood with an example. Imagine that Bob has the day off from work, and wants to relax. Therefore, he faces the following simple decision problem: either go have a stroll in the park, or watch a brand new TV Show on Netflix, at home. “Wanting to relax” is the most relevant element in Bob's set of desires. In the set there will also be all sorts of other desires, such as, for instance, “not wanting to sweat”, “wanting to avoid spending too much money”, “being back home for dinner”, etc. The set of belief is composed by propositions about the various features of the world that Bob deems to be true: for example, what will the weather be like, who stars in the TV Show, how long would it take to do either activity, but also every other belief, such as for instance how likely it is that a meteor shower will hit the park, what will he earn in the next ten years, what is the result of , whether Liverpool will win the premier league this year, etc. Some of these beliefs will matter more in the decision, some less, and most arguably not at all. Given this situation, if Bob decides to watch the TV Show, then a rational explanation is that he did so because he believed it was the best way to realise his desire of relaxing, all things considered.
Now, many of the philosophical problems for rational explanations, and in particular RCT, are connected to the question of explaining how the set of beliefs is generated and what are its properties. The standard theory, which is mainly based on Bayesian theory (see Bradley  for a recent introduction on the topic), stipulates that beliefs are caused by the evidence available to the agent and must be the best beliefs possible given such evidence [Elster 1988, p55]. Moreover, using Ramsey's terminology , evidence causes beliefs in a way that the “degree” to which agents deem their beliefs to be true is a function of the available evidence. Second, according to the theory, agents are not only rational in the sense that they do what they deem best, but are also “maximally opinionated” and “logically omniscient” [Bradley 2016, p. xx], meaning respectively that they must have beliefs about every fact of every (actual or possible) world and that the cognitive process by which agents derive such beliefs from evidence and connect them to their desires has to be logically flawless, i.e. agents have to believe all logical truths, be “fully aware” [Bradley 2016, p. 339] of the consequences of their decisions, and must make no mistakes in the inferences made.
These requirements seem relatively understandable if RCT is intended as a normative theory which aims to establish what ideal rational agents should do in decision problems. Difficulties arise when RCT is used, as orthodox economics does, as a descriptive (and, therefore, also predictive) theory of actual agents' behaviour in economic contexts. Most states of the world are uncertain: the available evidence allows to form aleatory beliefs about the relevant facts to consider in any decision problem. Yet, uncertainty is easily dealt with in RCT by employing probability theory, which allows to precisely measure uncertainty by matching each event to a single real number which corresponds to the agent's degree of belief of the truth value of such event. Issues occur when the available evidence causes ambiguity, i.e. it provides the agent with only some of the information needed to ‘attach' probabilities to events (see for example the Ellsberg Paradox, [Ellsberg 1961]). In these cases, agents do not have a precise degree of belief that can be univocally matched to a real number, but only to an interval of real numbers. Even more problematic is the extreme case in which agents have absolutely no relevant information to determine the likelihood of events, i.e. they are in complete ignorance, and hence subjective probability theory cannot match their degrees of beliefs to any numerical set.
Turning back to our example, in order to properly evaluate all relevant aspects in his decision problem, Bob has to make an educated guess about the possible weather conditions (uncertainty); he needs to form an opinion about whether he will like the TV Show or not: there are some actors he usually likes, but the director is terrible and the Show is new so there are no reliable reviews (ambiguity). Moreover, if he goes to the park he might meet someone that could eventually became his beloved partner for the rest of his life, which is something Bob really wants. Yet he has no idea of how likely such an event is (ignorance).
Another significant issue of applying RCT to economic models is related to an important subset of the set of beliefs: the one containing those beliefs regarding what will other agents do. In other words, people have expectations about how other individuals will behave, and they also have beliefs about what others expect them to do. In virtually all economic contexts, the outcome of a decision made by an agent will depend on what the other agents involved in the matter at hand will do. Game Theory has developed as a branch of RCT exactly to explain such interactions, yet it suffers the same problems discussed above, as the players of the games are the same ideal rational agents theorised by RCT.
Perhaps the most obvious objection to the homo oeconomicus model is that actual people never behave as perfectly rational agents (whether they should, is another interesting and complicated matter, which I will not address in this paper), as common sense but also many empirical studies and laboratory experiments suggest (see for example Tversky & Kahneman ; for a study relevant to the present discussion, see Zhang et al. ). In particular, these studies have shown that one of the main reason that could explain behaviour is social norm compliance. This important empirical finding is at the core of the homo sociologicus hypothesis, which sees individuals as agents that act according only to the norms, intended as behavioural rules, attached to the roles that they play in the society [Weale 1992].
The challenge is then to investigate whether homo oeconomicus and homo sociologicus can be brought together under a more general theory, based on rational choice explanations. In the next sections I will show how it is possible to model social norm compliance within a rational choice approach, by using the formal tools provided by stochastic evolutionary game theory. Before turning to the models, I will define more precisely the concept of ‘social norms' and explain why it is reasonable to hypothesise that they play a role in the decision making process of individuals, seen as boundedly rational agents, i.e. agents that are neither maximally opinionated nor logically omniscient.
2.2 Social Norms.
Despite the evidence that norms influence behaviour can be found in laboratory experiments as in field and historical data analysis, until recently orthodox economics has been quite reluctant in directly tackling the topic in a formal, analytic fashion. In fact, with few exceptions [Shelling 1960; Akerlof 1997; Sugden 1986], traditional economists have always considered norms as exogenous factors that may or may not occasionally distort the decision making process of rational agents. The disregard for social norms has many reasons. One lies in the methodology of mainstream economics, which by and large consists in two steps: first use the RCT apparatus to formally model the decision making process of the various representative microeconomic agents (consumers, firms, governments, banks, ecc.); secondly, derive the macroeconomic system by aggregating the micro-agents, as vectors in a mechanical physical system.
However, probably the main obstacle in the path of integrating social norms into the theoretical framework of rational choice explanations is probably that they are very complicated to define, both formally and informally. Often, the route taken by social scientists and philosophers is to connect the concept of social norms to other notions. To give some examples in the recent literature, Young [2003; (with Burke) 2011; 2015] defines them either as rules or patterns of behaviour to which individuals of a social group conform, or as “unwritten codes and informal understandings that define what we expect of other people and what they expect of us” [Young 2015, p. 360]. This last definition is similar to one of the ways that Bicchieri  uses to refer to them: she calls them “the grammar of society because, like a collection of linguistic rules that are implicit in a language and define it, social norms are implicit in the operations of a society and make it what it is” [p. ix].
The problem with these definitions is that they still leave ambiguity in what exactly social norms are from an ontological point of view. Since economists are usually uncomfortable when dealing with ‘mysterious' entities I think it is worth to be explicit in the ontological definition. Social norms are, in my view, no more than beliefs, hence mental states, whose logical content is of the form:
SN = “in S, it is best to do X”
where X is an action and S is a certain type of situation. Following Bicchieri's terminology, we can say that SN constitutes a kind of “behavioural rule” [p. 11]. These beliefs also need to satisfy two conditions in order to be possible for us to identify them and call them ‘social norms':
1) They must be shared by a sufficient number of individuals in a given society A (this is what makes them ‘social');
2) The individual's degree of belief in proposition SN, i.e. the individual's subjective measure of the probability of SN to be true, has to be directly proportional to i's expectations concerning the other individuals: the more he believes that they will do X in situations of type S and expect him to do X in situations of type S, the more he will believe SN to be true and have reasons to abide to it.
This definition is similar to the one provided by Bicchieri, yet it better emphasises that the ontological nature of social norms is that of a particular kind of belief shared by individuals. Another difference is that my formulation is not dependent on the concept of preference. In Bicchieri's “conditional preference” condition, it is necessary that i prefers to do X in S if and only if i believes that enough other individuals will do X in S and enough of them will either expect i to conform or will expect (and prefer) her to do X and sanction otherwise [p. 11]. Instead in my definition does not require that individuals prefer to do X in S, but only that they believe, to a certain degree, that it is indeed best to do X in S. I agree with Bicchieri that whether individuals will follow the behavioural rule or not is not necessary for it to be a social norm. Nonetheless, an individual might conform to the social norm even if she would not prefer to do so.
Condition 2) emphasises the feedback system that typically sustain social norms and differentiates them from other normative beliefs, such as personal moral rules. The reason why agents believe SN to be true is precisely the mutual expectation that they will actually do X in S. In other words, the fact that others expect me to behave in a certain way in S, when information concerning the decision problem at hand is lacking or ambiguous, is in itself a reason that causes my behaviour. Then, whenever an agent acts in the way that others were expecting him to, the mutual expectations are reinforced. In this sense, we can say that behaviour caused by the presence of a social norm is ‘rational': given the individual's set of desires, the relevant element in the set of beliefs becomes SN, and such belief will cause the individual to act in a way that he considers to be the best one to satisfy his desires.
The literature on social norms (see Bicchieri, Muldoon  for references) emphasises that individuals will more likely conform to social norms if some form of punishment (or appraisal) is also expected in the case that behaviour is not (or is) the one proscribed or prescribed by the social norm. The specific forms that the punishments or appraisals take can vary: in Section 4 we will see that in many economic contexts that involve cooperation to reach the best social outcome, social stigma, i.e. a disapproval from others, or even loss of social status could work as contingent reasons that motivate individuals to behave according to social norms.
Following my definition, an example of a social norm is reciprocity, viz. returning favours done by others [Gouldner 1960]. In this example, the situation of type S is one where the individual, say Nick, receives a favour of some kind by another individual, say Paul, for instance a gift. Nick believes that the best way to act is to do X, i.e. in this case give another gift to Paul. (Note that Nick might hate Paul and much rather prefer to not even talk to him, yet he might still believe it to be best to return the favour. We need not know the structure of Nick's preferences to make a prediction of what his behaviour will be, once we know that the social norm of reciprocity is present in the society). Moreover, Nick believes that Paul (and anyone else in his situation) would do the same, and also believes that Paul (and anyone else in his situation) would expect him to do so. If such set of beliefs is found to be shared by a significant number of individuals in a society A, then reciprocity can be identified as a social norm in society A.
Note two things: first, social norms might be the cause of behaviour also indirectly, for instance when individuals act in order to avoid finding themselves in situations of type S. In our example in Section 2.1, Bob's decision of staying at home might also be explained by the fact that, had he chosen to go out, he would have had to dress properly, because he believes that there is a social norm which prescribes to dress decently when going out in the park. Wanting to avoid compliance with the social norm also contributes to explain why he chose to stay home. Second, the behaviours explained by the existence of a social norm need not to be different from those which would have occurred had the individual's rationality not been bounded, yet, in some cases they might. In other words, explaining behaviour with reference to social norms can also be seen as a possible alternative explanation, even in contexts where individuals conform more closely to the paradigms of perfect rationality.
If social norms do indeed explain behaviour, it becomes crucial to address the natural questions that follow from such a hypothesis: how do social norms emerge? Which norms are more likely to survive and which to disappear in a given society? What are the characteristics of such dynamics? Is it possible to formalise their role into a general rational choice explanation framework? In order to answer this questions, in the next section I will present a general model of social norms dynamic based on SEGT.
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