Abstract
In this work, we present a mathematical model for the emergence of descriptive norms, where the individual decision problem is formalized with the standard Bayesian belief revision machinery. Previous work on the emergence of descriptive norms has relied on heuristic modeling. In this paper we show that with a Bayesian model we can provide a more general picture of the emergence of norms, which helps to motivate the assumptions made in heuristic models. In our model, the priors formalize the belief that a certain behavior is a regularity. The evidence is provided by other group members’ behavior and the likelihood by their reliability. We implement the model in a series of computer simulations and examine the group-level outcomes. We claim that domain-general belief revision helps explain why we look for regularities in social life in the first place. We argue that it is the disposition to look for regularities and react to them that generates descriptive norms. In our search for rules, we create them.
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Notes
We follow Bicchieri’s definition (Bicchieri 2006). More formally, a descriptive norm is a behavioral rule R for a population P in a context C where individuals in P have a conditional preference to follow R if they believe that a large enough proportion of the population P follows R in C. This belief is their empirical expectation of rule compliance.
Descriptive norms can be understood either as one-sided coordination problems, or as creating them in a similar manner to the Bicchieri (2006) account of social norms transforming mixed motive games into coordination games. Unlike a convention, which provides a solution to a two-sided coordination game, there is no need to coordinate expectations across parties. One party can simply choose to match what others do.
The distinction between descriptive norms and other informal norms, such as social norms or conventions, however, has fuzzy boundaries. Even in trivial cases, like following a fashion trend, a few individuals might follow them out of fear of punishment or of social rejection, even if no one else would even think of punishing them. Individuals can have a variety of motivations—sometimes one subset of people have normative expectations (the belief that others think you ought to follow the rule), while the rest of the population only has empirical expectations. For our purposes, we focus only on canonical cases of descriptive norms where people lack second-order normative beliefs.
Even if descriptive norms do not involve any normative component, they still differ from pure behavioral regularities, which exclusively depend on individual preferences. A classic example of a behavioral regularity is that people use umbrellas when it rains. They would do this regardless of what other people are doing, namely without being influenced by others’ behavior, as happens, by contrast, in the case of descriptive norms.
Whereas compliance with social norms can foster group identity and reinforce mutual cooperation, descriptive norms do not necessarily fulfill the same aim, as is shown by the fact that they continually change within the same group: they rapidly emerge, disappear, and come back, while social norms tend to be more stable and long-lasting.
Notice once more that, in contrast to other kinds of norms, such as social and moral norms, descriptive norms are behavioral rules which individuals follow on condition that their empirical expectations have been met. By definition, these norms are not based on normative expectations, namely on the belief that others expect us to comply and may sanction deviations. Take as an example the spread of various internet memes, like LOLCats. These memes spread very quickly, and can often fade away just as easily. While many people participate in the meme, there is no particular social sanction for failing to do so. Individual compliance mainly depends on a combination of personal preference and the wish to conform, but it doesn’t involve normative expectations about which is the appropriate behavior to follow.
Recall the ‘Brown is the New Black’ claim versus ‘Word Processors are superior to Typewriters’—we can have efficiency measures to compare the machines, but we would be at a loss for an equivalent measure for the colors.
The systematic tendency to imitate behaviors, which are perceived to be the norm, is a psychological mechanism that has been observed very early in human development. In a family of experiments on social imitation, Tomasello and his research group have shown that infants as young as two years are able to detect social regularities, imitate them and complain against defections, both when the behavior is a means for an intended goal and a goal in itself (See Carpenter et al. 2005; Rakoczy et al. 2008).
Nothing in our argument relies on Bayesian updating in particular—we employ Bayesian updating because it is a well-understood, straightforward model of domain-general belief revision.
See Hartmann and Sprenger (2010) for an introduction to Bayesian Epistemology.
See Hacking (2001) for a formal treatment of the aforementioned examples.
See Schelling (1978) for typical interactive, critical-mass models in the social sciences.
The assignment of the priors is analogous to the way in which in the natural world we assign priors to our hypothesis before starting to collect evidence in favor of that hypothesis. This assumption does not imply that the individuals have a pre-existing notion of what is in a norm. For instance, the priors can take very low values and it will be the evidence provided by other people’s behavior to trigger the process that can eventually lead to the emergence of a new norm.
See (Bovens and Hartmann (2003), chap. 3).
It might be asked why an individual should assume conditional independence, given that this assumption is false for her. The main rationale for the independence assumption is based on the psychological motivations underlying the individual decision. Consider again the example of fashion, fads and trends: people usually follow a new fashion trend thinking that they are among the first to do so, not that they belong to what is already a large majority of norm-followers. More generally, individuals have a tendency to disregard their own responsiveness to other people’s behavior and to believe that they are acting in conformity with the norm, rather than because others have influenced them. In this sense, the assumption of independence holds at the individual level of the decision-making process.
The actual model makes an assumption of independence across time within an individual, i.e. if an agent observes someone complying with the norm in a certain round this does not affect the probability assigned to that agent’s complying with the norm in subsequent rounds. The justification for this assumption is that people do not carefully track others inter-temporally, also in virtue of the fact that they have the possibility to change their decision from one round to the other.
Grunge clothing was popular for several years before it largely disappeared. Bangs are sometimes widely adopted, and then disappear for a while. Text messaging has largely supplanted once-dominant phone calls for quick messages amongst friends.
We implemented this simulation in Netlogo 4.0.4. The grid size is the simulation software’s default setting. We explored grids of different sizes, and did not see qualitative differences. We report on this population size as a compromise between the desire for a large social group, and the super-linear increase in computational costs (in terms of time) of the simulation as more agents are added.
The assumption of local information and some social hierarchy in our account of how descriptive norms emerge is based on the consideration that full information models are extremely unrealistic. Very rarely in our social lives do we have complete social information about an entire extended social group.
Think of clothing fashions, for example. Descriptive norms, especially ones that have any longevity, have to be associated with some public display or action, otherwise empirical expectations cannot be coordinated. Since there is no normative aspect, there is no reason to a have a descriptive norm about private behavior. Outside of actions influenced by our normative expectations, private behaviors do not have social motivations.
We do not specifically look at cases where group behavior contrasts with individuals’ preferences, insofar as our interest here mainly consists in analyzing the updating mechanism that leads people to assess other people’s behavior as a sign of the existence of a norm and behave accordingly. For a more detailed treatment of this case, consult (Muldoon et al. 2014).
All evidence being equal, in a Bayesian model the likelihood affects the judgment about whether the behavior in question is an instance of a norm; by contrast, in a pure imitation model, the emergence of the norm depends exclusively on the number of followers (if we consider the mode), regardless of their influence on each other.
It is not necessarily the case that, when there are no differential payoffs, the individual believes that there are in order to choose between the possible alternatives. Think for example of conventions, where a decision can be taken despite alternatives that appear to provide equal benefits.
In a further extension of the model, we intend to include a number of non-conformists, who react negatively to the emergence of a norm. In this scenario, the expected compliance parameter would be negatively correlated to the existence of the norm: positive evidence by a non-conformist suggests that there is no norm and negative evidence that there is a norm.
The tipping point after which the value of the epistemic sensitivity determines the emergence of the norm depends on the combination of the values of the other two parameters. It would be interesting to bound the value of the epistemic sensitivity parameter further, in the light of the costs that conformity has in terms of money and work. We predict that also this variation of the model would provide a limiting mechanism to the emergence of descriptive norms.
Several mechanisms might determine the decline of a norm. Two clear candidates are that either a new norm emerges and people switch to it or that an old norm simply fades over time. The former option can serve as a useful description of fashion cycles, while the latter option is particularly clear in the case of fads—eventually they just get old and unexciting. Since we are focusing on norm emergence we leave out considerations of norm decay in order to reduce the complexity of the model.
Again, we would like to note that Bayesian reasoning here is just an exemplar of domain-general reasoning about hypotheses and their evidence. Nothing hinges on Bayesianism in particular. Which means, if it turned out that a different inferential system were a more accurate representation of the individual reasoning process, then we would have to show how to adapt that system to the social domain, in order to see under which conditions it would explain the emergence of descriptive norms.
As discussed earlier, it is in part due to this insight that we chose the network structure that we did for our simulations.
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Acknowledgments
The authors would like to thank Jason McKenzie Alexander, Jan Sprenger, Kevin Zollman, and anonymous reviewers for their helpful comments on earlier drafts.
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Muldoon, R., Lisciandra, C. & Hartmann, S. Why are there descriptive norms? Because we looked for them. Synthese 191, 4409–4429 (2014). https://doi.org/10.1007/s11229-014-0534-y
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DOI: https://doi.org/10.1007/s11229-014-0534-y