Editing Social norm (section)

== Mathematical representations ==
Over the last few decades, several theorists have attempted to explain social norms from a more theoretical point of view. By quantifying behavioral expectations graphically or attempting to plot the logic behind adherence, theorists hoped to be able to predict whether or not individuals would conform. The return potential model and game theory provide a slightly more economic conceptualization of norms, suggesting individuals can calculate the cost or benefit behind possible behavioral outcomes. Under these theoretical frameworks, choosing to obey or violate norms becomes a more deliberate, quantifiable decision.

===Return potential model===
[[File:Return Potential Model, Jackson, 1965.jpeg|thumb|Figure 1. The return potential model (reproduced from Jackson, 1965).]]
Developed in the 1960s, the return potential model provides a method for plotting and visualizing group norms. In the regular coordinate plane, the amount of behavior exhibited is plotted on the X-axis (label ''a'' in [https://web.archive.org/web/20120626024217/http://www.tau.ac.il/~toury/works/GT-Role-Norms.htm Figure 1]) while the amount of group acceptance or approval gets plotted on the Y-axis (''b'' in Figure 1).<ref name="jackson"/> The graph represents the potential return or positive outcome to an individual for a given behavioral norm. Theoretically, one could plot a point for each increment of behavior how much the group likes or dislikes that action. For example, it may be the case that among first-year graduate students, strong social norms exist around how many daily cups of coffee a student drinks. If the return curve in Figure 1 correctly displays the example social norm, we can see that if someone drinks 0 cups of coffee a day, the group strongly disapproves. The group disapproves of the behavior of any member who drinks fewer than four cups of coffee a day; the group disapproves of drinking more than seven cups, shown by the approval curve dipping back below zero. As seen in this example, the return potential model displays how much group approval one can expect for each increment of behavior.
* '''Point of maximum return'''. The point with the greatest y-coordinate is called the point of maximum return, as it represents the amount of behavior the group likes the best.<ref name="jackson"/> While ''c'' in Figure 1 is labeling the return curve in general, the highlighted point just above it at X=6, represents the point of maximum return. Extending our above example, the point of maximum return for first-year graduate students would be 6 cups of coffee; they receive the most social approval for drinking exactly that many cups. Any more or any fewer cups would decrease the approval.
* '''Range of tolerable behavior'''. Label ''d'' represents the range of tolerable behavior, or the amount of action the group finds acceptable.<ref name="jackson"/> It encompasses all the positive area under the curve. In Figure 1, the range of tolerable behavior extends is 3, as the group approves of all behavior from 4 to 7 and 7-4=3. Carrying over our coffee example again, we can see that first-years only approve of having a limited number of cups of coffee (between 4 and 7); more than 7 cups or fewer than 4 would fall outside the range of tolerable behavior. Norms can have a narrower or wider range of tolerable behavior. Typically, a narrower range of behavior indicates a behavior with greater consequences to the group.<ref name="hackman"/>
* '''Intensity'''. The intensity of the norm tells how much the group cares about the norm, or how much group [[Affect (psychology)|affect]] is at stake to be won or lost. It is represented in the return potential model by the total amount of area subsumed by the curve, regardless of whether the area is positive or negative.<ref name="jackson"/> A norm with low intensity would not vary far from the x-axis; the amount of approval or disapproval for given behaviors would be closer to zero. A high-intensity norm, however, would have more extreme approval ratings. In Figure 1, the intensity of the norm appears high, as few behaviors invoke a rating of indifference.
* '''Crystallization'''. Finally, norm crystallization refers to how much variance exists within the curve; translated from the theoretical back to the actual norm, it shows how much agreement exists between group members about the approval for a given amount of behavior.<ref name="jackson" /> It may be that some members believe the norm more central to group functioning than others. A group norm like how many cups of coffee first years should drink would probably have low crystallization since a lot of individuals have varying beliefs about the appropriate amount of caffeine to imbibe; in contrast, the norm of not plagiarizing another student's work would likely have high crystallization, as people uniformly agree on the behavior's unacceptability. Showing the overall group norm, the return potential model in Figure 1 does not indicate the crystallization. However, a return potential model that plotted individual data points alongside the cumulative norm could demonstrate the variance and allow us to deduce crystallization.

===Game theory===
{{Main|Game theory}}
Another general formal framework that can be used to represent the essential elements of the social situation surrounding a norm is the [[repeated game]] of game theory. Rational choice, a branch of game theory, deals with the relations and actions socially committed among rational agents.<ref>Voss, Thomas. Game-Theoretical Perspectives on the Emergence of Social Norms. Social Norms, 2001, p.105.</ref> A norm gives a person a [[rule of thumb]] for how they should behave. However, a [[rationality|rational]] person acts according to the rule only if it is beneficial for them. The situation can be described as follows. A norm gives an [[Expectation (epistemic)|expectation]] of how other people act in a given situation (macro). A person acts optimally given the expectation (micro). For a norm to be [[Structural stability|stable]], people's actions must reconstitute the expectation without change (micro-macro feedback loop). A set of such correct stable expectations is known as a [[Nash equilibrium]]. Thus, a stable norm must constitute a Nash equilibrium.<ref>[[Cristina Bicchieri|Bicchieri, Cristina]]. 2006. The Grammar of Society: The Nature and Dynamics of Social Norms, New York: Cambridge University Press, Ch. 1</ref> In the Nash equilibrium, no one actor has any positive incentive in individually deviating from a certain action.<ref name=":0" /> Social norms will be implemented if the actions of that specific norm come into agreement by the support of the Nash equilibrium in the majority of the game theoretical approaches.<ref name=":0">Voss 2001, p. 105</ref>

From a game-theoretical point of view, there are two [[explanation]]s for the vast variety of norms that exist throughout the world. One is the difference in games. Different parts of the world may give different environmental contexts and different people may have different values, which may result in a difference in games. The other is [[equilibrium selection]] not explicable by the game itself. Equilibrium selection is closely related to [[Coordination game|coordination]]. For a simple example, driving is common throughout the world, but in some countries people drive on the right and in other countries people drive on the left (see [[coordination game]]). A framework called comparative [[institutional analysis]] is proposed to deal with the game theoretical structural understanding of the variety of social norms.