Social Norms and the Revelation Principle
Suppose that some agent i perfectly observe the value taken by some random variable g E [0, 1]. We may assume that g captures one of i’s personal attributes that affects her physical state and capacity, i.e., the degree of pain she is feeling and her ability to work. Agent i can send a message m(g) to an agent j about the value of g; more specifically, i can signal to j whether the actual value of g is above some threshold g* (by default, if i doesn’t send an explicit message, it is common knowledge that the implicit message is m(g) < g*).
If m(g) > g*, agent j has two options at his disposal. He can either grant i a temporary paid leave L or ask i to continue to provide the same level of effort at work NL. If m(g) < g*, j has no decision to make and NL automatically prevails. Suppose that if g > g*, then j is indifferent between choosing L and NL. However, if g < g* then j strictly prefers NL to L. Assume for the moment that i prefers L to NL for all values of g. If follows that i’s dominant strategy is t send a message m(g) > g* irrespective of the actual value of g. The message m is then anything but cheap talk. That means that it gives agent j no new information. Independently of j’s prior belief about the distribution of g along the [0, 1] interval, j will then choose NL. This is a fairly bad outcome because if i could truthfully reveal her private signal, j would have no reason to refuse to grant a temporary paid leave in case g is indeed above the threshold.
However, suppose now that there is social norm N prevailing in the community in which i is involved. In this community, it is common knowledge that sending a message m(g) > g* is socially inappropriate. Moreover, if such a message is sent to j, it is common knowledge that any other agent k who is a member of the community will receive it. Assume finally that everything else equals, i prefers to avoid sending a message m(g) > g*, i.e. sending such a message is costly, and that this is common knowledge. Denote such a cost c.
Hence, if j receives a message m(g) > g* from i, that means that i is willing to bear the associated cost c. If the cost is sufficiently high, an agent who has received a private signal g < g* may prefer avoiding bearing the cost c because the marginal gain of obtaining L rather than NL does not cover it. If g > g* however, c is more than covered by the marginal gain. If it is common knowledge, when j receives a message m(g) > g*, he knows that g > g* and he can rationally choose NL. Knowing this, i will send m(g) > g* if and only if g > g*. In this community, the norm N permits the implementation of an incentive-compatible direct revelation mechanism. At the (separating) equilibrium, each agent i truthfully reveals her private signal.
This simple model of (norm-based) mechanism design has many applications. It seems to apply for instance to the issue of the so-called “menstrual leave” which is currently debated in Spain. In this case, as in others, there are obviously complications not captured by the model (think of the worry that it may encourage ex ante discrimination against people more likely to receive a private signal g > g*). But consider also the counterintuitive implication: any “progressive” attempt to dislodge the social norm N by encouraging more open communication about issues that are more or less taboo would hinder the revelation mechanism.