Various prohibiting signs are posted in many places, saying for example “No smoking”, “No trespassing”, “No skateboarding”, etc. The language of a sign with the same message can be stronger or weaker, e.g. “Smoking prohibited” vs “No smoking. Strictly enforced” or “Trespassing forbidden” vs “Strictly no trespassing. Violators will be prosecuted to the fullest extent of the law.” It seems that there is a negative correlation between the strength of the language and the strength of enforcement. The rules stated on signs threatening strict enforcement or prosecution seem not enforced at all. Non-enforcement is certainly the case for the “Smoke-free campus. Strictly no smoking” signs around the Australian National University and for similar signs around other universities that I have visited.
Why might stronger language of the sign indicate non-enforcement? Stronger language is also longer, requiring a larger sign and more paint, which makes signs with stronger language slightly more expensive to put up. So why pay more for signs that suggest non-enforcement?
Local people learn the rules and their actual level of enforcement over time. For them, signs are not really necessary. Therefore, signs are put up only for first-time visitors or for legal reasons. Legalities usually just require some legible sign, not a long and strongly worded one, so to satisfy the law, the optimal choice is a shorter and simpler text that fits on a smaller, cheaper sign.
First-time visitors are either uncertain about the enforcement level or know it. If they know, then they are effectively locals – for them, there is no need for a long sign. If the visitors are uncertain, then they might infer the enforcement level from the strength of the language. This can go two ways. If the visitors are rational and the strength of the language is negatively correlated with the level of enforcement, then a shorter sign signals stronger enforcement and deters rule-breaking better. Then all signs would optimally be short. If the visitors are irrational and interpret the signs literally, then more strongly worded signs deter rule-breaking more. The negative correlation between strong language and enforcement suggests that people are irrational and take threats literally. Or that those putting up signs are irrational and for some reason choose the less effective strongly worded signs.
An alternative explanation is countersignalling (Feltovich, Harbaugh and To 2002). In this model, there are three types of sign-posters. The first type does not care much about whether the text of the sign is obeyed (may post the sign only for legal reasons). The second type cares a little bit, but not enough to pay for much enforcement. Still, the second type slightly enforces, so there is a small positive probability of some kind of punishment when breaking the rules. The third type really wants the rules to be followed and invests in enforcement correspondingly. The potential rule-breakers quickly learn from punishments whether they are dealing with the third type. So the third type does not need any particular kind of signs to distinguish himself from the first two.
The first two types are harder to tell apart. The first type is not interested in distinguishing himself from the others – in fact, being confused with the others is beneficial, because it is more likely to make people obey the rules. The second type would like to distinguish himself from the first type and be confused with the third type, but this desire is not strong enough to pay the same enforcement cost as the third. So the second type will settle for distinguishing himself from the first type. This is done by paying for slightly larger signs with stronger, longer language on them. In this case, in the absence of experienced enforcement, the potential rule-breakers respond more to strongly worded signs than to short ones.
For an external observer, it is difficult to distinguish a small amount of enforcement from none, so the perception arises that enforcement goes together with short signs, but non-enforcement sometimes with long, strongly worded signs and sometimes with short signs. So there is a negative correlation between the strength of enforcement and the strength of the language. This correlation is stronger if the fraction of the first type in the population of sign-posters is small, for example because some first types do not post signs at all. People posting signs are a selected sample from the population of those who want some rule obeyed. The selection oversamples those who care more.