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Giuseppe Dari-Mattiacci on Sanctions - Dictionary of Arguments

Parisi I 451
Sanctions/punishment/rewards/carrots/sticks/incentives/Dari-Mattiacci/De Geest: The fact that sticks need to be available for all potential violators needs to be reconsidered in light of the fact that individuals might not be able to coordinate their actions. If they are not able to coordinate, then in fact one stick might be enough to incentivize all potential violators (Dari-Mattiacci and De Geest, 2010)(1).
For all agents taken as a group, it might be better to violate the rule and allow one of them to be punished, yet no agent has an individual incentive to sacrifice himself. A necessary condition for this multiplication effect to hold is that all agents know the order in which the ruler will monitor and penalize them.
Parisi I 452
Two general principles:
First, the multiplication effect of sticks is stronger (giving a stronger advantage to sticks over carrots) as n grows, since the condition becomes more difficult to satisfy.
Second, this advantage also grows if the number of compliers increases. In normal circumstances, compliers outnumber violators and hence the condition becomes n < 1, so that carrots always yield a more stringent budget constraint for the ruler than sticks do.
Multiplication effect: The reason why only sticks have a multiplication effect is as follows. Carrots are applied upon compliance, sticks upon violation. If the agent complies, the carrot is used up but the stick is not. Although a stick can be applied only once, the threat to apply the stick can be repeated several times. Note that the multiplication effect is another qualification of the incentive equivalence result: a $100 stick can, under some conditions, have an incentive effect of more than $100; a $100 carrot, by contrast, can never have an incentive effect of more than $100.
The upside of the multiplication effect is that it makes law enforcement more effective: it allows governing a country of 300 million citizens with relatively few prison cells—it is sufficient that there are some empty prison cells. The downside
Parisi I 453
of the multiplication effect is that sticks carry an inherent risk of abuse, which is absent in carrots.
>Incentives/Dari-Mattiacci/De Geest.
Distributional effects: Sticks inherently undercompensate because the agent is always worse off compared to the status quo: either he incurs an effort cost or a penalty. Carrots, by contrast, have a built-in compensation mechanism in that they always allow the agent to opt for the status quo, in which the agent does not do the effort and simply does not receive the carrot.
While carrots can never be undercompensatory (because then they would violate the incentive compatibility constraint), the question remains why they would ever be overcompensatory. Why cannot the principal set the carrot equal to the effort cost, so that there is no overcompensation? A first reason is that the principal may have imperfect information on the individual effort cost.
>Transactional costs/Dari-Mattiacci/De Geest.
A second reason why carrots may be overcompensatory is that the principal makes monitoring errors by mistakenly concluding that some violating agents complied. Since violation leads to an (even small) expected rent, compliance needs to include this expected rent too in order to give sufficient incentives to comply.
Errors: Note that errors create fixed rents or impose fixed costs that are equal for all individuals in expected terms; therefore, the only distributional effects within the group of agents derive from differences in effort costs.

1. Dari-Mattiacci, Giuseppe and Gerrit De Geest (2010). “Carrots, Sticks, and the Multiplication Effect.” Journal of Law, Economics, and Organization 26: 365–384.

Giuseppe Dari-Mattiacci and Gerrit de Geest. “Carrots vs. Sticks”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University.

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Dari-Mattiacci, Giuseppe
Parisi I
Francesco Parisi (Ed)
The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017

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