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A Partial Rehabilitation of the Principle of Collective Punishment*

Published online by Cambridge University Press:  18 July 2014

Irwin Lipnowski
Irwin Lipnowski
Affiliation:
Department of Economics, University of Manitoba
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Extract

Most, if not all, high school graduates have experienced the following event at some stage of their academic careers. Their teacher wishes to leave the classroom but is fearful about the noise level that will ensue after he or she departs, and so issues the following stern warning to the class:

I shall be out of the classroom for a few minutes and during my absence, I want to be able to hear a pin drop from down the hall. If I hear so much as a peep coming from this classroom, everyone will have to remain for detention after class.

Type
Exchanges/Débate
Information
Canadian Journal of Law and Society / La Revue Canadienne Droit et Société , Volume 8 , Issue 1 , Spring/printemps 1993 , pp. 121 - 125
Copyright
Copyright © Canadian Law and Society Association 1993

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References

1 The situation described is an example of a “prisoner's dilemma” of either the two-person or multi-agent variety. To illustrate the two-person case of shirking in a team, consider two symmetric individuals belonging to a production team. The disutility to each individual from the effort expended when shirking would be -1 utils, while the disutility to each from the effort associated with not shirking would be - 4 utils. If both individuals do not shirk, the value of their jointly produced product would be 14 utils, to be divided equally, thereby yielding 7 utils each. Thus, each would realize a net payoff of 3 utils if neither shirked. If both shirk, the value of their jointly produced output would have a total value of 6 utils, to be divided equally, thereby yielding a net payoff of 2 utils to each individual. Finally, if one individual shirks and the other does not, the total value of their jointly produced output would be 10 utils, to be divided equally, thereby yielding a net payoff of 4 utils to the individual who shirks and 1 util to the individual who does not shirk. Depicting by S and *S the actions of “shirking” and “not shirking” respectively, we can summarize the above information in a payoff matrix where each cell contains an ordered pair of numbers indicating, respectively, the payoffs to “Row” and “Column.”

Column

Player

*S S

Row *S 3,3 1,4

Player S 4,1 2,2

Individual rationality dictates that in a single encounter, each player should shirk. As the payoff matrix shows, the payoff to each player is greater if he/she selects S irrespective of what the other player does. Thus, if Column independently selects *S, Row would do better by selecting S, securing a payoff of 4 utils, than by selecting *S, which secures a payoff of 3 utils. On the other hand, if Column selects S, Row would again do better by selecting S, thereby securing a payoff of 2 utils, than by selecting *S, which would yield a payoff of only 1 util. Thus, S is clearly a “dominant” strategy for Row. The symmetry of this situation implies that for Column, S is likewise the “dominant” strategy. However, the dilemma arises from the fact that when both Row and Column adopt their respective “dominant” strategies, the resulting outcome, wherein the payoff to each individual is 2 utils, is both individually and collectively inferior to (i.e., is “Pareto-dominated” by) the outcome that would result if neither individual shirked and each secured a payoff of 3 utils.

2. Hardin, G., “The Tragedy of the Commons” (1968) 162 Science 1243.Google ScholarPubMed