Abstract
This paper focuses on one possible measure for the severity of the problems of inefficiency, suboptimality and the Prisoner's Dilemma in voluntary public-good provision. The proposed measure is the probability of the emergence of the respective problem in an impartial environment where all feasible combinations of the parameters of the voluntary public good provision game are equally likely. These probabilities are derived using the game of voluntary binary contributions to the provision of public goods recently analyzed by Gradstein and Nitzan (1990). The severity of the three problems (Prisoner's Dilemma, suboptimality and inefficiency) is computed, respectively for games with up to N=12, N=6 and N=4 players. The decreasing order of N reflects the increasing complexity of the problems and, in turn, computation of their likelihood. It turns out that the likelihoods of all three problems are increasing with the number of players, N. More importantly, social optimality is more likely than suboptimality when N≤2, efficiency is more likely than inefficiency when N≤3 and no Prisoner's Dilemma is more likely than a Prisoner's Dilemma when N≤5.
Similar content being viewed by others
References
Chamberlin J (1985) Investigation into the relative manipulability of four voting systems. Behav Sci 30: 195–203
Cornes R, Sandler T (1986) The theory of externalities, public goods and club goods. Cambridge, Cambridge University Press
De Meyer F, Plott CR (1970) The probability of a cyclical majority. Econometrica 38: 345–354
Garman MB, Kamien M (1968) The paradox of voting: probability calculations. Behav Sci 13: 306–316
Gehrlein WV, Fishburn PC (1976) The probability of the paradox of voting: a computable solution. J Econ Theory 13: 14–25
Gradstein M, Nitzan S (1990) Binary participation and incremental provision of public goods. Soc Choice Welfare 7: 171–192
Nitzan S (1985) The vulnerability of point voting schemes to preference variation and strategic manipulation. Publ Choice 47(2): 349–370
Olson M (1965) The logic of collective action. Cambridge, Cambridge University Press
Peleg B (1979) A note on manipulation of large voting schemes. Theory Decision: 401–413
Saari D (1990) Susceptibility of manipulation. Publ Choice 64: 21–42
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nitzan, S. The likelihood of inefficiency, a prisoner's dilemma and suboptimality in games of binary voluntary provision of public goods. Soc Choice Welfare 11, 157–164 (1994). https://doi.org/10.1007/BF00179211
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00179211