Author(s)

Rajat Deb¹, Indranil K. Ghosh², Tae Kun Seo¹

¹Department of Economics, Southern Methodist University, Dallas, USA.
²Graham School of Management, Saint Xavier University, Chicago, USA.

In referenda, projects are approved if the support for the project exceeds a particular threshold or quota. The usual threshold is the requirement of majority support. The paper provides a theoretical analysis of referenda with different threshold quotas for the provision of a binary public good. Optimal quota sizes are characterized and how the optimal quota changes as the size of the society increases is studied. While the majority quota may or may not be optimal, the conditions which determine the significance of the loss of expected welfare from the (possibly inoptimal) use of the majority quota are analyzed and interpreted. It is shown that the welfare loss from using an inoptimal majority quota will be insignificant if the ratio of the average intensity of support for the project relative to the intensity of opposition to it is positively associated with the probability of a positive net valuation of the project.

Referendum, Optimal Quota, Optimal Proportion, Expected Welfare, Public Good

Deb, R. , Ghosh, I. and Seo, T. (2018) Referenda and the Provision of a Binary Public Good. Journal of Mathematical Finance, 8, 668-689. doi: 10.4236/jmf.2018.84042.