TITLE:
Referenda and the Provision of a Binary Public Good
AUTHORS:
Rajat Deb, Indranil K. Ghosh, Tae Kun Seo
KEYWORDS:
Referendum, Optimal Quota, Optimal Proportion, Expected Welfare, Public Good
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.8 No.4,
November
26,
2018
ABSTRACT: 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.