A Consequential Contingent Valuation Referendum: Still Not Enough to Elicit True Preferences for Public Goods!

Incentive properties of an advisory CV referendum when one of ps and pp is equal to 0 or 1 and the other probability takes a different value

Value of g(b)	Value of g(b) for b = 0	Incentive properties of the referendum
Case 1:ps(v) = 0 and 0 < pp(v) ≤ 1 g(b) = Pp(b + c)[U(–c\r) – U(0|r)]	g(0) = pp(v)[U(–c|r) – U(0|r)] < 0	EUy < EUN′ incentives to vote “no”
Case 1: ps(v) = 1 and 0 < pp(v).≤1 g(b) = [1 – pp(b + c)] U(b +c|r) + pp(b + c) U(b|r) – U(0|r)	g(0) = [1–pp(v)[U(c|r) – U(0|r)] > 0	EUy > EUN′ incentives to vote “yes”
Case 1: pp(v) = 0 and 0 < ps(v) < 1 g(b) = p(b + c)[U(b + c|r) – U(0|r)]	g(0) = ps(v)[U(c|r) – U(0|r)] > 0	EUy > EUN′ incentives to vote “yes”
Case 1:pp(v) = 1 and 0 < ps(v) < 1 g(b) = [1 – ps(b + c)] U(–c|r) + ps(b + c)U(b\r) – U(0|r)	g(0) = [1 – ps(v)][U(–c\r) – U(0|r)] < 0	EUy < EUN′ incentives to vote “no”

Individual i’s utility upon the authorities’ decision to implement the project

	Payment collected (pp,i (νi))	Payment not collected (1 – pp(νi))
The good successfully provided (ps,i(νi))	Ui (νi– ci|ri)	Ui (νi\ri)
The good not successfully provided (1 – pS,i(νi))	Ui (–ci\ri)	Ui(0|ri)