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) |