Problem
Status-quo bias. (Fernandez and Roderick, 1991.) There are two possible policies, A and B. Each individual is either one unit of utility better off under Policy A or one unit worse off. Fraction f of the population knows what its welfare would be under each policy. Of these individuals, fraction α are better off under Policy A and fraction 1 - α are worse off. The remaining individuals in the population know only that fraction β of them are better off under Policy A and fraction 1 - β are worse off.
A decision of whether to adopt the policy not currently in effect is made by majority vote. If the proposal passes, all individuals learn which policy makes them better off; a decision of whether to revert to the original policy is then made by majority vote. Each individual votes for the policy that gives him or her the higher expected utility. But if the proposal to revert to the original policy would be adopted in the event that the proposal to adopt the alternative policy passed, no one votes for the alternative policy. (This assumption can be justified by introducing a small cost of changing policies.)
(a) Find an expression for the fraction of the population that prefers Policy A (as a function of f , α, and β) for the case where fraction 1 - f of the population knows only that fraction β of them are better off under Policy A.
(b) Find the analogous expression for the case where all individuals know their welfare under both policies.
(c) Given your answers to parts (a) and (b), can there be cases when whichever policy is initially in effect is retained?