One of the recurring themes of the past three chapters has been that government intervention may be able to begin solving cases of market failure. For example, the government can regulate monopolies, break up cartels, inform consumers, and so on. What if the government is unable to effectively impact the market? What about the possibility of government failure? Social choice theory examines the difficulties in having a government that is supposed to make the best choice for all of society.
The Voting Paradox
For instance, does the system of majority rule voting always yield the socially optimal result? In 1951, Kenneth Arrow proved his impossibility theorem. This theorem says that no system of putting together the wills of a whole society will yield consistently socially optimal outcomes. The voting paradox highlights the problem with majority rule voting. Let us say there are three candidates running for office, and three people are voting for them using the majority rule. Each person has ranked their choices from most preferred to least preferred in the table following.
If candidate 1 runs against candidate 2, candidate 1 will win.
If candidate 2 runs against candidate 3, candidate 2 will win.
If candidate 1 runs against candidate 3, candidate 3 will win.
If 1 is better than 2 and 2 is better than 3, how could 3 be better than 1? This inconsistency is called the voting paradox. Thus, even when a government action is taken based on a decision made by majority rule, there is no certainty that the decision is the most desired option for the society.
Another problem with majority-rule voting is that it leads to logrolling, which occurs when representatives trade votes (I vote for your program if you vote for mine). It is not clear whether any bill could get through any legislature without logrolling. It is also not clear whether logrolling is, on balance, a good thing or a bad thing from the standpoint of efficiency. It may turn out beneficial legislation, or it may turn out unjustified pork barrel legislation.
A number of other problems result from voting as a mechanism for public choice. Voters do not have much of an incentive to become well informed, because the apparent costs may outweigh the apparent benefits. Also, choices are almost always limited to bundles of public goods, and we vote infrequently.