Public choice

1. Public choice Alexander W. Cappelen Econ 4620 091003

2. Collective decision-making • Public production and financing is a possible solution to important market failures. • But in the absence of a market - how can we solve the tasks that the market traditionally solves? • How do we decide what to produce and how much? • How do we ensure an efficient resource allocation? • How do we distribute costs of production? • The market resolves this questions by using the information in the price system. Collective decisions must rely on other types of information.

3. Collective decision-making • Different voting procedures are different ways to aggregate individual preferences • The most common voting procedure is simple majority voting • Qualified majority • ’Rank-order’ voting is an alternative • Two problems with collective decision making: • Preference revelation • Preference aggregation • People disagree about the optimal level of public expenditures • Differences in preferences • Differences in income • Differences in ‘price/tax-cost’

4. Different preferences Private goods B’s indifference curve A’s indifference curve Common budget restrictions Public goods

5. Different income Private goods A’s budget- restriction A og B’s indifference curve B’s budget- restriction Public goods

6. Different tax-cost Private goods A’s budget - restriction A og B’s indifference curve B’s budget- restriction Public goods

7. Utility Utility of rich Utility of middle income Utility of poor Public goods Utility as a function of public goods

8. The median voter • Who will decide if there exist a majority equilibrium? • The median voter (the median voter theorem) • The number of people who prefers a higher level of public goods than the median voter is equal to the number of people who prefers a lower level. • The median voter can thus always secure a majority for her preferred level. • Does the median voter choose an efficient level of public goods? • Is the median voters tax price equal to the average cost of public goods provision? • Is the income of the median voter equal to the average income?

9. Implications for the party structure • In a two-party system, where both parties want to maximize their votes, both parties position will be close to the median voters preferred level (Hotelling’s rule). • why? • Presupposes that • There is only two parties • Parties are only concerned with maximizing votes • Voters have single-peaked preferences

10. The voting paradox • Majority voting does not always give a stable equilibrium. • Condorcet • We can illustrate the problem in a simple model: • Three voters: I, II, III • Three alternatives: A, B, C • Preferences I: A > B > C II: B > C > A III: C > A > B

11. Majority voting • We do not have a stable equilibrium in this situation. We have three possibilities: • A against B: A wins • A against C: C wins • B against C: B wins • All three alternatives can win. • There does not exist any consistent social preference ordering and therefore no social welfare function. • We either get a cycle or, if we have a sequence of votes, the order in which the votes take place will determine the outcome.

12. Arrow’s impossibility theorem • Does there exist any political mechanism that avoids this problem? • Arrow formulates five minimal conditions that all political mechanism should satisfy. • Pareto-efficiency • Transitivity • Nondictatorial choice • Independence of irrelevant alternatives • Unrestricted domain

13. Arrow cont. • There does not exist any mechanism that satisfy these requirements (Arrow’s impossibility theorem) • ’Rank order’ does not satisfy independence of irrelevant alternatives. • What is the main problem? • Voting procedures do not give us enough information. • In particular we do not get information about the strength of people’s preferences. • What about the social welfare functions? • Do they satisfy Arrow’s five requirements?

14. Is this important? • An example illustrates the practical importance of Arrow’s insight. • The decision about a new airport in Oslo in 1992. • Three alternatives: Fornebu (F), Gardermoen (G) and Hobøl (H). • Studies of the preferences in the different political parties have shown that we probably would have got the following results: • H is preferred to G (101 – 64) • G is preferred to F (101 – 64) • F is preferred to H (105 – 60) • The chosen sequence of votes resulted in G, but all the alternatives could have won.

15. When is there an equilibrium • Arrow’s impossibility theorem tells us that there is no mechanism that always satisfies the five requirements. • However, majority voting satisfies these requirements in some situations: • For certain types of preferences: when the preferences are single-peaked.

16. Different preferences Single-peaked preferences Single-peaked preferences Double-peaked preferences

17. When do we have single-peaked and double-peaked preferences? • Preferences for single peaked preferences is generally single-peaked. • Preferences are generally not single-peaked if: • We vote over combinations of public goods. • We vote over public goods for which there is a private alternative. • We vote over issues of redistribution.

18. Alternative systems for determining public goods supply • Majority voting does not ensure an efficient supply of public goods. • A public goods that is only valued by a minority will not be supplied at all • Goods that everyone value equally will typically be oversupplied since the median voter does not pay the average cost of production. • Does there exist an alternative solution? • Lindahl equilibrium

19. Lindahl equilibrium • The Lindahl equilibrium is found at the intersection between the ‘collective’ demand cure and the supply curve. • Lindahls solution involves that everyone pays a tax (price) equal to her marginal willingness to pay (in the equilibrium). • The obvious problem is that people do not have any incentives to reveal their true willingness to pay.

20. Lindahl cont. Tax price Tax price Public expenditures Public expenditures Tax price Public expenditures

21. Politics and economics • We have studied an idealized version of democratic decision making. • Everyone do not vote • Is it rational? • Do people know their own best? • Lobby organizations have substantial influence • What motivates politicians?