Majority Rule and the Provision of Local Public Goods

Majority Rule and the Provision of Local Public Goods Motivation ▶ We have seen in the previous lecture that voluntary mechanisms of public good provision are likely to be very inefficient. ▶ In the U.S. and most other democratic countries, local residents of a city typically elect a mayor and members of the city council. ▶ The mayor and the city council then determine expenditure and tax policies. ▶ Hence, participation in the provision of public goods is no longer voluntary but enforced by the elected government. ▶ You have to pay taxes, whether you like it or not! Majority Rule ▶ Majority rule means that a majority of votes must favor a measure to gain approval. ▶ Although majority rule is a familiar concept, there are a number of potential problems. ▶ We need to establish conditions under which majority rule will lead to a well-defined, stable outcome. ▶ This does not have to be case since there may not exist a feasible policy that beats all other feasible policies in a pairwise vote. ▶ We also need to understand under what conditions majority rule will produce an efficient outcome. An Example ▶ There are 3 individuals who have to choose among 3 levels of provision of public education denoted by L (low), M (medium) and H (high). ▶ Levels of provision are ordered such that L < M < H. ▶ Preferences are shown in the following table: Choice Andy George Petra First L H M Second M M H Third H L L Figure: Single-peaked Preferences Utility Andy George P etra L M H Spending Single-Peaked Preferences ▶ A peak in an individual’s preferences is a point at which all neighboring points provide lower utility. ▶ Single peaked preferences: utility falls as we move away from most preferred outcome in any and all directions. ▶ You can easily verify that all individuals have single peaked preferences in example 1. A Majority Rule Winner ▶ Let’s do pairwise comparisons of alternatives. ▶ Policy M beats L by a vote of 2-1. ▶ Policy M also beats H by a vote of 2-1. ▶ Policy M is thus the majority rule equilibrium outcome. ▶ It is also called a Condorcet winner, named ofter the Marquis de Condorcet who was an early French political scientist who studied election rules. ▶ A Condorcet winner does not always exist as the next example illustrates. An Example without a Winner ▶ Preferences are given by in the following table: Choice Andy George Petra First L H M Second M L H Third H M L ▶ George’s preferences are the only ones that have changed. ▶ Policy L beats M by a vote of 2-1. ▶ Policy M beats H by a vote of 2-1. ▶ Policy H beats L by a vote of 2-1. ▶ There is no alternative that beats the two other alternatives in pairwise votes. Figure: Double-peaked Preferences Utility Andy George P etra L M H Spending Double-Peaked Preferences ▶ Double peaked preferences: utility initially falls as we move away from most preferred outcome, but then rises again. ▶ You can easily verify Andy and Petra have single peaked preferences while George has double peaked preferences in example 2. ▶ Unfortunately, we cannot rule out these types of preferences, and they are likely to be prevalent in many situations. Cycles and Agenda Manipulations ▶ Suppose we now adopt a sequential voting game: we eliminate an alternative if it is beaten by another alternative in a pairwise vote. ▶ The equilibrium of this game depends crucially on the order in which the votes are taken. ▶ The policy that is not considered in the first round will ultimately win in a sequential voting game. ▶ Agenda manipulation is the process of organizing the order of votes to assure a favorable outcome. ▶ If we do not adopt a sequential game, we face the problem of voting cycles: paired voting can go on forever without reaching a decision. The Median Voter Theorem ▶ A Majority Rule Equilibrium typically exists in the simultaneous voting game if a) all individuals have single-peaked preferences, and b) the vote is about a one-dimensional policy. Moreover, the median voter is the decisive voter who determines the outcome. ▶ When preferences are not single-peaked, there is no guarantee that a majority rule equilibrium exists. (See example 2.) ▶ When the policy space is higher dimensional, existence will also be a problem. Voting on Public Good Provision ▶ Let us assume for simplicity that n is an odd number so that a majority exists and there are no ties possible. ▶ Individuals have quasi-linear preferences over a public good and a private good: Ui = βi ln(G ) + zi i = 1, .., n (1) ▶ Individuals differ in their preferences for public goods. Without loss of generality, let us assume that we have ordered individuals such that β1 < β2 < ... < βn (2) Public Good Provision and Taxation ▶ Each individual has an exogenous income denoted by mi . ▶ The public good can be produced by converting one unit of income into one unit of the public good, i.e. c = 1. ▶ The cost of public good provision are shared equally among the n individuals, i.e. every individual pays n1 th of the total level of public good provision. ▶ We can, therefore, write each individuals budget constraint as: mi = zi + 1 G n (3) Preferred Levels of Public Goods ▶ Substituting the budget constraint into the utility function yields: Ui = βi ln(G ) + mi − 1 G n i = 1, .., n (4) ▶ Maximizing utility, each individual’s preferred level of public good provision is given by: βi 1 = ∗ Gi n i = 1, .., n (5) ▶ Hence, the bliss points are given by: Gi∗ = nβi ▶ Moreover, we can show that individual preferences are concave in G which implies single-peakedness. (6) Majority Rule ▶ Since preferences are single-peaked, the median voter theorem applies. The level of public good provision is determined by the median voter in the economy. ▶ The level of public good provision in voting equilibrium denoted by G v is given by: G v = n βm (7) were m = (n − 1)/2 + 1 denotes the voter with the median preference level. Majority Rule and Efficiency ▶ The efficient level of public good provision, G e , is characterized by the Samuelson condition: n X MRSi = i=1 n X βi = 1 = MC Ge (8) i=1 ▶ Hence we obtain: Ge = n X n 1X βi n βi = n ! (9) i=1 i=1 ▶ The majority rule equilibrium is thus efficient if and only if: n βm = 1X βi n i=1 (10) The Median Voter Theorem and Representative Democracy ▶ The median voter model may apply to representative democracies as shown by Downs (1957). ▶ One key assumption is politicians primarily care about maximizing the number of votes they get, i.e. winning is not everything, it’s the only thing politicians care about! ▶ The other key assumption is that politicians can commit themselves to policy platforms. ▶ Politicians will then strategically position themselves to get the most votes. ▶ The argument that establishes the result follows from the same logic as Hotelling’s (1929) model of spatial competition. Side Payments and Transferable Utility ▶ So far we considered a voting model without side payments. We can easily extend our analysis to account for bribes and vote buying (i.e. transferable utility). ▶ Consider the benefits from 3 different projects for 3 voters. ▶ Preferences are in dollars and reflect willingness to pay: Choice Andy George Petra Total Hospital 200 -50 -55 95 Library -40 150 -30 80 Pool -120 -60 400 220 Nothing 0 0 0 0 ▶ Negative values mean a net loss. Equilibrium without Sidepayments ▶ It is fairly straightforward to show that the only equilibrium in the simultaneous voting game without-side payments is that none of the three projects are built. ▶ Each project loses against the alternative “Do Nothing” by a 2 to 1 vote. ▶ The willingness to pay is negative for two voters in each case and positive for one. What happens if we allow for side-payments? ▶ The answer depends on the rules of the voting process. ▶ In the first stage, one individual is randomly chosen to become the “proposer”. ▶ In the second stage of the game, the proposer makes a take-it-or-leave-it offer selecting a project to be determined by an up-and-down vote. ▶ At the same time, the proposer can offer side-payments to any of the other two voters. The Importance of the Proposer ▶ It is easy to see that the proposer can always get his or her favorite project to be adopted by majority rule. ▶ For example, if Andy is chosen as a proposer, he would pick the hospital and offer George a side-payment of $50. ▶ In that case, the proposal would be accepted by a 2 to 1 vote since both Andy and George would be weakly better off in this case. ▶ You get similar results if you allow for bundling of projects without side-payments. Problems with the Median Voter Theorem There are a variety of plausible reasons why the median voter theorem may fail in practice. ▶ Policies are often more complicated which is not captured by the one-dimensional spatial model that we studied above. ▶ Besides ideology voters care about the competence of the politicians. ▶ Voters care whether the politician exerts effort and works on their behalf. ▶ Voter turn-out is often low in state and local elections. The Dimensions of the Policy Space ▶ Representatives for state and local governments are elected to vote on a sequence of different issues ranging from education policy to social policy. ▶ We may therefore conjecture that a much higher dimensional voting model would be necessary to explain the observed voting patterns of members of the legislature. ▶ We do not have much evidence at the state and local level to answer this question. ▶ We have much more compelling evidence for members of the U.S. House of Representatives and the U.S. Senate. Evidence from the U.S. Congress ▶ Research by Poole and Rosenthal (1985) show that this conjecture is not correct. ▶ Surprisingly, they find a one-dimensional voting model explains a large share of all roll call votes taken in the U.S. congress. ▶ These are votes in which each representative has to answer with “yea” or “nay.” ▶ A two dimensional model is all that it takes to account for the vast majority of the votes. ▶ See www.voteview.com. Ideology versus Competence ▶ Politicians also differ in competence or valence. ▶ Elections can not only eliminate extreme politicians, but also incompetent ones! ▶ If competence matters, voters need to trade-off competence versus ideology. ▶ A more competent politician can be more extreme in equilibrium. ▶ What’s the evidence at the state and local level? Accountability and Competence ▶ In addition to eliminating incompetent and extreme candidates, elections may also mitigate moral hazard by creating accountability. ▶ If politicians have to take costly actions, we need to motivate them. ▶ Managers we pay contingent on performance by using stock options and bonuses. ▶ We don’t use performance based pay with politicians, but voters must decide whether or not to reelect an incumbent. ▶ Has the incumbent performed well enough in office to deserve reelection? Do Voters Punish Incumbents for Bad Performance? ▶ Alt, de Mesquita and Rose (2011) exploit variation in U.S. gubernatorial term limits across states and time to empirically estimate two separate effects of elections on government performance. ▶ Holding tenure in office constant, differences in performance by reelection-eligible and term-limited incumbents identify an accountability effect: reelection-eligible governors have greater incentives to exert costly effort on behalf of voters. ▶ Holding term-limit status constant, differences in performance by incumbents in different terms identify a competence effect. The Empirical Model Formalizing these ideas, we obtain the following the regression model: performanceit = α1 first-term-eligibleit +α2 second-term-lame-duckit +α3 Xit + θi + δt + vit (11) where performance is measured by variables such as growth, debt finance costs, taxes per capita and expenditure per capita. Xit are control variables such as population growth, θi are state fixed effects and δt are time fixed effects. Comments ▶ The omitted category is first-term lame ducks. The coefficient on first-term- eligible, provides an estimate of the accountability effect, since it compares the performance of first-term eligibles to that of first-term lame ducks. ▶ The coefficient on second-term- lame-duck provides an estimate of the competence effect, since it compares reelected lame ducks to first-term lame ducks. ▶ Since performance is expected to be worst under first-term lame ducks, we expect both of these coefficients to be negative for spending, taxes, and borrowing costs and positive for economic growth. Accountability and Competence disentangling accountability and competence in elections 179 T ABLE 4 One-Term Limits vs. Two-Term Limits Dependent variables Expected signs on coefficients: Log of per capita spending 2 (1) (2) Log of per capita taxes 2 (3) (4) Borrowing cost 2 Economic growth 2 (5) (7) (6) First-term eligible 20.048** 20.065** 20.039** 20.039** 25.81** 214.04** 0.66** (Accountability) (0.012) (0.015) (0.014) (0.018) (2.18) (3.45) (0.27) Second-term lame 20.041** 20.050** 20.030** 20.029** 26.75** 214.54** 0.45** duck (Competence) (0.012) (0.015) (0.015) (0.018) (2.47) (3.44) (0.29) Sample includes governors Yes No Yes No Yes No Yes in office at time of two-term limit adoption? Observations 686 622 686 622 286 261 686 R2 0.98 0.98 0.98 0.98 0.72 0.75 0.69 (8) 0.82** (0.33) 0.54* (0.32) No 622 0.68 Note: The omitted category is first-term lame ducks. Controls: state income, population, percent elderly and school-aged, Democratic Governor, Democratic House, Democratic Senate, divided government, political competition in the House and Senate, governor’s years of prior political experience, state-specific time trends, state fixed effects, and year fixed effects. Robust standard errors in parentheses. *Significant at 10% level. **Significant at 5% level. Voter Turn-out ▶ The median voter theorem assumes that there no selective voting and differences in turn-out. ▶ Understanding voter turnout is a central problem in political economy. ▶ In large elections the probability of being pivotal or deciding the election is for all practical purposes zero. ▶ Hence, voters should not turn out to vote. ▶ Nevertheless, we see significant voter turn-out in important elections. ▶ The game theorists call this “the paradox of voting.” ▶ Most individuals probably vote because they consider it their civil duty. Conclusions ▶ In large cities residents have to delegate the decision making authority to members of a city council and a mayor who is the chief executive of the city. ▶ The core model of democracy suggests that elected governments will pursue policies preferred by the median voter. ▶ As a consequence, election efficiently solve the delegation problem. ▶ Moreover, elections allow voters to remove mayors from power that happen to turn out to be too extreme, incompetent or corrupt. ▶ This removal occurs at the ballot box and does not require the use of excessive force or even a public uprising against the elite which could be very costly. ▶ Elections only work if voters hold politicians accountable, i.e. if they do not reelect poorly performing politicians.