Voting for Public Goods (Fisher, Ch. 3) © Allen C. Goodman 2015

Bread and Schools Suppose that we live in a suburb. Suppose there are 10 residents. Each one earns $60,000. They can spend it on bread, or schools. 60 Bread Schools Prefers Bread Prefers Schools

Bread and Schools They have to pick a tax level that each one of them will pay. If they decide on $4,000, each will pay $4, Bread Schools Prefers Bread Prefers Schools

Bread and Schools Let’s add a few more “identical” people. 60 Bread Schools We have five possible levels of “schools” s1s1 s2s2 s3s3 s4s4 s5s5 s 1 > s 2 > s 3 > s 4 > s 5

Bread and Schools Alternatively, individuals 1-5 are willing to give up different amounts of bread to get school resources. 60 Bread Schools We have five different levels of taxes. s1s1 s2s2 s3s3 s4s4 s5s5 t 1 > t 2 > t 3 > t 4 > t 5

How do we decide? Consider a politician. She has to win an election, and she has to get enough votes by promising the “right” amount of school resources 60 Bread Schools Suppose she promises s 5. Person 5 is happy (he didn’t want much). But everyone else wanted more. So politician loses election 4-1 to someone who promises more. s1s1 s2s2 s3s3 s4s4 s5s Role Playing 2 Candidates

How do we decide? 60 Bread Schools Suppose she promises s 4. Persons 1, 2, and 3 are happier because they’re getting closer to what they want. But she’ll still lose 3-2. s1s1 s2s2 s3s3 s4s4 s5s Suppose she now promises s 3. She’ll win the election because Persons 1 and 2 are happier yet, and Person 3 is happiest, he’s getting exactly what he wants.

If you don’t believe me Bread Schools Suppose another politician promises s 2. Person 3 won’t be happy anymore because you’re providing MORE school resources than he wants … so he’ll vote against it. KEY POINT !!! The median voter is decisive. Eq’m school will be at s 3. Each voter will pay (60 - b 3 ) in taxes and get s 3. s1s1 s2s2 s3s3 s4s4 s5s b3b3

Median Voter and Optimum We’ve seen that we will agree on some particular amount, by majority vote. Is this amount economically optimal, based on the rule that we developed in the previous lecture? Why or why not!

What makes this work?

Single Peaked Preferences Suppose you had 3 people with indicated preferences. Suppose they’re not single-peaked, i.e. If they are single peaked, there is a clearly defined “winner” and the individual gets less satisfaction if he/she moves away from it. Less UEven less U lower Closer level to 1 st choice, but less preferred than 2 nd choice $ spent

Another Way to Look at It UAUA 468 UBUB 468 UCUC 468 Single peak Single peak ??

4,000 v. 6,000 UAUA 468 UBUB 468 UCUC 468 Single peak Single peak ?? Preferred! NOT We prefer 4,000 to 6,000!

6,000 v. 8,000 UAUA 468 UBUB 468 UCUC 468 Single peak Single peak ?? Preferred! NOT! Preferred We prefer 6,000 to 8,000!

4,000 v. 8,000 UAUA 468 UBUB 468 UCUC 468 Single peak Single peak ?? Preferred! NOT! NOT BUT!!! We prefer 8,000 to 4,000!

So? $4,000 beats $6,000 $6,000 beats $8,000, BUT $8,000 beats $4,000! Choices aren’t transitive

Why does this happen? Person C does not have single-peaked preferences, but is rather an extremist! … alternatively he/she HATES mediocrity. C becomes less and less happy until spending gets very low. C is unhappy with moderate positions. You can get fancier, but “single-peaked preferences” are desirable if we want to reach voting equilibria.

How much should we worry? If we believe in standard demand theory, we shouldn’t worry too much about the single-peaked problem Why? Price in $ Quantity Q* At Q*, we have optimal amount of Q. As we go further away in either direction, happiness ↓. Demand theory is broadly consistent with Single-Peaked preferences

Median Voter Theorem If voters’ preferences are single- peaked, if the choice to be made by voting is represented along a single continuum, if all alternatives are voted on, and if voters act on their true preferences, THEN the choice selected by majority vote is the median of the desired outcomes.

What does median voter model say? If you have some number of jurisdictions, one can argue that the levels of schools, fire protection, police protection are broadly consistent with consumer preferences. Is it perfect? –No, not all citizens vote. –If there are a lot of issues, the same citizen is not likely to be the median voter on every issue.

Median and Optimum Median may be close to optimum as determined by theoretical criteria. BUT, it may be either greater than or less than the optimum. By the very nature of the equilibrium, some substantial number might want more … and some other substantial number might want less.

C1C1 Other Models Some (generally conservative) economists propose a model in which government officials wish to: –Maximize the amount of government spending. –Remain in office. How does this work? Expenditure EvEv Price ($) E v is preferred by median voter If referendum is rejected, Expenditures revert to E r. ErEr Loss of Consumer Surplus of C 1.

C1C1 C1C1 Other Models Instead, according to these models, government officials, in trying to maximize expenditures, pick as much as E M. Why? How does this work? Expenditure EvEv Price ($) E v is preferred by median voter If referendum is rejected, Expenditures revert to E r. ErEr Loss of Consumer Surplus of C 1. C1C1 C1C1 EMEM

Comments Median voter model seems to address consumer preferences, BUT a large group of people are dissatisfied. Monopoly models may appeal to some voters, BUT they don’t explain how a government that continually does not satisfy median voter stays in power. Michigan’s Headlee Amendment makes it very difficult to raise taxes. Suggests that at least a lot of Michigan voters are concerned about governmental powers. NEXT! Chapter 4 NEXT! Chapter 4