Politics through the Lens of Economics

Lecture 2: Median Voter Theorem

Masayuki Kudamatsu

11 October, 2017

Did you pick a policy?

(for your written assignment)

How to make a case in writing

"Five Paragraph Essay" (taught in US high schools)

1 Motivation & Main Idea

5 Conclusion

4 Deal with counter arguments

3 Cases for Main Idea

2 Background

Motivation & Main Idea

Main idea: Statement that you will prove to be the case

"Median Voter Theorem cannot explain why the gun control hasn't been adopted in the United States."

Motivation: Reasons why we should care about your statement

1st paragraph

"The lack of the gun control in the U.S. causes the high murder rate in the country..." (then cite statistics etc.)

Better to be short, at most 2 paragraphs

e.g.

Background

Any information that will repeatedly be used in the arguments below

Description of political institutions in the U.S.

History of (lack of) gun control in the U.S.

2nd paragraph

DO NOT include unnecessary information in this paragraph

e.g.

Better to be short unless it's really necessary to provide lots of information beforehand

Cases for Main Idea

Reasons why the main idea is correct

"Opinion polls suggest the vast majority of Americans are in favour of gun control." (and then cite statistics)

3rd paragraph

e.g.

Use more than one paragraph if there are many reasons

Deal with counter-arguments

Reasons why the counter-arguments are wrong

"The majority of Americans may not trust in government to enforce gun control. But ..."

4th paragraph

e.g.

Talk to people to learn the list of counter-arguments

Use more than one paragraph if there are many counter-arguments

It's okay to admit the limitation of your argument

Conclusion

Restate the main idea

"For all the reasons described above, the Median Voter Theorem cannot explain why Americans have failed to adopt the gun control.

5th paragraph

e.g.

Then add a statement for future

"We need a better theory of politics so that we will be able to find a solution to stop Americans from dying by gunshots."

e.g.

A great textbook for written assignments

Buy at amazon.co.jp

Read pages 24-108 twice

First, before starting to write

Second, when done with the first draft

The book also discusses how to write

Novels (pp. 110-183)

Blog posts (pp. 186-242)

Motivational Examples

for

Median Voter Theorem

Motivational example #1: Japan

Similar economic policies between LDP and DPJ in the mid-2000s.

Figure 3 of Kubo (2016)

Motivational example #2: UK

"Third Way" by Tony Blair (Prime Minister 1997-2007)

keeptonyblairforpm.wordpress.com/2012/05/01/a-new-dawn-remembered-1997-tony-blair-new-labours-first-election-victory/

Image sources:

chapter6economictimeline.wikispaces.com/Blair%27s+Third+Way

Motivational example #3: USA

Donald Trump advocates for big government

(Talking about healthcare) Everybody’s got to be covered. This is an un-Republican thing for me to say... Everybody’s going to be taken care of much better than they’re taken care of now. ...the government’s gonna pay for it.

Image/quote source: thefederalist.com/2016/01/27/5-times-trump-told-you-he-loves-big-government/

Median Voter Theorem says

these are all politicians' optimal behaviour

Today's Road Map

What is Median Voter Theorem?

Evidence for the theorem

Limitations of the theorem

Graphic proof of the theorem

Three assumptions for the theorem

Today's Road Map

What is Median Voter Theorem?

Evidence for the theorem

Limitations of the theorem

Graphic proof of the theorem

Three assumptions for the theorem

("Model of the World")

(Optimization + Equilibirum)

(Empiricism)

What is Median Voter Theorem?

We break down this question into three:

What is Median?

What is Median Voter?

What is Median Voter Theorem?

Median

image source: betterexplained.com/articles/how-to-analyze-data-using-the-average/

50% below

50% above

Median Voter

The voter whose ideal policy takes the median value

Let's find the median voter in this class room.

What is your ideal consumption tax rate?

Value-added tax rate across OECD countries in 2015

image source: www.abc.net.au/news/2015-07-30/fact-check-rate-of-gst/6650406

VAT tax revenue as % of total tax revenue in 2014

Source: OECD (2017) "Goods and services as percentage of total taxation" Government At A Glance 2017

Median Voter Theorem

Median voter's ideal policy is implemented

Voters care about one single policy

Two candidates compete

Winner keeps electoral promise

In a model of the world where:

Today's Road Map

What is Median Voter Theorem?

Three assumptions for the theorem

Graphic proof of the theorem

Limitations of the theorem

Evidence for the theorem

Voters care about one single policy

Two candidates compete

Winner keeps electoral promise

There are so many policy issues

But an opinion on one policy often predicts the one on another

abortion

marijuana

same-sex marriage

e.g.

We can bundle policies into a few

Social: Conservative vs Liberal

Economic: Small vs Big government

Diplomatic: Hawk vs Dove

Assumption #1

Voters care about one single policy

Two candidates compete

Winner keeps electoral promise

But do voters care about

only one bundle of policies?

Very strong assumption

But simple enough as a starting point

Assumption #1

Voters care about one single policy

Two candidates compete

Winner keeps electoral promise

Quite common for plurality elections

e.g. Osaka gubernational election in 2015

Assumption #2

Voters care about one single policy

Two candidates compete

Winner keeps electoral promise

But not plausible for proportional representation electoral system

Proportional representation

Plurality

Mixed

Image source: thepoliticalforums.com/threads/8211-The-Case-For-Proportional-Representation

Assumption #2

Voters care about one single policy

Two candidates compete

Winner keeps electoral promise

Assumption #3

Perhaps unrealistic assumption

Image source: http://blog.goo.ne.jp/raymiyatake/e/9064fbdfab41c2a66881f1403be58494

Voters care about one single policy

Two candidates compete

Winner keeps electoral promise

Plausible if breaking promise means defeat in next election

Assumption #3

Image source: https://blogs.yahoo.co.jp/nisekoannnuburi/26318040.html

Today's Road Map

What is Median Voter Theorem?

Three assumptions for the theorem

Graphic proof of the theorem

Limitations of the theorem

Evidence for the theorem

To see why the theorem holds,

use the two defining features of economics:

optimization & equilibrium

Look at voters' optimization

Figure out which candidate wins

Consider candidate's optimization

Check whether it's the equilibrium

Step 1

Step 2

Step 3

Step 4

Voter's

ideal

Policy

Candidate A's promise

Candidate B's promise

Vote for A

Voter's optimization

Choose the candidate whose promise is closer to their ideal policy

Step 1

Voter's

ideal

Policy

Candidate A's promise

Candidate B's promise

Vote for B

Choose the candidate whose promise is closer to their ideal policy

Voter's optimization

Step 1

Voter's

ideal

Policy

Candidate A's promise

Candidate B's promise

Vote for B

Choose the candidate whose promise is closer to their ideal policy

Voter's optimization

Step 1

Voter's

ideal

Policy

Candidate A's promise

Candidate B's promise

Vote for A

Choose the candidate whose promise is closer to their ideal policy

Voter's optimization

Step 1

Choose the candidate whose promise is closer to their ideal policy

Policy

Candidate A's promise

Candidate B's promise

Vote for A

Vote for B

Voter's optimization

Step 1

This is each voter's best affordable option

Which candidate wins?

Depends on where the median voter is

50% below

>50%

Which candidate wins?

Step 2

Summary

>50%

Candidate's optimization

Step 3

Policy

Candidate A's promise

Candidate B's promise

Median

Voter

Both candidates want to be closer to median than the other

Candidate's optimization

Step 3

A wants to pick x to be closer to median than B

Policy

Candidate A's promise

Candidate B's promise

Vote for A

Vote for B

Median

Voter

>50%

Candidate's optimization

Step 3

How about Case 3?

B wants to pick x to be closer to median than A

Policy

Candidate A's promise

Candidate B's promise

Vote for A

Vote for B

Median

Voter

>50%

Candidate's optimization

Step 3

In Case 4

In Case 5, each wants to be closer to median to win for sure

Policy

Candidate A's promise

Candidate B's promise

Vote for A

Vote for B

Median

Voter

Candidate's optimization

Step 3

Policy

Candidate A's promise

Candidate B's promise

Median

Voter

Both candidates want to be closer to median than the other

Candidate's optimization

Step 3

In all cases

What is the equilibrium?

Step 4

Remember what the equilibrium is?

What is the equilibrium?

Candidates change their policy when neither picks median

Policy

Median

Voter

Step 4

Candidate picks median if the other already picks median

Policy

Median

Voter

What is the equilibrium?

Step 4

When both promise median...

Policy

Every voter is indifferent between A & B

A & B

Median

Voter

What is the equilibrium?

Step 4

Policy

Median

Voter

Every voter votes randomly

A & B

When both promise median...

What is the equilibrium?

Step 4

Policy

Median

Voter

Each candidate wins 50% of the chance

A & B

When both promise median...

What is the equilibrium?

Step 4

Policy

Median

Voter

Each candidate wins 50% of the chance

A & B

When both promise median...

Neither A nor B benefits from changing their choice

What is the equilibrium?

Step 4

Policy

Median

Voter

Each candidate wins 50% of the chance

A & B

This is the equilibrium!

When both promise median...

Neither A nor B benefits from changing their choice

Policy

Median

Voter

A & B

This is the equilibrium!

Winning candidate will then implement

median voter's ideal policy

Policy

Median

Voter

Each candidate wins 50% of the chance

A & B

Equilibrium is stark, not very realistic

Policy

Candidate A's promise

Candidate B's promise

Median

Voter

But the main lesson is the centripetal force in politics

Economics is sometimes a bit like a fairy tale

Unrealistic, but a lesson relevant for reality

Today's Road Map

What is Median Voter Theorem?

Three assumptions for the theorem

Graphic proof of the theorem

Limitations of the theorem

Evidence for the theorem

Limitations of Median Voter Theorem

Important to understand for you to figure out

whether the Theorem can explain the policy of your choice

for term paper

Limitation of Median Voter Theorem #1

e.g. economic policy + foreign policy

We take up this issue in Lecture 6: Probabilistic Voting Model

When voters care about more than one policy

Hawk

Dove

Small govt.

Big govt.

When politicians cannot commit to electoral promise

Limitation of Median Voter Theorem #2

Image source: www.cartoonstock.com/directory/p/political_commitment.asp

Plausible if politicians have their own ideal policy

With no commitment,

Winning candidate will be the one

whose ideal policy is closest to median

Limitation of Median Voter Theorem #2

Policy

A wins!

Vote for A

Vote for B

Median

Voter

>50%

Then why the median voter doesn't become a candidate?

We will look at this issue in Lecture 4: Citizen-candidate Model

Limitation of Median Voter Theorem #2

Policy

Median

Voter

("I will run for office!")

Limitation of Median Voter Theorem #3

e.g. Tokyo gubernatorial election in 2016

image source: headlines.yahoo.co.jp/hl?a=20160719-00010001-bfj-soci

When there are more than two candidates

Policy

Median

Voter

A & B & C

Suppose all three parties promise median voter's ideal policy

Limitation of Median Voter Theorem #3

When there are more than two candidates

Policy

Median

Voter

A & B

Any party (say, C) wants to deviate a little

Vote for C

(almost 50%)

Vote for A or B

(each gets 25%)

Limitation of Median Voter Theorem #3

When there are more than two candidates

We need to consider what determines # of candidates

When there are more than two candidates

Limitation of Median Voter Theorem #3

We will look at this issue in Lecture 4: Citizen-candidate Model

As we see

economists start with a simple (if unrealistic) model of the world

Using this simple model as the benchmark

economists modify the model to understand the world further

image source: babsreviews.com/online-marketing-this-week.html

Today's Road Map

What is Median Voter Theorem?

Three assumptions for the theorem

Graphic proof of the theorem

Limitations of the theorem

Evidence for the theorem

Remember the 3rd defining feature of economics?

Evidence for Median Voter Theorem

Collect many observations to see if we get the graph below

median voter's ideal policy

politician's policy

Evidence for Median Voter Theorem

We do see this graph for homogeneous districts in U.S. (Gerber and Lewis 2004)

median voter's ideal policy

C causes A & B

Women's suffrage

in US states

in early 20th century

Image Source: crazymaggiethecat.wordpress.com/2015/09/03/obamas-our-wives-our-mothers-our-daughters-rhetoric/

Women care more about children

Female suffrage will move the median voter's ideal policy more child-friendly

Natural experiment:

Spending on child health

Median

before

women's suffrage

image source: www.wired.com/2015/05/redesigned-ladies-restroom-icon-cleverly-skirts-skirt/

Men

Women

Spending on child health

Median

after

women's suffrage

Median

before

women's suffrage

image source: www.wired.com/2015/05/redesigned-ladies-restroom-icon-cleverly-skirts-skirt/

Year of Women's Suffrage across US States

Figure I of Miller (2008)

Municipal health spending rose after women's suffrage

Figure II of Miller (2008)

Hygiene campaign spending

Child mortaliry dropped after women's suffrage

Figure IV of Miller (2008)

(accounting for 10% of the decline during 1900-1930)

Summary

Policy

Median

Voter

Politicians tend to pick the policy closer to median

Next lecture

We will apply the Median Voter Theorem to understand...

Income Redistribution

image source: whitewraithe.files.wordpress.com/2014/01/richpoor.jpg

Next lecture

We will apply the Median Voter Theorem to understand...

Democratization

image source: en.wikipedia.org/wiki/Liberty_Leading_the_People

Medium Voter Theorem

Chapter 1 of Gelbach (2013)

Evidence for Medium Voter Theorem

Miller (2008)

This lecture is based on the following academic articles and books: