Politics through the Lens of Economics
Lecture 12: Voter Turnout
20 December, 2017
Masayuki Kudamatsu
Term Paper Timeline
| Wed 17 January | My last lecture |
| Wed 24 January | Workshop |
| Thu 15 February (9 am) | Submission deadline |
Read pages 24-108 of this book during the winter holidays
Recap of
when we can say a theory explains reality
Theory
II
Assumptions
Predictions
+
Hold in reality?
Consistent with reality?
The political agency model
Theory
II
Assumptions
Predictions
+
Citizens want a particular policy
Incumbent will be kicked out
if he/she fails to deliver the policy
Can the political agency model explain
why the sales of cigarettes isn't banned in Japan
Discussion Time
Aim to fail !
Motivation for Today
Citizens always vote, never abstain
In the previous lectures we assumed:
In reality:
Not every voter turns out at national elections
Question for Today
Why do some people vote while others abstain?
Four models of voter turnout
Information aggregation model
Mobilization model
Pivotal voter model
Ethical voter model
Today's Road Map
Four models of voter turnout
Information aggregation model
Mobilization model
Pivotal voter model
Ethical voter model
Today's Road Map
Economists think... (cf. Lecture 1)
We take an action if
Benefit
>
Cost
Applying this logic to going to poll
Benefit
>
Cost
Citizens go to poll if
Citizens abstain if
Benefit
Cost
<
Applying this logic to going to poll
Benefit
>
Cost
Citizens go to poll if
Citizens abstain if
Benefit
Cost
<
What's the benefit of going to poll?
Benefit of going to poll
Victory of my favorite candidate
weighted by
Probability
of my vote being pivotal
If I vote A, A wins.
But if I vote B, B wins.
Benefit of going to poll
Victory of my favorite candidate
weighted by
Probability
of my vote being pivotal
If I vote A, A wins.
But if I vote B, B wins.
How large is this probability?
Probability of my vote being pivotal
In a large election (e.g. national elections)
An individual vote will almost never change the election outcome
100,000,000+ voters across Japan
Your single vote matters only when
those who vote are equally split between two top candidates
Probability of my vote being pivotal
If we assume whether each citizen votes is random
we can calculate the probability of being pivotal
See Myerson (2000) for detail.
With 5 million citizens, it's only
0.00000081079%
Optimal behavior of citizens
>
Citizens go to poll if
Cost
Victory of my favorite candidate
x
Probability of my vote being pivotal
0.00000081079%
1 yen
124 million yen
This seems very unlikely
Implication
Only a small cost of voting
Bad weather
Schedule conflict
will then dissuade everyone from voting in national elections
Take to data...
In reality, many people, if not all, do vote in a large election
In poorer countries, people even form a long queue to vote
Image source: The Telegraph (2014)
South Africa in 2014
Take to data...
Very small
benefit from
going to poll
Non-zero
turnout
in reality
vs
Zero
To solve this puzzle, we need to assume the cost of voting is
or
Negative
(i.e. voting per se makes people happier)
Four models of voter turnout
Information aggregation model
Mobilization model
Pivotal voter model
Ethical voter model
Today's Road Map
Cost of voting
Zero
Negative
Negative
Each approach has a challenge
If the cost of voting is zero
Why do some people abstain from voting?
If the cost of voting is negative
Why do some people value voting per se?
Four models of voter turnout
Information aggregation model
Mobilization model
Pivotal voter model
Ethical voter model
Today's Road Map
The full-fledged model is highly mathematical
Here we see a simple version of the model
Information aggregation model
Voter 1: always prefer candidate 1
Consider an election with two candidates, 1 and 2
(Could also be a referendum on the proposed policy)
Suppose there are four voters
Voter 2, 3, 4: prefers the "correct" candidate
Voters 2, 3: do not know which candidate is "correct"
Voter 4: knows which candidate is "correct"
The majority rule decides which candidate wins
Flip a coin if it's a tie
Information aggregation model (cont.)
Citizen 1's optimal voting
Go to poll and vote candidate 1
Cost of voting is zero
A very small probability of being pivotal
is enough for citizen 1 to go to poll
Citizen 4's optimal voting
Go to poll and vote the correct candidate
Cost of voting is zero
A very small probability of being pivotal
is enough for citizen 4 to go to poll
Summary so far
Voter 1 goes to poll and vote candidate 1 (by assumption)
Voter 4 goes to poll and vote candidate 1 if 1 is correct
candidate 2 if 2 is correct
Summary so far
Voter 1 goes to poll and vote candidate 1 (by assumption)
Voter 4 goes to poll and vote candidate 1 if 1 is correct
candidate 2 if 2 is correct
If 1 is correct
2 vs 0
If 2 is correct
1 vs 1
Proposed equilibrium
Voter 2 votes 2
Voter 3 abstains
We check if these actions are optimal
given the other voter's behavior
Voter 2's optimal voting
Given that voter 3 abstains...
If 1 is correct
2 vs 0
If 2 is correct
1 vs 1
Voter 2's optimal voting
If 1 is correct, 1 will win anyway
If 1 is correct
2 vs 0
Voter 2's optimal voting
If 2 is correct, 2 will win for sure by voting 2
If 2 is correct
1 vs 1
Voter 2's optimal voting
If 1 is correct, 1 will win anyway
Voting 2 is optimal
If 1 is correct
2 vs 0
If 2 is correct
1 vs 1
If 2 is correct, 2 will win for sure by voting 2
Voter 2's optimal voting
Voting 2 is optimal
If 1 is correct
2 vs 1
If 2 is correct
1 vs 2
If 1 is correct, 1 will win anyway
If 2 is correct, 2 will win for sure by voting 2
Voter 3's optimal voting
Given that voter 2 votes 2...
If 1 is correct
2 vs 1
If 2 is correct
1 vs 2
Voter 3's optimal voting
If voting 1...
Voter 3's optimal voting
If 1 is correct
2 vs 1
If voting 1...
The outcome won't change if 1 is correct
Voter 3's optimal voting
If 2 is correct
1 vs 2
If voting 1...
A wrong candidate can win if 2 is correct
Voter 3's optimal voting
If 2 is correct
1 vs 2
If voting 1...
A wrong candidate can win if 2 is correct
The outcome won't change if 1 is correct
No reason to vote 1
If 1 is correct
2 vs 1
Voter 3's optimal voting
If voting 2...
Voter 3's optimal voting
If 2 is correct
1 vs 2
If voting 2...
The outcome won't change if 2 is correct
Voter 3's optimal voting
If 1 is correct
2 vs 1
If voting 2...
A wrong candidate can win if 1 is correct
Voter 3's optimal voting
If 1 is correct
2 vs 1
If 2 is correct
1 vs 2
If voting 2...
The outcome won't change if 2 is correct
A wrong candidate can win if 1 is correct
No reason to vote 2
Voter 3's optimal voting
If abstaining...
Voter 3's optimal voting
If 1 is correct
2 vs 1
If 2 is correct
1 vs 2
If abstaining...
The correct candidate wins in both cases
Abstention is optimal
Summary of uninformed voters' behavior
Voter 3 abstains to let the informed voter 4 be decisive
Given that voter 2 votes 2
Voter 2 votes 2 to let the informed voter 4 be be decisive
Voter 1 always votes 1 even if 1 is wrong
By voting 2, it's a tie so the informed voter 4 can decide
Given that voter 3 abstains
Implication
Some people advocate we must go to the polls
Don't listen to them
if you really don't know whom to vote
and no candidate is ideologically popular
Do uninformed citizens really abstain?
Many studies show the correlation
But those who want to vote may try harder to obtain information
A referendum in Copenhagen has a better answer
Do uninformed citizens really abstain?
Decentralization experiment in Copenhagen
Jan 1997
Primary schools, daycare, elderly care, etc.
Experiment was evaluated by a consulting firm
4 out of 15 districts start the experiment
of decentralizing the city administration
Late 1999
Sep 2000
Referendum on whether to extend decentralization
to all districts or abolish it
The majority vote for abolishing
Jan 2002
Experiment was terminated
Testing whether information raises turnout
Citizens in the 4 experiment districts
More informed about the benefit of decentralization
Turnout should be higher than in the other 11 districts
Not by their own choice but by external forces (i.e. city govt)
Data collection
Telephone survey of citizens in Copenhagen
conducted 2 months after the referendum
Ask their opinions on the decentralization experiment
Measuring informed-ness
Went well
Medium well
Bad
Don't know
Informed
Uniformed
Evidence from a referendum in Copenhagen
| Districts | % of informed citizens | Turnout (%) |
|---|---|---|
| Experiment | ||
| Other |
Source: Table 2 of Lassen (2005)
Evidence from a referendum in Copenhagen
| Districts | % of informed citizens | Turnout (%) |
|---|---|---|
| Experiment | 61.9 | |
| Other | 49.1 |
Source: Table 2 of Lassen (2005)
Evidence from a referendum in Copenhagen
| Districts | % of informed citizens | Turnout (%) |
|---|---|---|
| Experiment | 61.9 | 78.4 |
| Other | 49.1 | 69.0 |
Source: Table 2 of Lassen (2005)
More voters abstain in response to a larger cost of voting such as
Bad weather
Registration requirement (not in Japan, though)
Time to think about whom to vote
Distance to the polling station
So the cost of voting is NOT zero...
Data shows
Limitation of the information aggregation model
The cost of voting is assumed to be zero
We need to assume voting per se is valuable
Where does the benefit of voting come from?
Voters belong to groups of like-minded people
with the same preference over candidates
Cast a ballot if there is a consumption benefit from doing so
Two approaches
Mobilization model
Ethical voter model
Some economists propose group-based voting models in which
Four models of voter turnout
Information aggregation model
Mobilization model
Pivotal voter model
Ethical voter model
Today's Road Map
The leader of like-minded people's group
determines the level of turnout among his/her group
To do so, the leader allocates costly resources to voters
Mobilization model
e.g.
Trade Union (such as 連合 with 6m+ members)
Environmental groups
Religious groups (such as 創価学会 with 8m+ households)
Then it boils down to a model of costly voting with a few voters
Mobilization model (cont.)
With a few voters, the probability of being pivotal is not too small
Each group's leader
chooses # of votes for his/her favorite candidate
Limitation of the mobilization model
Unclear how leaders affect each voter's decision to vote
Social pressure?
Then why does each voter punish those abstaining?
How does each voter monitor the behavior of each other's?
Four models of voter turnout
Information aggregation model
Mobilization model
Pivotal voter model
Ethical voter model
Today's Road Map
Ethical Voter Model
Basic idea: "rule-utilitarian"
e.g.
Why don't some people throw away rubbish on street?
They choose the behavior that
if everyone follows the same behavior
society is in the best shape
Ethical Voter Model
This seems applicable to voting
Voters are motivated by a sense of civic duty
They cast a vote based on how well society is
(e.g. unemployment rate)
not just on how well they themselves are doing
Basic idea: "rule-utilitarian"
Again the full-fledged model is quite mathematical
We discuss a simple version of the model to show the main idea
Ethical Voter Model (cont.)
Consider two voters in a referendum
Both voters prefer
a proposal to be approved
The proposal is approved
if at least one voter votes yes
Ethical Voter Model (cont.)
Cost of voting on the day of the referendum: uncertain
Weather, How busy they are, Illness, etc.
Voters collectively decide
a cutoff voting cost below which they go to poll
By following this rule
they derive psychological benefits larger than the cost of voting
2's cost
1's cost
2's cost
1's cost
Cutoff
Cutoff
2's cost
1's cost
Cutoff
Cutoff
At least one voter casts a yes vote
so the proposal passes
2's cost
1's cost
Cutoff
Cutoff
Neither votes
so the proposal is rejected
2's cost
1's cost
Cutoff
Cutoff
A higher cut-off makes the adoption more likely
But the expected cost of voting increases
Extra
cost
Cutoff
The higher the cutoff, the larger the extra cost
Increase the cutoff from 10 to 11: extra cost is 11
11 to 12
12
Extra
benefit
Cutoff
The higher the cutoff, the smaller the extra benefit
2's cost
1's cost
Cutoff
Cutoff
The higher the cutoff, the smaller the extra benefit
Extra
benefit
or cost
Cutoff
Optimal cutoff maximizes the net benefit
Optimal
cutoff
Extra benefit
Extra cost
Extra
benefit
or cost
Cutoff
If the benefit from passing the proposal is larger
Optimal
cutoff
Extra benefit
Extra cost
Extra
benefit
or cost
Cutoff
If the benefit from passing the proposal is larger
Optimal
cutoff
Extra benefit
That is, turnout is higher
Extra cost
Turnout is higher for more important elections
Turnout for national elections in Japan
Lower House
Upper House
Supporting evidence:
Limitation of ethical voter model
How can voters collectively decide the cost cutoff?
Today's lessons
1
2
3
The standard logic of economics
cannot explain why some people go to poll and others don't
(If the cost of voting is zero)
Uninformed citizens may prefer abstaining
Some citizens must benefit from voting per se
but we don't exactly know why
Next Lecture...
Lobbying
Image source: www.thenation.com/article/shadow-lobbying-complex/
Merry Xmas & Happy New Year !
This lecture is based on the following academic articles:
Feddersen, Timothy J. 2004. “Rational Choice Theory and the Paradox of Not Voting.” Journal of Economic Perspectives 18(1): 99–112.
Lassen, David Dreyer. 2005. “The Effect of Information on Voter Turnout: Evidence from a Natural Experiment.” American Journal of Political Science 49(1): 103–18.
Politics through the Lens of Economics (2017): Lesson 12 Voter Turnout
By Masayuki Kudamatsu
