Prof.
Bryan Caplan
bcaplan@gmu.edu
http://www.bcaplan.com
Econ
854
Week 2:
Voting, I: The Basics
I.
Rational, Instrumental Voting
A.
Let us begin with two standard assumptions about voters. We will think about relaxing these in
the second part of the course, but for now we will stick with them.
B.
Assumption #1: Rational expectations. Voters are often wrong, but their errors
balance out to zero.
C.
Assumption #2: Instrumental goals.
Voters care about nothing except the policies they get. They aren't interested in personalities,
entertainment, impressing their friends with their social conscience, etc.
D.
Neither of these require that voters be selfish. They might be rational, instrumental
voters who care only about the liberalism/conservatism of policy, for example.
II.
Single-Peaked Preferences
A.
Next, let us assume that voters' preferences are
"single-peaked." This
means that voters have an "ideal point" (aka "bliss
point"), and their utility declines monotonically as policy moves away
from it.
B.
For example, one voter's ideal point might be a world where people are
allowed to own any weapon up to and including a machine gun. This voter would be less happy in both:
1.
A world where fewer weapons were legal (e.g. where the semi-automatic
gun is the most dangerous legal weapon).
2.
A world where more weapons are legal (e.g. artillery, tanks, nuclear
bombs).
C.
Aren't all preferences "single-peaked"? Probably not. A classic example involves a wealthy
parent. If spending on education is
high, she sends her kids to public school.
But otherwise she sends them to private school, and gets no benefit from
education spending. So her
preferences would look like this:
1.
#1 pick: high spending
2.
#2 pick: low spending
3.
#3 pick: medium spending
III.
Two-Party, Winner-Take-All Elections
A.
Suppose we have a two-party (or two-candidate) election. Voters care about and are perfectly
informed about party positions on exactly one issue: liberalism versus
conservatism.
B.
The electoral rule is "winner-takes-all" - whoever gets more
votes wins.
1.
Picky point - ties. When in
doubt, assume ties are resolving by flipping a coin.
C.
Assumption about party/candidate motivation: They want to win, and care
more about that than everything else put together.
D.
The two parties compete in exactly one way: By taking a stand on the issue.
E.
Imagine graphing the distribution of voter ideal points. (Non-normality is OK).
F.
The electorate may be divided into three groups: those who definitely
vote for the more liberal party, those who definitely vote for the more
conservative party, and the people in the middle, who pick whichever party is
closer to them.
IV.
Political Competition and Platform Convergence, I
A.
Question: How can you get
more votes?
B.
Answer: Move to the
center. You don't lose any of the
extreme votes, and get more of the "swing" votes.
C.
In equilibrium, parties' platforms cannot be different, because both
parties gain votes by moving closer to each other. 
.
1.
So you can't have an equilibrium where one party gets more than 50% of
the votes. You can always win 50%
by simply offering exactly the same platform as your competitor.
D.
Thus, equilibrium platforms "converge" - both parties offer
the same policy. But to what?
E.
Could the equilibrium platform ever be one where both parties are above
the median of the distribution of voter preferences? No.
Why? Because one party would
get more than 50% of the votes by moving a little closer to the median. So 
.
F.
Could the equilibrium platform ever be one where both parties are below
the median of the distribution of voter preferences? No, for the same reason. So 
.
G.
Could the equilibrium platform be the median of the
distribution? Yes! If both parties are at the median, then
staying there gets you 50% of the votes, but moving a little to the left or
right gets you fewer than 50%.
H.
Thus, we arrive at the famous Median Voter Theorem: 
. Given the
preceding assumptions, both parties offer platforms identical to the bliss
point of the median voter.
V.
Voter Participation and Franchise Restrictions
A.
There are many factors that affect participation: age, education,
what's on the ballot... even the weather.
B.
If proportional amounts of all political persuasions don't vote,
the median stays the same, and so does the electoral outcome.
C.
But if participation changes in a disproportionate way, this changes
the median, and thereby changes the nature of the winning platform.
D.
There are also legal restrictions on voting.
1.
Non-citizens normally can't vote at all.
2.
Citizens have to register in advance to vote.
3.
Non-residents in a state can't vote in that state.
4.
Convicted felons and children can't vote.
E.
In the past, there were other legal restrictions on the franchise.
1.
Non-property-holders
2.
Non-whites
3.
Women
4.
18-21 year-olds
F.
In the past, some countries (like
G.
Corporations have voting proportional to shares ownership, and turnout
of small share-holders is typically very low. Thus, the median corporate voter is
usually a large shareholder with a big stake in the company's financial
success.
VI.
The Effect of Fringe Parties
A.
In many cases, we see people with extreme preferences deciding not to
vote because "their" candidate is an unprincipled
"sell-out."
B.
Fringe, "extremist" parties do much the same thing. For example, if a far-left Green Party
exists, then the Democrats have to worry about two things:
1.
Extremists stay home
2.
Extremists vote Green
C.
If extremists drop out irrevocably, and no one else has a chance
of joining them, this moves the median voter - and both parties - in the
opposite direction! If the 5% of
most-left-wing Democrats vote Green, the median of the remaining voters shifts
to the right.
D.
If extremists drop out conditional on "their" party's
position, it induces platform divergence.
Real-world parties have to trade-off extra moderate votes for foregone
extremist votes.
VII.
Multi-Peaked Preferences and Intransitivity
A.
With multi-peaked preferences, the analysis of elections becomes far
more complicated because electoral outcomes may cease to be transitive.
B.
Transitivity seems like a trivial assumption for individual choice, and
for the most part it is. (Though
there are many experiments that "trick" people into making
intransitive choices).
C.
If someone has intransitive preferences, it is unclear what they would
choose. You could also become a
"money pump."
D.
Key conclusion: With multi-peaked preferences, electoral outcomes can
be intransitive, even though no individual voter has intransitive preferences!
E.
Proof by example. Going back to the school
case, imagine we've got 3 voters.
F.
Voter #1's preference ordering: {high, low, medium}
G.
Voter #2's preference ordering: {medium, high, low}
H.
Voter #3's preference ordering: {low, medium, high}
I.
Imagine giving this 3-person electorate two choices at a time.
1.
High versus low: 2 for, 1 against
2.
Low versus medium: 2 for, 1 against
3.
Medium versus high: 2 for, 1 against
J.
Notice: High beats low, low beats medium, and medium beats high!
K.
For many, this example shows that the "will of the people"
may be meaningless. What level of
education spending does "the people" "will" in this
example?
VIII.
Multiple Voting Dimensions
A.
The Median Voter Theorem only strictly holds if there is a single
issue.
B.
If there are two or more issues that parties take stands on, but only
one election, there is no guarantee that the median voter's preference will
prefer on any issue.
C.
Moreover, even with single-peaked preferences, multiple voting
dimensions make it possible for voting cycles to arise.
D.
At this point, you might say: "But all real-world elections
have multiple issues. So the Median
Voter Theorem is useless."
E.
Possibly so. But as we
shall see, there is considerable empirical evidence that platforms empirically
boil down to a single dimension - in the
IX.
Tiebout and Inter-Governmental Competition; Perverse Incentives
A.
For sub-national democracies, the “median voter” may be
even more endogenous than you think: People can move to the jurisdictions where
they are relatively close to the median voter, mitigating many complaints about
majority rule.
B.
The economist Tiebout went further, suggesting that democracy at the
local level is superfluous.
C.
Why? Because you can think
about local governments as perfectly competitive suppliers of local public
goods.
1.
If the benefit and tax package in a local area is unattractive,
residents move away to other localities with more attractive benefit/tax
packages. Thus, on the local level,
politicians face economic competition from other localities, as well as
political competition from other politicians.
2.
If there are decreasing returns to scale, localities can sub-divide to
the efficient level.
D.
Upshot: So even if you have doubts about the efficiency of democracy,
you might still conclude that local governments work well.
E.
One big problem with this argument: It assumes that competition between
non-profits works just like competition between for profits. Two problems:
1.
Problem #1: Lack of incentives - politicians don't get paid more when
the local economy does better
2.
Problem #2: Perverse incentives - their lives may be easier when things
don't go well
3.
The case of school choice
X.
Federalism: For and Against
A.
Within any nation, there are normally districts, states, or other
"sub"-governments.
B.
Definition: The more independent and powerful these sub-governments
compared to the central government, the more "federalist" they are.
C.
There are many popular arguments in favor of federalism that sound a
lot like standard economic arguments:
1.
Benefits of competition (Tiebout)
2.
Diversity of tastes
3.
Level of innovation
D.
However, throughout this century the
E.
Economic rationales?
1.
Externalities (e.g. cross-state pollution)
2.
Cost savings of uniformity
F.
Classic inter-state externality argument: "The race to the
bottom." States allegedly
competitively cut welfare spending to encourage recipients to leave the state.
G.
Then again, you might view "The race to the bottom" as a
pejorative way of describing the competitive outcome, and federal grants as a
grand effort to eliminate inter-state competition.
H.
Application: The race to the top?
The case of law enforcement.
I.
Question: Why doesn’t Tiebout competition prevent redistribution
from e.g. the childless to families, or from business to residential real
estate owners?