Prof. Bryan Caplan

Econ 849

Fall, 2001


Week 4: 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 often 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 Sweden) also had "plural voting," with extra votes for the aristocracy.  For a while Great Britain had plural votes for the well-educated.

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 a meaningless concept.  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 U.S., position on the liberal-conservative spectrum.