Suppose we have single-peaked voters

Suppose we have single-peaked voters located on a one-dimensional left-right dimension.

Suppose that voters vote for the candidate closest to them in distance and that they flip a coin if

two candidates are equally distant (so that we can count one-half vote for each candidate from

that voter). Further suppose that we know which party each voter belongs to, and that the eleven

voters are located as follows:

Voter
Albert
Beth
Curt
Eustice
Frank
Gail
Hope
Ivan
Joe
Katherine
Larry

Ideological Location
1
1
3
4
6
6
7
8
9
9
10

Party
D
D
D
D
D
R
R
R
R
R
R

The letter “D” stands for “Democrat” and the letter “R” for Republican. These are the party
affiliations of the voters.

a) [2 pts] Given this distribution of voters, where should the two parties, Democrats and
Republicans, locate in a general election (where everyone can vote) if they can locate
anywhere they want to and they know this distribution of voters and all they care about is
winning elections.
b) [4 pts] Suppose there are primaries in each party in which only the members of that party
can vote:
i. If there are two candidates in the Democratic primary, where should they locate if
they can move anywhere they want to and if they only care about winning the
primary?
j. If there are two candidates in the Republican primary, where should they locate if
they can move anywhere they want to and if they only care about winning the
primary? Write in space below:
c) [4 pts] Suppose once the party’s candidates have taken a position in the primary as in (b)
above, they must stay there. Who will win the general election (when everybody can
vote and one candidate emerged victorious in each party’s primary)? Indicate what the
vote will be in the general election for each candidate.
d) [3 pts] NOW suppose that as in (b) above there are primaries in each party but the
Democratic party primary is uncontested (no opposition for the candidate) while the
Republican party primary is contested with two candidates.
i. [1 pt] If there is only one candidate in the Democratic primary (which assures the
victory of that candidate), where should the candidate locate if he or she can move
anywhere and would also like, if possible, to be in a good position for the general
election?
j. [2 pts] If there are two candidates in the Republican primary, where should they
locate if they can move anywhere they want to and if they must first win the
primary, but would also like, if possible, to be in a good position for the general
election?
e) [2 pts] Suppose once the party’s candidates have taken a position in the primary as in (d)
above they must stay there. Who will win the general election (when everybody can
vote)? Indicate what the vote will be (for each party) in the general election.

f) [5 pts] Comment on this: “Primaries can put a party’s candidates in a bad position to win
the general election.” Is this always true? What has to be true of the party for it to be
true?

Explanation & Answer

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