Party Move and
the Median Voter Theorem
1

Definition of the median voter theorem
= Political parties will pursue policies that appeal most to
the median voter.
= It explains why political parties often promote the similar
policies (예: 복지정책) to appeal to independent (moderate)
voters

One big condition is about the ideological distribution
of voters.
The theorem works if voters’ ideological distribution is a
normal distribution (bell-shaped).
 What happens if voters’ ideological distribution is bimodal?

Spatial Competition and
the “Power of the Median Voter”
2
Voting in a Congressional Committee over
Two Minimum Wage Proposals, X and Y
Five Senators A, B, C, D, and E and their minimum
wage level preferences as follows
Senator A:
Senator B:
Senator C:
Senator D:
Senator E:
the minimum wage should be abolished.
$2.00 per hour
$5.50 per hour
$6.50 per hour
$10 per hour (the highest level)
Five senators on the committee and
their minimum wage level preferences
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The Power of the Median Voter
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1) If senators choose between the two minimum wage
proposals, X ($3.50) and Y($7.00), which proposal will
prevail in this committee, X or Y?
Senators A, B prefer X vs. Senators C, D, E prefer Y
 3-2 majority decision in favor of proposal Y
The Power of the Median Voter
5
2) Suppose it was possible to make amendments and option X
was changed into $5.00/hr, leaving Y unchanged. Then,
which proposal will be chosen, X or Y?
This time, senators A, B, C prefer X vs. senators D, E prefer Y
 3-2 decision in favor of proposal X
The Power of the Median Voter
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3) Allow one more amendment and this time moving
Y precisely to Sen. C’s ideal minimum wage ($5.50),
then, what happens?
3-2 (C, D, E vs. A, B) majority favors proposal Y.
The Power of the Median Voter
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Then, no other amendment to X would allow it to
unambiguously defeat proposal Y.
The best thing supporters of proposal X could hope to do
would be to amend it so that X, too, perfectly correspond
to Sen. C’s position.
In conclusion, the motions in this example tend to
converge on Sen. C’s ideal minimum wage level.
By the way, who is Senator C?
Senator C is the median member (voter) of the
committee.  The Power of the Median Voter
Who in 2009 was going to be a critical member of the Senate
during the first year of the Obama presidency?
 한국 대통령과 정당정치에 적용 가능성? If Not, Why Not?
8
Woon (April 2009, 331): Predicting policy change in the Obama presidency
Party Position vs. My Position
Mean & Standard Deviation
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When a voter is deciding her electoral choice,
both party position & party unity (split)
matter.
 (Average)
mean.
 Party
Party position is represented by
unity(split) is represented by standard
deviation.
Party Position vs. Party Split
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


If the Democratic Party’s policy position is closer to
the voter’s ideal policy position, the voter will vote
Democratic.
What if, however, Democrats are too much divided?
Then, it is possible that this voter would end up
voting Republican, instead.
Hinich and Munger (1997, 125)
Mean and Standard Deviation:
(Ex) Party Position and Voters’ Choice
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

Voter i’s ideal policy position: X i
Party’s average policy position:
 Mean
X R for Rep

vs. X D for Dem
Party’s split:
 Standard Deviation
ER for R vs. ED for D
Mean vs. Standard Deviation:
(Ex) Party Position and Voters’ Choice
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IF ( X i  X R ) 2  ER  ( X i  X D ) 2  ED
Then, voter i will vote for Republican Party.
BECAUSE,
1) The smaller the difference between voter’s position and
party’s position, the better.
2) The smaller the party split, the better.
3) With both party position and split taken into account,
vote i will vote for R, when the condition above is met.
If X i  6, X R  2, X D  4, ER  2, ED  16
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
If we partially use the formula to only consider the
difference between this voter and mean party position,
then
( X i  X R ) 2  (6  2) 2  16

( X i  X D ) 2  (6  4) 2  4
Which party shows a smaller distance with voter i’s
position?
 It is D (4), not R (16)
 So, will this voter vote for the Democratic Party,
whose average policy position is closer to his or
hers?
Wait a minute!!! We also have to consider party split as
well as party average position. Now, let’s use the full
formula to consider party split as well.
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As for the Republican Party,
( X i  X R ) 2  ER  (6  2) 2  2  18
As for the Democratic Party,
( X i  X D ) 2  ED  (6  4) 2  16  20
Now, after taking party split (sd) into account, which
party is a better fit to this voter?
 It is the Republican Party! (18), not the Democratic Party
(20)
Mean and SD for party politics
16



In short, this voter will vote for Republican Party after
considering not only party position (mean) but also party split
(standard deviation).
Conclusion:
“In spite of party position (mean) being close to a voter’s
preference, the voter could end up supporting the rival party,
due to party split (standard deviation).”
Again, party labels offer a shorthand cue that keeps
voting decisions cheap and simple, if and only if the labels
are fully informative.
 A high level of division  a high level of uncertainty 
then, party labels are not necessarily informative
Which Party System do you prefer?
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


Party Polarization
(정당양극화)
No room for negotiation
What about “Responsible
Party System”?



Ready to compromise
No difference between
the parties
What about “Third Party
or 안철수 현상”?