Munger and Munger Slides for Chapter 5 Politics as Spatial Competition Outline of Chapter 5 Spatial model and spatial theory Spatial utility functions Assumptions and definitions Median voter theorem ID: 362196
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Slide1
Choosing in GroupsMunger and Munger
Slides for Chapter 5Politics as Spatial CompetitionSlide2
Outline of Chapter 5 Spatial model and spatial theory
Spatial utility functionsAssumptions and definitionsMedian voter theoremImplications of non-single-peaked preferences
Slides Produced by Jeremy Spater, Duke University. All rights reserved.
2Slide3
Spatial modelNature of voter preferences
Preferences represented by weighted distancesPrefer candidate who is “closest” to ideal pointEndogenous platform selectionCandidates select position based on predicted voter choices
Predictions about outcomes
Analyst can predict outcome from voter preferences and candidate positions
Allows analysis of counterfactuals
Slides Produced by Jeremy
Spater
, Duke University. All rights reserved.
3Slide4Slide5
Spatial theoryDifferent from weak orderings approach
Explicit utility function: distanceMedian voter determines election: Median Voter Theorem (MVT)Voters on edges can change their positions without influencing outcome
Outcome is stable under some circumstancesUnder some conditions, candidates converge in center
Under other conditions, outcome is polarized or indeterminate
Slides Produced by Jeremy Spater, Duke University. All rights reserved.
5Slide6
Foundations of spatial modelsPeople use “left”, “right”, and “center” to describe political positions
This usage originated in the French RevolutionPhysical positions of parties in National Assemblies and National ConventionLeft: Jacobins; Right:
GirondinsLeft generally refers to those wanting change
Right generally refers to those who prefer status quo or return to earlier policies
Slides Produced by Jeremy Spater, Duke University. All rights reserved.
6Slide7
Spatial utility functionsVoter perceives candidate as “platform” or “point in space”
Cartesian product of all policy positions taken by candidateEach issue is assigned a “salience” or weightIssues more important to the voter have higher weights
Some issues might have zero weightExample: Committee voting
Three committee members
Different ideal points
Differently-shaped utility functions
Reflecting intensity and symmetry of preferences
Example: Mass election
Individual ideal points aren’t important
Median of all voters determines outcome
Slides Produced by Jeremy
Spater
, Duke University. All rights reserved.
7Slide8Slide9Slide10
AssumptionsExamples above rely on certain assumptions:
(a) Issue space is unidimensional (one issue)(b) Preferences are single-peakedUtility declines monotonically from ideal point(c) Voting is sincere
Vote for most preferred alternative in immediate contest
Don’t look ahead to see effect of vote on future contests
Symmetry
Deviations from ideal point in either direction have same effect
This assumption is sometimes but not always invoked in this chapter
Slides Produced by Jeremy
Spater
, Duke University. All rights reserved.
10Slide11
More careful definitionsRepresentative citizen
i (one of N) with unique ideal point xiPreference:
Indifference:
Median position:
Slides Produced by Jeremy
Spater
, Duke University. All rights reserved.
11Slide12
Odd N, even N, and uniquenessWith single-peaked preferences over a unidimensional issue space: median exists
For odd N, the median is a single pointFor even N with no shared ideal points, median is a closed intervalFor even N with some shared ideal points, median may be unique
or interval
Slides Produced by Jeremy
Spater
, Duke University. All rights reserved.
12Slide13Slide14
Median Voter TheoremMedian Voter Theorem:
Suppose xmed is a median position for the society. Thenthe number of votes for
x
med
is greater than or equal to the number of votes for
any other alternative
z
.
A median position can never lose in a majority rule vote.
It might tie against another median (if median is an interval)
Slides Produced by Jeremy
Spater
, Duke University. All rights reserved.
14Slide15
Median Voter Theorem (2)Corollary:
If y is closer to xmed than z, then
y beats
z
in a majority rule election.
If
y
and
z
are on the same side of
xmed, it is not necessary to invoke symmetry.
But if
y
and
z
are on opposite sides of
x
med
, symmetry is required.
This result requires two additional assumptions:
x
med
is unique
Voter preferences are symmetric
For any pair of proposals, the one closer to the median will win (if preferences are symmetric).
Slides Produced by Jeremy
Spater
, Duke University. All rights reserved.
15Slide16
What if preferences aren’t single-peaked?Median position may not exist
Example: Health care reformReformers have double-peaked preferences, so a majority opposes all options!
Slides Produced by Jeremy
Spater
, Duke University. All rights reserved.
16
Reformers
Incrementalists
Conservatives
Best
P
O
S
S
P
O
Worst
O
S
P
Table 5.1: Preferences on Health Care ReformSlide17Slide18