NOTE: To change the image on this slide, select the picture and delete it. Then click the Pictures icon in the placeholder to insert your own image. CHOOSING IN GROUPS 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  Implications of non-single-peaked preferences Slides Produced by Jeremy Spater, Duke University. All rights reserved.2

Spatial model  Nature of voter preferences  Preferences represented by weighted distances  Prefer candidate who is “closest” to ideal point  Endogenous platform selection  Candidates 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.3

Spatial theory  Different from weak orderings approach  Explicit utility function: distance  Median voter determines election: Median Voter Theorem (MVT)  Voters on edges can change their positions without influencing outcome  Outcome is stable under some circumstances  Under some conditions, candidates converge in center  Under other conditions, outcome is polarized or indeterminate Slides Produced by Jeremy Spater, Duke University. All rights reserved.5

Foundations of spatial models  People use “left”, “right”, and “center” to describe political positions  This usage originated in the French Revolution  Physical positions of parties in National Assemblies and National Convention  Left: Jacobins; Right: Girondins  Left 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.6

Spatial utility functions  Voter perceives candidate as “platform” or “point in space”  Cartesian product of all policy positions taken by candidate  Each issue is assigned a “salience” or weight  Issues more important to the voter have higher weights  Some issues might have zero weight  Example: 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.7

Assumptions  Examples above rely on certain assumptions:  (a) Issue space is unidimensional (one issue)  (b) Preferences are single-peaked  Utility 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.10

More careful definitions  Representative citizen i (one of N) with unique ideal point x i  Preference:  Indifference:  Median position: Slides Produced by Jeremy Spater, Duke University. All rights reserved.11

Odd N, even N, and uniqueness  With single-peaked preferences over a unidimensional issue space: median exists  For odd N, the median is a single point  For even N with no shared ideal points, median is a closed interval  For even N with some shared ideal points, median may be unique or interval Slides Produced by Jeremy Spater, Duke University. All rights reserved.12

Median Voter Theorem Median Voter Theorem: Suppose x med is a median position for the society. Then the 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.14

Median Voter Theorem (2) Corollary: If y is closer to x med than z, then y beats z in a majority rule election. If y and z are on the same side of x med, 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.15

What if preferences aren’t single-peaked?  Median position may not exist  Example: Health care reform  Reformers have double-peaked preferences, so a majority opposes all options! Slides Produced by Jeremy Spater, Duke University. All rights reserved.16 Table 5.1: Preferences on Health Care Reform