Spatial Theory in 2-space Fall 2016
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1 Spatial Theory in 2-space Fall
2 Throat-clearing Fundamental finding of unidimensional spatial model Pure majority rule: the median prevails More generally: the pivot prevails Fundamental finding of multidimensional spatial model The center doesn t hold Preferences can t induce equilibria ˆ institutions (or something else) must enter to provide stability 2
3 Basic set-up: Ideal points Rand Paul Libertarianism Jeb Bush Barack Obama Ted Cruz Gov t intervention in economy 3
4 Basic set-up: Utility curves U (x x) 2 ( y y) 2 ( x x)( y y) Obama Obama Obama Obama Obama " Libertinism Obama 4
5 Basic set-up: Indifference curves U (x x) 2 ( y y) 2 Obama Obama Obama Libertinism Barack Obama Gov t intervention in economy 5
6 Basic set-up: Indifference curves U (x x) 2 ( y y) Obama Obama Obama 2, Libertinism Barack Obama Gov t intervention in economy 6
7 Basic set-up: Indifference curves 2 U (x x) ( y y ) 2, Obama Obama Obama Libertinism Barack Obama Gov t intervention in economy 7
8 Why this makes a difference: Voter ID (the Wall?) Security Convenience 8
9 The Simple Euclidean System: The Equation U (x x) 2 ( y y) 2 i i i U (x x) 2 ( y y) 2 i i i 9
10 The Simple Euclidean System: The Picture Ideal points Status quo Indifference curves A n B C 10
11 The Simple Euclidean System: Preference relations U ( ) U ( P ) U ( P ) B B 1 B 2 A B P 2 U ( P B 3 ) U ( ) B n P 3 P 1 C Guns 11
12 The Simple Euclidean System A B n C Guns 12
13 The Win Set, W(n) A B n C Guns 13
14 The Contract Curve A B n C Guns 14
15 The Pareto Set nn A B n C Guns 15
16 You are always off a contract curve A B Etc. C Guns 16
17 McKelvey Chaos Theorem With multiple attributes and multiple decisionmakers There is no equilibrium of tastes Anything can happen I.e., the median voter result doesn t hold This is really important 17
18 What Might Induce Stability? Tastes Uncertainty Impatience Rules 18
19 Tastes may induce stability Ideology Medianin all directions Nuclear deal w/ Iran Abortion Availability 19
20 Tastes may induce stability (Make s.q. the median s ideal point, then draw the indifference curves) Nuclear deal with Iran Abortion Availability 20
21 (Rotate this graph) Nuclear deal with Iran Abortion Availability 21
22 22
23 The result is knife-edged Nuclear deal with Iran Abortion Availability 23
24 Uncertainty may induce stability Policy w/ certainty Policy w/ uncertainty Withdrawing from Iraq Abortion Availability 24
25 Rules may induce stability Floor rules, e.g. vote on status quo last Not stability so much as guarding against anything can happen Germaneness rules Committees 25
26 Status quo last C is Speaker A B C Guns 26
27 Germaneness A B Guns C 27
28 Germaneness A B Guns C 28
29 Germaneness A B Guns C 29
30 Stability-inducing powers of leaders and committees Committees reduce dimensionality Committees and leaders have agendasetting powers 30
31 Examples of Multidimensionality in Action Informal decisionmaking Riker s heresthetics Heresthetics: the strategic introduction of extraneous issues Classic example: Popular election of Senators Human trafficking 31
32 Simple human trafficking bill B Human trafficking ϕ 32
33 Abortion gets introduced Abortion ϕ B Human trafficking 33
34 Unresolved Issues Salience Sophistication 34
35 Abortion ϕ B Human trafficking 35
36 Abortion not salient Abortion ϕ B Human trafficking 36
37 Abortion made salient Abortion ϕ B Human trafficking 37
38 Salience can distort the win set A B A B Guns C Guns C 38
39 Salience can distort the win set A B A B Guns C Guns C 39
40 Sophisticated Voting The strategy of preferring one alternative at time t even through the immediate alternative is better, in order to prevent an even worse outcome in the future 40
41 Sophisticated Voting Example Democrats Hawkish R Dovish R Negotiate with anyone Negotiate, but not with terrorists Don t negotiate Don t negotiate Negotiate with anyone Negotiate, but not with terrorists Negotiate, but not with terrorists Don t negotiate Negotiate with anyone 41
42 Agenda Add proviso to negotiation strategy If the proviso passes, pair the negotiation strategy proviso against the status quo (continue no negotiation) If the proviso fails, pair the negotiation strategy against the status quo Neg., not with terr. Neg., not Q with terr. Q Neg. with anyone Neg. with anyone 42
43 Agenda Democrats Hawkish R Dovish R Negotiate with anyone Negotiate, but not with terrorists Don t negotiate Don t negotiate Negotiate with anyone Negotiate, but not with terrorists Negotiate, but not with terrorists Don t negotiate Negotiate with anyone Neg., not with terr. (DR) Neg. with anyone (D+HR) The proviso passes The amended negotiation fails, even though a majority would have favored the original strategy over the status quo Neg., not Q Q Neg. with with terr. (HR+DR) anyone (D) 43
44 Outcome The proviso passes The amended treaty fails, even though a majority would have favored the original treaty over the status quo How to save ourselves? Sophistication Backward induction 44
45 Agenda Democrats Hawkish R Dovish R Negotiate with anyone Negotiate, but not with terrorists Don t negotiate Don t negotiate Negotiate with anyone Negotiate, but not with terrorists Negotiate, but not with terrorists Don t negotiate Negotiate with anyone Neg., not with terr. (DR) Q Neg. X with anyone (D+HR) Neg., not Q Q Neg. with with terr. (HR) (HR+DR) anyone (D+DR) (D) 45
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