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Spatial Theory in 2-space

Spatial Theory in 2-space. 17.251 Fall 2004. 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

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Spatial Theory in 2-space

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  1. Spatial Theory in 2-space 17.251 Fall 2004

  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 •  institutions (or something else) must enter

  3. Basic set-up: Ideal points Jesse Ventura Walter Mondale Libertinism Norm Coleman Jerry Falwell Gov’t intervention in economy

  4. Basic set-up: Utility curves  Utility Libertinism Gov’t intervention Mondale

  5. Basic set-up: Indifference curves Walter Mondale Libertinism Gov’t intervention in economy

  6. Basic set-up: Indifference curves Walter Mondale Libertinism Gov’t intervention in economy

  7. Basic set-up: Indifference curves Walter Mondale Libertinism Gov’t intervention in economy

  8. Why it matters: Jerry Falwell vs. George Bush Libertinism Fallwell indifference curve Bush indifference curve Gov’t intervention in economy

  9. The Simple Euclidean System: The Equation

  10. The Simple Euclidean System: The Picture Ideal points A Status quo B Indifference curves  C

  11. The Simple Euclidean System: Preference relations P2 A B  Butter P3 P1 C Guns

  12. The Simple Euclidean System A B  Butter C A’s “preferred-to set” B’s “preferred to set” Guns

  13. The Win Set, W() A B  Butter C Guns

  14. The Contract Curve A B  Butter C Guns

  15. The Pareto Set A B  Butter C Guns

  16. You are always off a contract curve A B Etc. Butter C Guns

  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

  18. What Might Induce Stability? • Tastes • Undertainty • Impatience • Rules

  19. Tastes may induce stability • Ideology • “Median in all directions” Appeasing Iraq Abortion Availability

  20. Tastes may induce stability (Make s.q. the “median’s” ideal point, then draw the indifference curves) Appeasing Iraq Abortion Availability

  21. Appeasing Iraq Abortion Availability (Rotate this graph)

  22. The result is knife-edged Appeasing Iraq Abortion Availability

  23. Policy w/ certainty Uncertainty may induce stability Policy w/ uncertainty Appeasing Iraq Abortion Availability

  24. Impatience may induce stability • Rubenstein bargaining

  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

  26. Status quo last “C” is Speaker A B Butter C Guns

  27. Germaneness A B Butter C Guns

  28. Germaneness A B Butter C Guns

  29. Germaneness A B Butter C Guns

  30. Committees (and subcommittees) reduce policy dimensionality A (Butter Committee) B Butter C (Guns committee) Guns

  31. Stability-inducing powers of leaders and committees • Committees reduce dimensionality • Committees and leaders have agenda-setting powers

  32. Examples of Multidimensionality in Action • Informal decisionmaking • Riker’s “heresthetics” • Heresthetics: the strategic introduction of “extraneous” issues

  33. Unresolved Issues • Salience • Sophistication

  34. A A B B Butter Butter C C Guns Guns Salience can distort the win set

  35. 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

  36. Sophisticated Voting Example Note that a majority prefers ratification of an unadorned treaty to rejection

  37. Agenda • Add “proviso” to treaty • If the proviso passes, pair the treaty with the proviso against the status quo (rejection) • If the proviso fails, pair the treaty against rejection Treaty+ Treaty Treaty Q Treaty+ Q

  38. 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

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