1. 12 April: The Politics of Flatland Last time: Introduction to the unidimensional spatial model of voting and elections. Today: Extending the spatial model to more complicated choice contexts

2. Lineland The major take-home points when the choice context is “simple”: –winning coalitions are “connected” –the set of possible winning policies is confined to a “central” interval in the space –candidates who want to win will tend to converge their platform strategies on a “central” interval in the space

3. Some terms Binary relation Rationality –Transitivity, completeness, efficiency Single-peaked preferences Utility; expected utility Nash equilibrium Status quo ante/reversion point Preferred-to set Indifference curve/set Win set Pareto set

4. The median voter theorem If choosers have single-peaked preferences over a set of feasible alternatives that can be ordered on a single dimension (e.g., smallest to biggest) and they choose via a binary agenda process with no abstention, then the median voter’s most preferred alternative on the agenda will be the winner. The alternative closest to the median chooser’s “ideal point” (in-principle most favored alternative) will also be a Condorcet winner (can beat any other alternative in pairwise vote). In 2-candidate elections, adopting a Condorcet-winner platform would be part of a Nash equilibrium In legislating, the procedural objective may often be to introduce/block the introduction of the median voter’s favorite policy

5. A spatial model X5X5 X1X1 X2X2 X3X3 X4X4 q X 3 is the favorite point of voter 3; q is the status quo ante (policy or incumbent’s platform), and points on the X line inside the half-circle centered on X 3 going through q are points that 3 likes better than q, i.e., 3’s “preferred-to set of q”, P 3 (q). Voter 3 is the median voter in this space, so only things that she likes better than q can win by majority-rule vote if preferences are single-peaked. We predict that in any binary choice, the alternative closest to X 3 will win

6. Extending the one-dimensional model of group choice Median voter theorem tells us that under certain conditions, group choice tends toward “central” outcomes Multi-candidate elections: look for Nash equilibria Informational concerns: what do strategic actors know and when do they know it? Are voters risk- averse? Agenda control models –If the median dude’s favorite choice can’t get on the agenda, then he takes his favorite thing that DOES get on the agenda

7. Flatland In one dimension, preferred-to sets (individuals) and win sets (intersections of preferred-to sets for all possible winning coalitions) are intervals (with single-peaked prefs) In two dimensions, preferred-to sets are areas within ellipses (with single-peaked prefs) and win sets are intersections of these elliptical areas for all possible winning coalitions. –Example: with 3 voters (1, 2 and 3) and maj. rule, winning coalitions are 1 & 2, 2 & 3 and 1 & 3.

8. Why do we care? What does this geometry buy us? Median voter theorem says that policies tend toward the middle when questions are simple. Leaders’ influence is straightforward and its limits are clear But when questions are complicated, understanding outcomes may be complicated as well. –Is there a multidimensional analog to the median voter?

9. The chaos argument When policies have 2+ dimensions, there generally is no “best” policy, in the sense of a Condorcet winner. This means that we have no reason to expect policy to be stable over time Through a (short) sequence of elections with winners a, b, …, n, we could elect a candidate n who is unanimously regarded as worse than a. Similarly, leaders with agenda powers may be able via a sequence of choices to get a group to choose a policy that EVERYONE else thinks is worse than what the group started with

10. Dealing with complexity How do real legislatures deal? –backwards agendas –endogenous choices of rules, procedures, leaders (perhaps within a constitutional structure and/or expectations conditioned by history) Instead of “preference-induced equilibria” we expect (or search for) “structure- induced equilibria”.

11. SIE: an example The legislature is divided into conservative Republicans, moderate Republicans, and Democrats. Suppose Speaker Schlabotnik wants to revise two aspects of tax policy (the progressivity of the code, and the level of taxation). Schlabotnik wants slightly lower progressivity and much lower tax levels. But Republicans are divided between conservatives who want to sharply lower taxes and sharply lower progressivity; and moderates who would like moderately lower rates, but not much redistribution. Democrats want somewhat lower revenues and a more progressive tax code. Assume that any two of these groups can pass legislation. If Schlabotnik can propose any agenda she chooses and she can induce the leg. to give her what she wants (in terms of agenda), how close can she get to her ideal point?

12. Structure-induced equilibrium Equilibrium: a “stable” outcome –if the s.q. is such that no majority can agree to an alternative, it is a “preference-induced equilibrium” –if there are alternatives to which a majority would agree, but rules, procedures or leaders block change, it is a “structure-induced equilibrium”

13. Back to Line Land Gatekeeping power: Legislation may be considered in a policy area X iff (if and only if) the gatekeeper gives the go-ahead –once the standing rules of the House have been adopted, a “special rule” for considering a bill can only come to the floor if reported by the Rules Committee –A Constitutional Convention for generally revising the Constitution can only be called by Congress after petition by the legislatures of 2/3 of the states –single amendments can be put before the states only by Congress (following passage of the resolution by 2/3 of each chamber)

14. More Line Land Agenda control: who may offer specific alternatives to the status quo/reversionary policy? –closed rule: no alternatives to the bill may be offered by anyone –modified closed rule: only specific alternatives may be offered –modified open rule: only specified parts of the bill are open to amendment –open rule: all parts of the bill are open to amendment

15. The setter model Referendum voting: a bureaucrat or the legislature places a measure on the ballot. How large a policy change can be effected? –hypothetical example: current tax policy will raise $100B. The median legislator would most like that to be cut to $80B. The chairman of the tax committee is authorized to propose a bill under a closed rule. –What does she propose if her ideal tax level is $50B? $70B? $110B?

16. Organizing chaos How do real legislatures deal with complex questions? Bills are written in titles, parts, sections, subsections, etc. –the House typically marks up one title/part/section/whatever at a time –amendments in the House must be germane to the part of the bill open for amendment Complex questions may be divided on motion (may require implicit or explicit majority support) unless division is prevented by a special rule So, in principle, complex, multidimensional questions may be broken up into a series of simpler, one-dimensional questions –each issue has a median voter –issue-by-issue median or issue-by-issue setter