1. Dynamics of Political Parties • Aldrich, “A Spatial Model with Partisan Activists,” 1983 • Aldrich, Rohde, and Tofias, “Examining Congress with a Two-Dimensional Space,” unpub • Kollman, Miller, Page, “Adaptive Parties in Spatial Elections,” 1992

2. Aldrich, 1983 • M: To extend a model of persistent party divergence in a one-dimensional space (in spite of the median voter result) to an n-dimensional space (persistently, in spite of non-eq. results) • NH: In n-dimensions “anything can happen” and the results are “chaotic.”

3. Aldrich, 1983 • P: • N-dimensions • Euclidean-based preferences • Activists reach contribution decisions to give a numerarie (money, time) to a party equivalently to how they decide to vote for a party’s candidate • Activists evaluate a party as the (possibly weighted) mean of current activists • They consistently revaluate choices as the party means move

4. Aldrich, 1983 • C: • General existence of equilibrium (defined as a pair of party means with Nash-like eq. in which no citizen changes their activist decision). • Prop 5: If f(x) is unimodal, and if there is a major axis, a unique convergent equilibrium will be along it, with minor axes having unstable eq. • A proper subset of Sundquist’s conditions for partisan realignment fit prop 4 and 5

5. Aldrich, 1983 • Sundquist’s conditions: • Realignment precipitated by rise [of salience] of new issue • New issue must cross cut the old aligning issue • To bring about realignment the salience of new must dominate that of the old issue • Old issue must fade in salience • Normal first response of both parties is to straddle the new issue • Realignment is set in motion when moderates in one party loss control of party on the new issue

6. ART, 2D • M: Assess whether members voting their preferences would choose to empower a majority leadership to control the policy agenda. • NH: Members would not freely do so. • P: • 0. Inherited status quo and exogenous elections determine legislature. We consider the all of the inputs into the legislature to be exogenously determined. • 1. Organizational vote. A pre-vote takes place, in which the legislature decides which agenda mechanism to employ. This is equivalent to the majority party deciding whether or not to empower its leadership. The outcome is determined by majority rule. • 2. Agenda selection. Nature draws an alternative policy position using the rule determined by the action taken in the previous organizational vote. • 3. Legislative vote. In a binary vote, each legislator selects either the status quo or the alternative policy. The outcome is determined by majority vote and in turn determines the legislators realized utility.

7. ART, 2D • (The Agenda Mechanism). Let R(×) denote various possible probability density function of points in the policy space. Nature draws an alternative policy point from the PDF setting up a binary vote between v and s . • (The Party Regime). Allow a “non-policy” pre-vote between the use of different agenda mechanisms. Recall the standard mechanism R(x) and let the agenda mechanism of the party regime be R(xM + ). Where R(xM + ) denotes the probability that x is chosen, given that the majority party has chosen to enact the party regime. • (Party Regime Enactment). We can formulate the party differential, Di for any i Î N : Di = EUi (x M+)-EUi (x) If Di > 0, the legislator expects that the party regime will give i greater expected returns than the unconditional arrangement. The party regime is enacted if i Î M :Di > 0 > i Î M :Di £ 0 .

8. ART, 2DC:

9. ART, 2DC:

10. Kollman, Miller, Page • M: Assess partisan locations in a complex issue space • NH: Issue spaces simple, and so, with a fixed incumbent, opposition always wins in multidimensional spaces • P: • Parties informed only by polls (with a finite number), where polls are head to head contest results, given positions) • Parties are adaptive agents, not optimizers • Parties are either office seeking or ideological • Parties constrained in changes to policy permitted each time

11. Kollman, Miller, Page • C: • As the length of campaigns increases or as parties have more information about voters, parties tend to converge toward centrist outcomes. • Extreme candidates rarely emerge as national candidates; and when they do, they lose by a wide margin. Yet at the local level, extremists can thrive.

12. KMP

13. KMP