Political Competition: Theory and Applications
John E. Roemer
Language: English
Pages: 352
ISBN: 0674021053
Format: PDF / Kindle (mobi) / ePub
In this book, John Roemer presents a unified and rigorous theory of political competition between parties. He models the theory under many specifications, including whether parties are policy oriented or oriented toward winning, whether they are certain or uncertain about voter preferences, and whether the policy space is uni- or multidimensional. He examines all eight possible combinations of these choice assumptions, and characterizes their equilibria.
He fleshes out a model in which each party is composed of three different factions concerned with winning, with policy, and with publicity. Parties compete with one another. When internal bargaining is combined with external competition, a natural equilibrium emerges, which Roemer calls party-unanimity Nash equilibrium.
Assuming only the distribution of voter preferences and the endowments of the population, he deduces the nature of the parties that will form. He then applies the theory to several empirical puzzles, including income distribution, patterns of electoral success, and why there is no labor party in the United States.
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t2 ⇒ λ (a, b) | a+b ≤ t1 2 >λ (a, b) | a+b ≤ t2 2 , and so the same inequality holds when we substitute F for λ, which means is strictly increasing. Continuity of is obvious. Premise (b) is true by choice of (a1, b1) and (a2, b2). We are left with A3 and A5; we check A3 first. A type (a, b) is indifferent between policies t 1 and t 2 exactly when (t 1 − a)2 + (t 1 − b)2 = (t 2 − a)2 + (t 2 − b)2, which reduces to t 1 + t 2 = a + b. For given (t 1, t 2), the set {(a, b) | a + b = t 1 + t
Wittman equilibrium (t11, t12, π1) in the first period, where π1 = π(t11, t12). Now we generate a random number η in the interval [0, 1] according to the uniform distribution on [0, 1] : if η ≤ π1, we declare the Left party the winner of the election, and if η > π1, then the Right party is the winner. (These events occur with probabilities π1 and 1 − π1, respectively.) Now the values r2R and r2L , and hence m2 and b2, are determined, and so we have the new probability distribution S2 = B(2, b2).
not clear that it solves the problem of competitive, popular elections. Of course, the existence of legislatures means that it is incorrect, strictly speaking, to assume that the policy of the winning party in an election will be implemented, for legislation is a process that occurs after the election. Nevertheless, if elections are “the central act of democracy” (Riker 1982, 5), then the modeler should not abdicate from modeling them as they appear to be, namely, as simultaneousmove games
) − vL (t R , GR ) ∇vR (t R , GR ) − π(t L , GL , t R , GR )) + =0 L L R R R 1 − π(t , G , t , G ) vR (t , GR ) − vR (t L , GL ) R ∇R (1 ; but these are just the first-order conditions for a weighted Nash bargaining solution, where γ L is the relative power of the factions in L, and γ R is the relative power of the factions in R! This shows us how to calculate the relative power of the factions in a PUNE. We now parameterize the model as follows. F is the lognormal distribution with median 30
units of the private good (her after-tax income) and tμ units of the public good. We now define the voter h’s indirect utility function over policies, which is (1.1) v(t, h) = (1 − t)h + 2α(tμ)1/2; v measures the utility of type h as a function of the tax rate. Notice that voters of different types (where type is h) have different preferences over policies. The ideal policy of voter h is the value of t which maximizes his utility. Since v is concave in t, we may find this point by setting ∂v/∂t