e propose a comprehensive statistical model for analyzing multiparty, district-level elections. This model, which provides a tool for comparative politics research analogous to that which regression analysis provides in the American two-party context, can be used to explain or predict how geographic distributions of electoral results depend upon economic conditions, neighborhood ethnic compositions, campaign spending, and other features of the election campaign or aggregate areas. We also provide new graphical representations for data exploration, model evaluation, and substantive interpretation. We illustrate the use of this model by attempting to resolve a controversy over the size of and trend in the electoral advantage of incumbency in Britain. Contraiy to previous analyses, all based on measures now known to be biased, we demonstrate that the advantage is small but meaningfkl, varies substantially across the parties, and is not growing. Finally, we show how to estimate the party from which each party's advantage is predominantly drawn. w e propose the first internally consistent statistical model for analyzing multiparty, districtlevel aggregate election data. Our model can

We derive a unified statistical method with which one can produce substantially improved definitions and estimates of almost any feature of two-party electoral systems that can be defined based on district vote shares. Our single method enables one to calculate more efficient estimates, with more trustworthy assessments of their uncertainty, than each of the separate multifarious existing measures of partisan bias, electoral responsiveness, seats-votes curves, expected or predicted vote in each district in a legislature, the probability that a given party will win the seat in each district, the proportion of incumbents or others who will lose their seats, the proportion of women or minority candidates to be elected, the incumbency advantage and other causal effects, the likely effects on the electoral system and district votes of proposed electoral reforms such as term limitations, campaign spending limits, and drawing majority-minority districts, and numerous others. To illustrate, we estimate the partisan bias and electoral responsiveness of the U.S. House of Representatives since 1900 and evaluate the fairness of competing redistricting plans for the 1992 Ohio state legislature.

We analyze the effects of redistricting as revealed in the votes received by the Democratic and Republican candidates for state legislature. We develop measures of partisan bias and the responsiveness of the composition of the legislature to changes in statewide votes. Our statistical model incorporates a mixed hierarchical Bayesian and non-Bayesian estimation, requiring simulation along the lines of Tanner and Wong (1987). This model provides reliable estimates of partisan bias and responsiveness along with measures of their variabilities from only a single year of electoral data. This allows one to distinguish systematic changes in the underlying electoral system from typical election-to-election variability. KEY WORDS: Bayesian estimation; Elections; Political science; Random effects; Simulation. State and national legislators in the United States are largely elected by plurality vote in individual geographic districts, whose boundaries are redrawn after every decennial census. In addition to ensuring equal populations in each district, redistricting affects which candidates are elected, the relative strengths of the two parties in a legislative house, and other features of the electoral system in a state.

This paper develops an approach to studying how bias in favor of one party due to the pattern of electoral districting affects policy choice. We tie a commonly used measure of electoral bias to the theory of party competition and show how this affects party strategy in theory. The usefulness of the approach is illustrated using data on local government in England. The results suggest that reducing electoral bias leads parties to moderate their policies.

We develop a simple formal model of the redistricting process that highlights the importance of two factors: first, partisan or bipartisan control of the redistricting process; second, the nature of the reversionary outcome, should the state legislature and governor fail to agree on a new districting plan. Using this model, we derive various predictions about the levels of partisan bias and responsiveness that should be observed under districting plans adopted under various constellations of partisan control of state government and reversionary outcomes, testing our predictions on postwar (1946--70) U.S. House electoral data. We find strong evidence that both partisan control and reversionary outcomes systematically a#ect the nature of a redistricting plan and the subsequent elections held under it. Further, we show that the well-known disappearance circa 1966 of what had been a long-time pro-Republican bias of about 6% in nonsouthern congressional elections can be explaine...

In an election the probability that a single voter is decisive is a#ected by the electoral system---that is, the rule for aggregating votes into a single outcome. Under the assumption that all votes are equally likely (i.e., random voting), we prove that the average probability of a vote being decisive is maximized under a popular-vote (or simple majority) rule and is lower under any coalition system, such as the U.S. Electoral College system, no matter how complicated. Forming a coalition increases the decisive vote probability for the voters within a coalition, but the aggregate e#ect of coalitions is to decrease the average decisiveness of the population of voters. We then review results on voting power in an electoral college system. Under the random voting assumption, it is well known that the voters with the highest probability of decisiveness are those in large states. However, we show using empirical estimates of the closeness of historical U.S. Presidential elections that voters in small states have been advantaged because the random voting model overestimates the frequencies of close elections in the larger states. Finally, we estimate the average probability of decisiveness for all U.S. Presidential elections from 1960 to 2000 under three possible electoral systems: popular vote, electoral vote, and winner-take-all within Congressional districts. We find that the average probability of decisiveness is about the same under all three systems.

We utilize the Cox and Katz (1998, 2002) bargaining model of the redistricting process and data from the 1972-2000 House elections to answer two questions: first, does the creation of majority-minority districts increase the likelihood that minority candidates will be elected in those districts? Second, does the creation of majority-minority districts also generate pro-Republican gerrymanders? We demonstrate that after controlling for the proportion of minorities in a state, as the proportion of majorityminority districts increases, the proportion of minorities elected to the House increases as well, regardless of which party controls the redistricting process. This result is consistent with previous research. To test the hypothesis that majority-minority districting has “perverse-effects, ” the seats-votes curves are estimated for each election, allowing for the partisan or bipartisan control of the redistricting process and the presence of majority-minority mandates. We demonstrate that there is no significant difference in the level of partisan bias observed under redistricting plans with majority-minority districts and those without majority-minority districts. The claim that majority-minority districting has “perverse-effects ” is not supported by the data. Paper prepared for presentation at the annual meeting of the Midwest Political Science Association, April

In a substantial contribution to positive political economy, Rogowski and Kayser (2002, p. 526) finds that “systems of proportional representation... systematically advantage producers and disadvantage consumers. ” I find that there is no evidence to sustain that conclusion. The original study extrapolates severely due to the fact that proportional representation countries are systematically different from majoritarian district countries in their background characteristics. Accounting for these differences by matching on the propensity score forces us to discard observations that severely extrapolate from the data, yielding estimates of such high variance that we cannot find evidence for the price-level effect. The only way to reassess the hypothesis without bias or implausible assumptions is to gather a larger dataset, which by including non-OECD democracies increases potential observations. Yet even with this data the price-level effect remains undetectable. The conclusion of a price-level effect thereby rests on modeling assumptions that are theoretically and empirically unjustified.

This paper provides a welfare economic analysis of the problem of districting. In the context of a simple micro-founded model intended to capture the salient features of U.S. politics, it studies how a social planner should allocate citizens of different ideologies across districts to maximize aggregate utility. In the model, districting determines the equilibrium seat-vote curve which is the relationship between the aggregate vote share of the political parties and their share of seats in the legislature. To understand optimal districting, the paper first characterizes the optimal seat-vote curve which describes the ideal relationship between votes and seats. It then shows that under rather weak conditions the optimal seatvote curve is implementable in the sense that there exist districtings which make the equilibrium seat-vote curve equal to the optimal seat-vote curve. The nature of these optimal districtings is described. Finally, the paper provides a full characterization of the constrained optimal seat-vote curve and the districtings that underlie it when the optimal seat-vote curve is not achievable.

While the effects of redistricting on electoral outcomes have extensively been studied, little is known about its impact on policy outcomes. This paper argues that redistricting changes the incentives of legislators to serve their constituencies. This possibility arises because congressional redistricting in the United States typically involves violations of political boundaries. Examining the flow of federal assistance to counties before and after the 2000s rounds of redistricting, we find that when political subdivisions are split into multiple congressional districts, they receive less federal assistance than they did before the split. The result is robust to different specifications and holds even when we take into account other factors that can have an impact on the amount of transfers, such as the effect of being represented by non-incumbent House members, the presence of split-party county “delegations,” and the