0 District Complexity and the Congressional Incumbency Advantage Michael J. Ensley Indiana University Michael W. Tofias University of Wisconsin, Milwaukee Scott de Marchi Duke University Contact Information Michael J. Ensley Department of Political Science 1100 E. Seventh Street Indiana University Bloomington, IN 47405 Phone: 812-855-5098 Fax: 812-855-2027 [email protected] Abstract Many scholars of congressional elections have argued that an increase in the diversity of preferences in a district increases the level of electoral competition. We argue that there is strong reason to believe that the opposite is true. As the diversity of preferences increases, and thus as the complexity of the electoral landscape increases, challengers will have a more difficult time locating an optimal platform when facing an incumbent. Using data form the 2000 National Annenberg Election Study, we construct a measure of district complexity for U.S. House districts and test whether the entry of quality challengers and the incumbent‟s share of the two-party vote are affected by the complexity of the electoral landscape. We find strong support for the hypothesis that complexity benefits incumbents for both indicators of electoral competition.2 Many studies of congressional elections characterize district preferences along a single partisan or ideological dimension. One implication of this perspective is that competition between candidates is reduced to a simple problem: locate at the position of the median voter. While a single dimension may adequately define the space of elite partisan conflict in Congress (Poole and Rosenthal 1997), public opinion across major policy issues can not be reduced to a single dimension of conflict (Carsey and Layman 2002). This suggests that our understanding of electoral competition is at best incomplete (Lodge and Taber 200X). Specifically, the complexity of the electoral landscape may affect the character and degree of competition, such as the size of the incumbency advantage or the emergence of quality challengers. Research based on the work of Fenno (1978) and much of the formal literature of spatial competition suggests that as district complexity increases, incumbents become more vulnerable because there are a potentially large number of platforms that will defeat even a well-positioned, but relatively fixed incumbent. Of course, this abstraction depends on the assumptions that incumbent movement is restricted, challengers can freely locate, and information about the electorate is complete. However, research on complexity and bounded rationality suggests that increasing district complexity would actually benefit incumbents because it becomes more difficult for a challenger to locate a winning platform (Kollman, Miller, and Page 1992, 1998; Ensley, de Marchi and Munger 2007). Information about the electorate is costly to obtain and it is a non-trivial exercise to derive an optimal platform given the available information.3 Incumbent platforms are the result of a series of successful searches. Alchian (1950) explains how markets with boundedly-rational actors might reasonably look like the markets of textbook, neo-classical economic competition; those firms that have more efficiently produced the goods and services that consumers want will survive the selective pressures of competition. Similarly, models of elections with boundedly- rational actors will select candidates that have more effectively solved the optimization problem of platform location (see Zaller 1998 for a clever exposition on this point). By definition, incumbents have selected a better platform in an earlier election and thus are better than the modal candidate. The more complex the landscape is the more difficult the optimization problem is; thus the difficulty on beating an incumbent should increase the more complex the district. While some previous studies have focused on the somewhat related notions of diversity and heterogeneity, very few scholars have examined how the complexity of the electoral landscape affects a candidate‟s ability to choose an optimal policy location.1 Further, articles that have examined the relationship between diversity and electoral competition have relied on proxy measures of public opinion (e.g. demographics, partisanship, population size), which are not always well motivated and do not accurately capture the actual political space that candidates and parties compete in. Using data from the 2000 National Annenberg Election Study, we construct a district-level measure of political complexity based on public opinion across two major issues dimensions. We use this measure to test if district complexity increases or decreases electoral competition. Specifically, we estimate the effect of complexity on the likelihood of a quality challenger entering a race against an incumbent and on the incumbent‟s share of the two-4 party vote. We find that district complexity benefits incumbents, which stands in stark contrast to most of the existing literature. The paper proceeds as follows. First we review the existing perspectives on the relationship between electoral landscapes and electoral competition. We then discuss our measure of complexity constructed using data from the 2000 National Annenberg Election Study. This is followed by a presentation of the data and the regression models of challenger quality and incumbent vote share. Finally, we offer some concluding thoughts and directions for future research. Electoral Landscapes and Electoral Competition The formal theory of electoral spatial competition has a lengthy and illustrious history but it‟s certainly not devoid of controversy (Grofman 2004). Since Downs (1957) established this groundbreaking approach to studying elections, scholars have been busy specifying how various electoral rules and institutions, as well as behavioral assumptions about candidates, voters, and interest groups, impact the positions candidates adopt. In particular the focus has been on whether candidates diverge or converge in the policy space. While game theory has greatly improved our understanding of electoral competition, there are certainly limits to the analytical approach (de Marchi 2005). From the perspective of bounded rationality, we can relax the assumption that candidates have the ability to solve the platform selection problem. Candidates cannot always calculate the outcome of