Incumbency Advantage

Proof that previously used estimators of electoral incumbency advantage were biased, and a new unbiased estimator. Also, the first systematic demonstration that constituency service by legislators increases the incumbency advantage.

How to Estimate the Electoral Advantage of Incumbency

Estimating Incumbency Advantage Without Bias
Proves that all previous measures of incumbency advantage in the congressional elections literature were biased or inconsistent, and develops an unbiased estimator based on a simple linear regression model. Gelman, Andrew, and Gary King. 1990. Estimating Incumbency Advantage Without Bias, American Journal of Political Science 34: 1142–1164.Abstract
In this paper we prove theoretically and demonstrate empirically that all existing measures of incumbency advantage in the congressional elections literature are biased or inconsistent. We then provide an unbiased estimator based on a very simple linear regression model. We apply this new method to congressional elections since 1900, providing the first evidence of a positive incumbency advantage in the first half of the century.
A Statistical Model for Multiparty Electoral Data
A general purpose method for analyzing multiparty electoral data, including estimating the incumbency advantage. Katz, Jonathan, and Gary King. 1999. A Statistical Model for Multiparty Electoral Data, American Political Science Review 93: 15–32.Abstract
We propose a comprehensive statistical model for analyzing multiparty, district-level elections. This model, which provides a tool for comparative politics research analagous 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 electoral advantage of incumbency in Britain. Contrary to previous analyses, all based on measures now known to be biased, we demonstrate that the advantage is small but meaningful, 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.
A generalization of the previous article, more practical for larger numbers of parties (part of a symposium in the same issue of Political Analysis). Honaker, James, Gary King, and Jonathan N Katz. 2002. A Fast, Easy, and Efficient Estimator for Multiparty Electoral Data, Political Analysis 10: 84–100.Abstract
Katz and King (1999) develop a model for predicting or explaining aggregate electoral results in multiparty democracies. This model is, in principle, analogous to what least squares regression provides American politics researchers in that two-party system. Katz and King applied this model to three-party elections in England and revealed a variety of new features of incumbency advantage and where each party pulls support from. Although the mathematics of their statistical model covers any number of political parties, it is computationally very demanding, and hence slow and numerically imprecise, with more than three. The original goal of our work was to produce an approximate method that works quicker in practice with many parties without making too many theoretical compromises. As it turns out, the method we offer here improves on Katz and King’s (in bias, variance, numerical stability, and computational speed) even when the latter is computationally feasible. We also offer easy-to-use software that implements our suggestions.

Causes and Consequences

Constituency Service and Incumbency Advantage
The first systematic evidence that constituency service increases the electoral advantage of incumbency. King, Gary. 1991. Constituency Service and Incumbency Advantage, British Journal of Political Science 21: 119–128.Abstract
This Note addresses the long-standing discrepancy between scholarly support for the effect of constituency service on incumbency advantage and a large body of contradictory empirical evidence. I show first that many of the methodological problems noticed in past research reduce to a single methodological problem that is readily resolved. The core of this Note then provides among the first systematic empirical evidence for the constituency service hypothesis. Specifically, an extra $10,000 added to the budget of the average state legislator gives this incumbent an additional 1.54 percentage points in the next election (with a 95% confidence interval of 1.14 to 1.94 percentage points).
Systemic Consequences of Incumbency Advantage in the U.S. House
King, Gary, and Andrew Gelman. 1991. Systemic Consequences of Incumbency Advantage in the U.S. House, American Journal of Political Science 35: 110–138.Abstract
The dramatic increase in the electoral advantage of incumbency has sparked widespread interest among congressional researchers over the last 15 years. Although many scholars have studied the advantages of incumbency for incumbents, few have analyzed its effects on the underlying electoral system. We examine the influence of the incumbency advantage on two features of the electoral system in the U.S. House elections: electoral responsiveness and partisan bias. Using a district-level seats-votes model of House elections, we are able to distinguish systematic changes from unique, election-specific variations. Our results confirm the significant drop in responsiveness, and even steeper decline outside the South, over the past 40 years. Contrary to expectations, we find that increased incumbency advantage explains less than a third of this trend, indicating that some other unknown factor is responsible. Moreover, our analysis also reveals another dramatic pattern, largely overlooked in the congressional literature: in the 1940’s and 1950’s the electoral system was severely biased in favor of the Republican party. The system shifted incrementally from this severe Republican bias over the next several decades to a moderate Democratic bias by the mid-1980’s. Interestingly, changes in incumbency advantage explain virtually all of this trend in partisan bias since the 1940’s. By removing incumbency advantage and the existing configuration of incumbents and challengers analytically, our analysis reveals an underlying electoral system that remains consistently biased in favor of the Republican party. Thus, our results indicate that incumbency advantage affects the underlying electoral system, but contrary to conventional wisdom, this changes the trend in partisan bias more than electoral responsiveness.

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