The relationship between bias and swing ratio in the Electoral College and the outcome of presidential elections

ABSTRACT

In this paper, I assess how the outcomes of presidential elections are affected by the presence (or lack) of partisan bias in the Electoral College. There have been three instances (1876, 1888 and 2000) since the end of the Civil War where the party that lost the popular vote won the Electoral College. These instances raise the question of whether partisan bias consistently influences presidential election outcomes? I answer this question by first measuring partisan bias and then using these estimates to assess how partisan bias affects a party's odds of winning a presidential election. I find that the presence of partisan bias provides a sizable, but not insurmountable, obstacle for the disadvantaged party.

KEYWORDS:

• Electoral College
• partisan bias
• swing ratio
• presidential elections

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Joshua Zingher http://orcid.org/0000-0003-3928-4269

Notes on contributor

Joshua Zingher is an assistant professor of political science at Old Dominion University. His research focuses on the links between electoral behavior and representation.

Notes

¹All states are guaranteed at least three electoral votes regardless of population (each state has two senators and one representative). In addition, additional apportionment bias is introduced due to rounding issues, a state cannot be afforded an additional half an electoral vote if there population would merit it. This is the so-called “integer problem” that arises in the apportionment process and leads to citizens receiving slightly different vote weights as a result of rounding.

²There are other potential sources of partisan bias in addition to the three sources outlined above. Others (Pattie and Johnston 2014) have demonstrated that the presence of third-party candidates and the interactions between these sources might introduce additional bias into the system. I account for the presence of these additional sources of bias by lumping them in with turnout bias to form a “residual bias” category. I also perform a more fine-grained analysis where I collect turnout data and separate residual bias from turnout bias. I find that turnout bias accounts for the vast majority of this “residual bias” category.

³There have been other methods developed to calculate bias and swing ratio in electoral systems. King and Gelman (1991, 1994) Judgeit software features an algorithm designed to calculate bias and swing ratio via simulation. In addition, King and Browning (1987) and Garand and Parent (1991) utilized a bi-logit method to estimate partisan bias, but this method does not produce an estimate of swing ratio that is comparable to the logged odds method. Grofman, Brunell, and Campagna (1997) demonstrated that the logged odds and Judgeit simulation method produced very similar results; the biggest difference was that the estimated swing ratio is generally higher when using the logged odds method than when it is estimated via simulation. For more on these other approaches, please consult the online appendix.

⁴As Grofman, Brunell, and Campagna note (1997, fn 13), failure to center the seats-votes curve at the 50% threshold can result in improperly high estimates of bias using the logged odds method. Likewise, estimating the seats–votes equation on a range of values that extends beyond the 40 through 60 range can lead to depressed estimates of swing, because above and below these points it is often not possible to win (or lose) additional seats in the Electoral College.

⁵Some scholars (e.g. King and Gelman 1991) have criticized the assumption that imposes a uniform vote-swing across every state. The criticism of this assumption stems from that vote swings are rarely uniform across states; rather, candidates perform better in some regions than others. I choose to implement this uniform vote swing assumption for two reasons: (1) the method is transparent and (2) it is easily reproducible.

⁶See http://uselectionatlas.org/

⁷It is important to note that the average state-level two-party vote share is not the same thing as the national two-party vote share due to the fact that average state-level two-party vote is not weighted by state population or turnout. For example, California and North Dakota receive the same importance when making this calculation, even though California contributes millions of more votes to the national total than does North Dakota.

⁸My results and those of Grofman, Brunell, and Campagna (1997) are very similar but not identical. There are two potential sources of this discrepancy: the use of different rounding techniques or different approaches for dealing with instances where a presidential candidate did not appear on the ballot (which was relatively common for Republican candidates in the South during the first half of the twentieth century and then again for Democratic candidates during the middle of the twentieth century).

⁹This method does not perfectly account for the integer problem associated with districting plans, but it does address the major source of apportionment bias that occurs as a result of the two electoral votes that correspond with each state's Senate seats. Any unaccounted for apportionment bias will fall into the residual bias category.

¹⁰Again, I am using Tufte's logged odds method. I have omitted the table containing these estimates from the manuscript due to space and clarity considerations. These results can be found in the online appendix.

¹¹Estimating turnout bias in this way effectively relegates turnout bias into a residual category that captures all remaining sources of bias. The vast majority of the bias captured in this residual category is attributable to turnout bias, but unaccounted for apportionment and third-party biases may also be present. For more on this distinction, please consult the online appendix.

¹²All of the calculations used to generate the hypothetical seats–votes curves used in this analysis were constructed using the Republican Party's share of the two-party vote as the cornerstone. I have made no concerted effort to assess the effects of serious third-party candidacies; therefore, my estimate of turnout bias likely includes the effect of any third-party bias that exists in years with strong third-party candidacies. Therefore, estimates of bias and swing ratio in years where third parties mounted serious electoral challenges (e.g. 1912, 1968, 1992 and 1996) should be interpreted with some caution. For more on approaches that systematically incorporate the presence of third parties, please consult the appendix.

¹³The one important exception to this was 1896, when William Jennings Bryan swept the small states (seven new states entered the Union between the 1892 and 1896 election, each with three or four electoral votes apiece. Bryan won six of these seven new states, in addition to Nevada (3), Florida (4) and Colorado (4). Nearly sweeping the small states afforded Bryan a considerable and to date unmatched vote bonus. However, Bryan was not able to maintain his previous dominance in the Great Plains in Mountain West when he ran again four years later.

¹⁴A way of assessing these estimates is to compare them to the three instances where there is known bias in the Electoral College, 1876, 1888 and 2000. In all three of these instances the elections were razor close and the party that lost the popular vote won the Electoral College. My analysis did not indicate the presence of a statistically significant partisan bias in either direction in 1876 or 1888. There is a reason to suspect a distortion of the seat–votes relationship by widespread electoral fraud and the eventual allocation of 20 disputed electoral votes to Hayes by an Electoral Commission set up by Congress. In instances like 1876, where a number of Electoral votes were awarded by a Commission to Hayes (opposed to Tilden, who won the popular vote in many of these disputed states) means there was a disjunction between the popular vote and the Electoral College winners and losers in the states. As a result, Hayes won the Electoral College not because of partisan bias but because a dispute over the popular vote led to Electoral College votes being allocated on the basis of something other than the popular vote in certain states.

¹⁵This was a topic discussed at length by Nate Silver as well. See http://fivethirtyeight.blogs.nytimes.com/2011/09/20/would-al-gore-have-won-in-2000-without-the-electoral-college/?_php=true&_type=blogs&_r=0