Resolving contested elections: the limited power of post-vote vote-choice data

In close elections, the losing side has an incentive, to obtain evidence that the election result is incorrect. Sometimes this evidence comes in the form of court testimony from a sample of invalid voters, and this testimony is used to adjust vote totals (Belcher v. Mayor of Ann Arbor 1978; Borders v. King County 2005). However, while courts may be reluctant to make explicit findings about out-of-sample data (e.g., invalid voters that, do not testify), when samples are used to adjust vote totals, the court is making such findings implicitly. In this paper, we show that the practice of adjusting vote totals on the basis of potentially unrepresentative samples can lead to incorrectly voided election results. More generally, we demonstrate that even when frame error and measurement error are minimal, random samples of post-vote vote-choice data can have limited power to detect incorrect election results without high response rates, precinct level polarization, or the acceptance of large Type 1 error rates. Therefore, in U.S. election disputes, even high-quality post-vote vote-choice data may be insufficient to resolve contested elections without the use of modeling assumptions (whether or not these assumptions are acknowledged). KEY WORDS: Election challenge: Nonresponse; Power analysis.