Sharper p-Values for Stratified Election Audits
Name
HigginsRivestStark-SharperPValuesForStratifiedElectionAudits.pdf
Description
Accepted version
Size
1.02 MB
Format
Adobe PDF
Checksum (MD5)
ecf5710991c2c7702a45a1e7b4ed6fd0
Author(s)
Higgins, Michael J.
Rivest, Ronald L
Stark, Philip B.
Date Issued
October 2011
Journal
Statistics, Politics and Policy
Publisher
Walter de Gruyter & Co.
Citation
Higgins, Michael J., Ronald L. Rivest and Philip B. Stark. "Sharper p-Values for Stratified Election Audits." Statistics, Politics, and Policy, 2.1 (2011).
Version
Author's final manuscript
Abstract
Vote-tabulation audits can be used to collect evidence that the set of winners of an election (the outcome) according to the machine count is correct — that it agrees with the outcome that a full hand count of the audit trail would show. The strength of evidence is measured by the p-value of the hypothesis that the machine outcome is wrong. Smaller p-values are stronger evidence that the outcome is correct. Most states that have election audits of any kind require audit samples stratified by county for contests that cross county lines. Previous work on p-values for stratified samples based on the largest weighted overstatement of the margin used upper bounds that can be quite weak. Sharper p-values can be found by solving a 0-1 knapsack problem. For example, the 2006 U.S. Senate race in Minnesota was audited using a stratified sample of 2–8 precincts from each of 87 counties, 202 precincts in all. Earlier work (Stark 2008b) found that the p-value was no larger than 0.042. We show that it is no larger than 0.016: much stronger evidence that the machine outcome was correct. We also give algorithms for choosing how many batches to draw from each stratum to reduce the counting burden. In the 2006 Minnesota race, a stratified sample about half as large — 109 precincts versus 202 — would have given just as small a p-value if the observed maximum overstatement were the same. This would require drawing 11 precincts instead of 8 from the largest county, and 1 instead of 2 from the smallest counties. We give analogous results for the 2008 U.S. House of Representatives contests in California. Keywords: post-election audits; knapsack problem
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.2202/2151-7509.1031
