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Statistics, Politics and Policy

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Risk-limiting Audits and the Margin of Victory in Nonplurality Elections

Anand D. Sarwate / Stephen Checkoway / Hovav Shacham
  • Department of Computer Science and Engineering, University of California, San Diego, La Jolla, CA, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-01-11 | DOI: https://doi.org/10.1515/spp-2012-0003

Abstract

Post-election audits are an important method for verifying the outcome of an election. Recent work on risk-limiting, post-election audits has focused almost exclusively on plurality elections. Several organization and municipalities use nonplurality methods such as range voting, the Borda count, and instant-runoff voting (IRV). We believe that it is crucial to develop effective methods of performing risk-limiting, post-election audits for these methods. We define a general notion of the margin of victory and develop risk-limiting auditing procedures for these nonplurality methods. For scored systems, we show how to adapt methods from plurality auditing. For IRV, the situation is markedly different. We provide a risk-limiting method for auditing the candidate elimination order. We provide a more efficient audit for the elections in which the margin of the IRV election can be efficiently calculated or bounded. We provide efficiently computable upper and lower bounds on the margin and, where possible, compare them to the exact margins for a large number of real elections.

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About the article

Corresponding author: Anand D. Sarwate, Toyota Technological Institute at Chicago, 6045 S. Kenwood Ave, Chicago, IL 60637, USA


Published Online: 2013-01-11


Wikipedia lists 60 organizations which use the Schulze Method in some form. http://en.wikipedia.org/w/index.php?title=Schulze_method&oldid=434396935#Use_of_the_Schulze_method. Accessed 2011-06-15.

This is Hare’s rule for ballot transfers (Tideman 1995).

San Francisco allows voters to rank no more than three of the candidates for each race.

In a presentation at the EVN 2011 conference, Emily Shen gave another such example.

A simpler form of auditing simply recounts ballots to confirm the winner, called a ballot polling audit in Lindeman and Stark (2012).

The remainder of this subsection is adapted from the authors’ earlier work on risk-limiting, post-election audits (Checkoway, Sarwate, and Shacham, 2010).

Intermediate sub-precinct audit units, such as individual voting machines, appear to provide littlegain in statistical power, but may reduce the cost of locating the ballots to audit.

This is not without loss of generality—if more information is known about the reported margins,more targeted sampling can be more efficient (Stark 2009b).

To use ɛ in Definition 3, the ballots must first be converted from ordered lists to pairs of scores: (1,2), (1) → (1,0); (2,1), (2) → (0,1); and ( ) → (0,0) which is to say that only the top-ranked candidate on the ballot gets a score of 1.

S.F., Cal., Charter art. XIII, § 13.102(e) (Mar. 2002), “If the total number of votes of the two or more candidates credited with the lowest number of votes is less than the number of votes credited to the candidate with the next highest number of votes, those candidates with the lowest number of votes shall be eliminated simultaneously and their votes transferred to the next-ranked continuing candidate on each ballot in a single counting operation.”

For example, with the base IRV elimination rule, if the two candidates with the fewest number of top-choice votes in a round have the same number of votes, then the candidate to be eliminated may be chosen by some other mechanism such as a coin flip.

http://www.openstv.org.

All of our code is available at https://www.cs.jhu.edu/∼s/elections/irv.html.

A priority queue is an abstract data type which is conceptually a set of elements each of which has an associated priority. Common implementations of priority queues support fast insertion of a new element with arbitrary priority and fast removal of the element with the highest priority.

Cf., Ala. Code §17-16-20 (2010) or Fla. Stat. §102.141 (2010).

I. D. Hill describes a slightly different example of instability in a real Single Transferable Vote election—the multiseat analogue of instant-runoff voting. Hill points out that a change in a single ballot’s 15th choice (out of 23) would result in a different winner. In this case, it was the difference between voting for one of the (eventual) winners and the closest runner up rather than between two losers (Hill 2004).


Citation Information: Statistics, Politics and Policy, ISSN (Online) 2151-7509, ISSN (Print) 2194-6299, DOI: https://doi.org/10.1515/spp-2012-0003.

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