# BatchVote: Voting Rules Designed for Auditability

## Abstract

We propose a family of novel social choice functions. Our goal is to explore social choice functions for which **ease of auditing** is a primary design goal, instead of being ignored or left as a puzzle to solve later.

Our proposal, “**BatchVote**,” creates a social choice function *f* from an arbitrary “inner” social choice function *g*, such as instant-runoff voting (IRV), and an integer *B*, the number of batches.

We aim to preserve flexibility by allowing *g* to be arbitrary, while providing the ease of auditing of a plurality election.

To compute the winner of an election of *n* votes, the social choice function *f* partitions the votes into *B* batches of roughly the same size, pseudorandomly. The social choice function *g* is applied to each batch. The election winner, according to *f*, is the weighted plurality winner for the *B* outcomes, where the weight of each batch is the number of votes it contains. The social choice function *f* may be viewed as an “interpolation” between plurality (which is easily auditable) and *g* (which need not be).

Auditing is simple by design: we can view *f* as being a (weighted) plurality election by *B* “*supervoters*,” where the *b*th supervoter’s vote is determined by applying *g* to the votes in batch *b*, and the weight of her vote is the number of votes in her batch. Since plurality elections are easy to audit, the election output can be audited by checking a random sample of “supervotes” against the corresponding paper records.

## Notes

### Acknowledgments

Ronald L. Rivest gratefully acknowledges support for his work on this project received from the Center for Science of Information (CSoI), an NSF Science and Technology Center, under grant agreement CCF-0939370, and from the Department of Statistics, University of California, Berkeley, which hosted his sabbatical visit when this work began.

## References

- 1.Benaloh, J., Jones, D., Lazarus, E., Lindeman, M., Stark, P.B.: SOBA: secrecy-preserving observable ballot-level audit. In: Proceedings of 2011 Electronic Voting Technology Workshop/Workshop on Trustworthy Elections (EVT/WOTE 2011), (2011). http://static.usenix.org/events/evtwote11/tech/final_files/Benaloh.pdf
- 2.Bretschneider, J., Flaherty, S., Goodman, S., Halvorson, M., Johnston, R., Lindeman, M., Rivest, R.L., Smith, P., Stark, P.B.: Risk-limiting post-election audits: why and how? (ver. 1.1), October 2012. http://people.csail.mit.edu/rivest/pubs.html#RLAWG12
- 3.Checkoway, S., Sarwate, A., Shacham, H.: Single-ballot risk-limiting audits using convex optimization. In: Jones, D., Quisquater, J.-J., Rescorla, E. (eds.) Proceedings of 2010 EVT/WOTE Conference. USENIX/ACCURATE/IAVoSS, August 2010Google Scholar
- 4.Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A.: Using complexity to protect elections. CACM
**53**(11), 74–82 (2010)CrossRefGoogle Scholar - 5.Hall, J.L., Miratrix, L.W., Stark, P.B., Briones, M., Ginnold, E., Oakley, F., Peaden, M., Pellerin, G., Stanionis, T., Webber. T.: Implementing risk-limiting post-election audits in California. In: Proceedings of 2009 Electronic Voting Technology Workshop/Workshop on Trustworthy Elections (EVT/WOTE 2009, Montreal, Canada). USENIX, August 2009. http://www.usenix.org/event/evtwote09/tech/full_papers/hall.pdf
- 6.Johnson, K.: Election verification by statistical audit of voter-verified paper ballots. http://ssrn.com/abstract=640943. Accessed 31 Oct 2004
- 7.Lindeman, M., Halvorseon, M., Smith, P., Garland, L., Addona, V., McCrea, D.: Principle and best practices for post-election audits (2008). www.electionaudits.org/files/best%20practices%20final_0.pdf
- 8.Lindeman, M., Stark, P.B.: A gentle introduction to risk-limiting audits. IEEE Secur. Priv.
**10**, 42–49 (2012)CrossRefGoogle Scholar - 9.Lindeman, M., Stark, P.B., Yates, V.S.: BRAVO: ballot-polling risk-limiting audits to verify outcomes. In: Halderman, A., Pereira, O. (eds.) Proceedings of 2012 EVT/WOTE Conference (2012)Google Scholar
- 10.Norden, L., Burstein, A., Hall, J.L., Chen, M.: Post-election audits: restoring trust in elections. Technical report, Brennan Center for Justice and Samuelson Law, Technology & Public Policy Clinic (2007)Google Scholar
- 11.California Secretary of State. Post-election risk-limiting audit pilot program (2011–2013). http://www.sos.ca.gov/elections/voting-systems/oversight/post-election-auditing-regulations-and-reports/post-election-risk-limiting-audit-pilot-program/
- 12.Sarwate, A.D., Checkoway, S., Shacham, H.: Risk-limiting audits and the margin of victory in nonplurality elections. Polit. Policy
**3**(3), 29–64 (2013)Google Scholar - 13.Schulze, M.: A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method. Soc. Choice Welf.
**36**(2), 267–303 (2011)MathSciNetCrossRefzbMATHGoogle Scholar - 14.Stark, P.B.: Risk-limiting vote-tabulation audits: the importance of cluster size. Chance
**23**(3), 9–12 (2010)CrossRefGoogle Scholar - 15.Stark, P.B., Wagner, D.A.: Evidence-based elections. IEEE Secur. Priv.
**10**(05), 33–41 (2012)CrossRefGoogle Scholar - 16.Stark, P.B.: Conservative statistical post-election audits. Ann. Appl. Stat.
**2**, 550–581 (2008)MathSciNetCrossRefzbMATHGoogle Scholar - 17.Stark, P.B.: A sharper discrepancy measure for post-election audits. Ann. Appl. Stat.
**2**, 982–985 (2008)MathSciNetCrossRefzbMATHGoogle Scholar - 18.Stark, P.B.: Auditing a collection of races simultaneously (2009). https://arxiv.org/abs/0905.1422v1
- 19.Stark, P.B.: CAST: canvass audits by sampling and testing. IEEE Trans. Inf. Forensics Secur.
**4**(4), 708–717 (2009)CrossRefGoogle Scholar - 20.Stark, P.B.: Efficient post-election audits of multiple contests: 2009 California tests. In: 2009 Conference on Empirical Legal Studies (2009). http://ssrn.com/abstracts=1443314
- 21.Stark, P.B.: Risk-limiting post-election audits: P-values from common probability inequalities. IEEE Trans. Inf. Forensics Secur.
**4**, 1005–1014 (2009)CrossRefGoogle Scholar - 22.Stark, P.B.: Super-simple simultaneous single-ballot risk-limiting audits. In: Proceedings of 2010 EVT/WOTE Workshop (2010). http://www.usenix.org/events/evtwote10/tech/full_papers/Stark.pdf
- 23.Stark, P.B.: Tools for comparison risk-limiting election audits (2015). http://www.stat.berkeley.edu/~stark/Vote/auditTools.htm
- 24.Stark, P.B., Teague, V.: Verifiable European elections: risk-limiting audits for D’Hondt and its relatives. USENIX J. Elect. Technol. Syst. (JETS)
**1**(3), 18–39 (2014)Google Scholar - 25.Tideman, T.N.: Independence of clones as a criterion for voting rules. Soc. Choice Welf.
**4**(3), 185–206 (1987)MathSciNetCrossRefzbMATHGoogle Scholar - 26.Wald, A.: Sequential tests of statistical hypotheses. Ann. Math. Stat.
**16**(2), 117–186 (1945)MathSciNetCrossRefzbMATHGoogle Scholar - 27.Wald, A.: Sequential Analysis. Dover, Mineola (2004)zbMATHGoogle Scholar
- 28.Wikipedia: Voting system. https://en.wikipedia.org/wiki/Voting_system
- 29.Xia, L.: Computing the margin of victory for various voting rules. In: Proceedings of 13th ACM Conference on Electronic Commerce (EC-2012) (2012)Google Scholar