Efficiency and equity are the two crucial factors to be considered when allocating public resources such as voting machines. Existing allocation models are all single-objective, focusing on maximizing either efficiency or equity despite the fact that the actual decision-making process involves both issues simultaneously. We propose a bi-objective integer program to analyse the tradeoff between the two competing objectives. The new model quantifies the sacrifice in efficiency in order to achieve a certain improvement in equity and vice versa. Using data from the 2008 United States Presidential election in Franklin County, Ohio, we demonstrate that our model is capable of producing significantly more balanced allocation plans, in terms of efficiency and equity, than current practice or other competing methods.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
The actual values of the average waiting times used in this case study, w ij , are available from the authors upon request.
Model B1 for Z2 only before linearization includes 1065 variables and 26 600 constraints for the case of 532 precincts and 50 possible machine assignments. After linearization, as shown in B1_Z2_Linear, the number of variables only increases by 1, but the number of constraints increases by 282 492.
Allen TT (2013). Delving into the reasons for long lines can bring solutions. Orlando Sentinel, 8 January, http://articles.orlandosentinel.com/2013-01-08/news/os-ed-long-lines-voting-florida-010813-20130107_1_long-lines-ballot-length-turnout, accessed 30 october 2013.
Allen TT and Bernshteyn MB (2006a). Mitigating voter waiting times. Chance 19 (4): 25–36.
Allen TT and Bernshteyn MB (2006b). Optimal voting machine allocation analysis. In: Hertzberg S (ed). Analysis of May 2006 Primary Cuyahoga County. Election Science Institute: Ohio, pp 71–89.
Belenky AS and Larson RC (2008). To queue or not to queue? Analytics. Spring: 22–26.
Bertsimas D, Farias VF and Trichakis N (2012). On the efficiency-fairness trade-off. Management Science 58 (12): 2234–2250.
Bérubé JF, Gendreau M and Potvin JY (2009). An exact ɛ-constraint method for biobjective combinatorial optimization problems: Application to the traveling salesman problem with profits. European Journal of Operational Research 194 (1): 39–50.
Cohon JL (1978). Multiobjective Programming and Planning. Academic Press: New York.
Demir E, Bektas T and Laporte G (2014). The bi-objective pollution-routing problem. European Journal of Operational Research 232 (3): 464–478.
Edelstein WA and Edelstein AD (2010). Queuing and elections: Long lines, DREs and paper ballots. Proceedings of the 2010 Electronic Voting Technology Workshop/Workshop on Trustworthy Elections, Washington, DC.
Ehrgott M and Gandibleux X (2002). Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. Springer: Norwell, MA.
Feldman D and Belcher C (2005). Voting experience survey. Democracy at risk: The 2004 election in Ohio. Democratic National Committee. http://a9.g.akamai.net/7/9/8082/v001/www.democrats.org/pdfs/ohvrireport/section03.pdf, accessed 15 March 2013.
Fessler P (2012). Fixing long election lines may be easier said than done. http://www.npr.org/blogs/itsallpolitics/2012/11/08/164651410/fixing-long-election-lines-may-be-easier-said-than-done, accessed 15 March 2013.
Geoffrion AM (1968). Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Application 22 (3): 618–630.
Grant FH (1980). Reducing voter waiting time. Interfaces 10 (2): 19–25.
Keeney RL (1980a). Equity and public risk. Operations Research 28 (3): 527–534.
Keeney RL (1980b). Utility functions for equity and public risk. Management Science 26 (4): 345–353.
Laumanns M, Thiele L and Zitzler E (2006). An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169 (3): 932–942.
Levine A (2008). Excitement, frustration as early voters brave long lines. http://www.cnn.com/2008/POLITICS/11/02/early.voting/index.html, accessed 15 March 2013.
Lindner-Dutton L, Batta R and Karwan MH (1991). Equitable sequencing of a given set of hazardous materials shipments. Transportation Science 25 (2): 124–137.
Mavrotas G (2009). Effective implementation of the ɛ-constraint method in multi-objective mathematical programming problems. Applied Mathematics and Computation 213 (2): 455–465.
McDonald M (2012). The United States Elections Project, http://elections.gmu.edu/voter_turnout.html, accessed 31 October 2013.
Mebane WR (2006). Voting machine allocation in Franklin County, Ohio, 2004: Response to U.S. Department of Justice Letter of June 29, 2005. http://www-personal.umich.edu/~wmebane/franklin2.pdf, accessed 6 November 2013.
Miettinen KM (1999). Nonlinear Multiobjective Optimization. Kluwer Academic: Norwell, MA.
Mulligan GF (1991). Equality measures and facility location. Regional Science 7 (4): 548–561.
Ogryczak W (2009). Inequality measures and equitable locations. Annals of Operations Research 167 (1): 61–86.
Ripley A (2008). Secrets of What Makes Your Polling Place Work—Or Not. Time, 3 November, http://content.time.com/time/politics/article/0,8599,1855861,00.html, accessed 30 October 2013.
Smith M (2012). Long lines but few snags in U.S. election. CNN, 6 November, http://www.cnn.com/2012/11/06/politics/election-voting/index.html, accessed 15 March 2013.
Steuer RE (1986). Multiple Criteria Optimization, Theory, Computation and Application. Wiley: New York.
Tricoire F, Graf A and Gutjahr WJ (2011). The bi-objective stochastic covering tour problem. Computers & Operations Research 39 (7): 1582–1592.
Ulungu L and Teghem J (1995). The two phase method: An efficient procedure to solve bi-objective combinatorial optimization problems. Foundations of Computing and Decision Sciences 20 (2): 149–165.
Yang M, Allen TT, Fry MJ and Kelton WD (2013). The call for equity: Simulation optimization models to minimize the range of waiting times. IIE Transactions 45 (7): 781–795.
Yang M, Fry MJ, Kelton WD and Allen TT (2014). Improving voting systems through service-operations management. Production and Operations Management 23 (7): 1083–1097.
Rights and permissions
About this article
Cite this article
Wang, X., Yang, M. & Fry, M. Efficiency and equity tradeoffs in voting machine allocation problems. J Oper Res Soc 66, 1363–1369 (2015). https://doi.org/10.1057/jors.2014.107
- efficiency-equity tradeoff
- efficient allocation
- voting operations
- public service