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Going from theory to practice: the mixed success of approval voting

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Abstract

Approval voting (AV) is a voting system in which voters can vote for, or approve of, as many candidates as they like in multicandidate elections. In 1987 and 1988, four scientific and engineering societies, collectively comprising several hundred thousand members, used AV for the first time. Since then, about half a dozen other societies have adopted AV. Usually its adoption was seriously debated, but other times pragmatic or political considerations proved decisive in its selection. While AV has an ancient pedigree, its recent history is the focus of this paper. Ballot data from some of the societies that adopted AV are used to compare theoretical results with experience, including the nature of voting under AV and the kinds of candidates that are elected. Although the use of AV is generally considered to have been successful in the societies—living up to the rhetoric of its proponents—AV has been a controversial reform. AV is not currently used in any public elections, despite efforts to institute it, so its success should be judged as mixed. The chief reason for its nonadoption in public elections, and by some societies, seems to be a lack of key “insider” support.

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Notes

  1. For other retrospective studies of elections, including the 1992 presidential election involving Bill Clinton, George Bush, and Ross Perot, see the citations in Brams and Fishburn (2002).

  2. Perhaps the best recent example of voters who faced this dilemma were supporters of Ralph Nader in the 2000 U.S. presidential election. Although Nader received less than 3% of the popular vote in this election, polls show that if his supporters could have voted for a second choice, Al Gore would have been the choice of most. Thereby Gore would have won Florida and its electoral votes, making him rather than George W. Bush the winner.

  3. For a sampling of this debate, see Arrington and Brenner (1984) and Brams and Fishburn (1984); Niemi (1984, 1985) and Brams and Fishburn (1985); Saari and Van Newenhizen (1988), Brams et al. (1988); Brams and Fishburn (2001) and Saari (2001a); and Brams and Herschbach (2001a, 2001b) and Richie et al. (2001). Recent popular accounts of the controversy over voting systems by science writers include MacKenzie (2000), Guterman (2002), Klarreich (2002), and Begley (2003).

  4. Donald G. Saari has been a proponent of BV, most recently in Saari (2001b), but we know of no recent adoptions of BV, though it and a variant have been used in two small Pacific Island countries, beginning about 30 years ago (Reilly 2002). Proponents of instant runoff voting (IRV), based on STV, recently succeeded in getting it enacted in elections in San Francisco; they formed an organization, the Center for Voting and Democracy (CV&D), which now has a staff of about ten people that includes the authors of Richie et al. (2001) and Hill (2002). As noted in Brams and Herschbach (2001a), IRV supporters have done little serious analysis to back up their claims, although other studies of STV (e.g., Dummett 1984) have been more probing. On the other hand, CV&D does have human and monetary resources that few academics can claim.

  5. The MAA is the more teaching-oriented of the two major American mathematical societies at the college-university level.

  6. It was adopted in part because counting votes by hand under STV proved to be too onerous, and computerizing the counting was not feasible at the time. Even so, AV was adopted only for those offices of the AMS that did not require an amendment to the bylaws, which would have required considerable effort to enact; voting for other offices is still by PV (Daverman 2002, and Fossum 2002). Patently, pragmatic considerations played a key role in the AMS's choices.

  7. By no means do we suggest that AV is a panacea in all elections, especially those involving multiple winners; for such elections, see the AV-related reforms in Brams (1990), Fishburn and Brams (1991), Brams and Fishburn (1992b), and Potthoff and Brams (1998).

  8. According to the IEEE Executive Director, Daniel J. Senese, AV was abandoned in 2002 because “few of our members were using it and it was felt that it was no longer needed.” Brams responded in an e-mail exchange (June 2, 2002) that since “candidates now can get on the ballot with ‘relative ease’ [according to former IEEE president Henry L. Bachman in the same e-mail exchange] . . . the problem of multiple candidates [in the late 1980s] might actually be exacerbated . . . and come back to haunt you [IEEE] some day.”

  9. It is worth noting that the usual reason for the nonexistence of a Condorcet candidate is because of a Condorcet paradox, whereby majorities cycle. In this election, however, it is a projected tie that precludes one candidate from defeating the others in pairwise contests. That there is no cycle, and that A in fact would lose to both B and C, is shown by ranking data in Fishburn and Little (1988).

  10. The 1999 election for president of the Social Choice and Welfare Society, which was decided by two approval votes among 76 cast, is the only exception we know of: the second-place AV candidate in this election would have defeated the AV winner by four votes in a head-to-head contest, based on the hypothetical use of BV, for which voters ranked candidates. Brams and Fishburn (2001) deem this “nail-biting” election essentially a toss-up, whereas Saari (2001a) argues that most positional methods would have chosen the Condorcet candidate (including BC, wherein the Condorcet winner would have defeated the AV winner 60–59); see Laslier (2003a) for more details on voting patterns in this election. Regenwetter and Grofman (1998), using a random-utility model to reconstruct voter preferences in several elections—including some discussed here—show that AV, BV, and Condorcet winners generally coincide. Laslier (2003b) and Laslier and Vander Sraeten (2003) analyze data from a field experiment with AV in the 2002 French presidential election, which involved over 5,000 voters in two French towns, and conclude that AV was easily understood, readily accepted, and provided a more complete picture of the “political space.” Earlier theoretical analyses as well as computer simulations (Brams and Fishburn 1983; Lijphart and Grofman 1984; Nurmi 1987; Merrill 1988) demonstrate that AV almost always elects a Condorcet winner if there is one. If there is not one, as in the 1985 TIMS election experiment, then proponents of AV argue that AV provides a compelling way to break either a cycle or a tie.

References

  • Amendment to ASA By-Laws (1987) AMSTAT News 135:1

  • Arrington TS, Brenner S (1984) Another look at approval voting; Arrington and Brenner to Brams and Fishburn. Polity 17(1):118–134, 144

    Google Scholar 

  • Begley S (2003) Why we sometimes get tofu for president when we want beef. Wall Street J B1

  • Boehm GAW (1976) One fervent vote against wintergreen. Preprint

  • Brams SJ (1982) The AMS nomination procedure is vulnerable to truncation of preferences; Rejoinder [to Chandler Davis]. Not Am Math Soc 29(2):136–138

    MathSciNet  Google Scholar 

  • Brams SJ (1988) MAA elections produce decisive winners. Focus: the newsletter of the Mathematical Association of America 8(3):1–2

    ADS  Google Scholar 

  • Brams SJ (1990) Constrained approval voting: a voting system to elect a governing board. Interfaces 20(5):67–80

    Google Scholar 

  • Brams SJ, Fishburn PC (1978) Approval voting. Am Polit Sci Rev 72(3):831–847

    Google Scholar 

  • Brams SJ, Fishburn PC (1979) Reply [to Gordon Tullock]. Am Polit Sci Rev 73(2):552

    Google Scholar 

  • Brams SJ, Fishburn PC (1983) Approval voting. Birkhäuser Boston, Cambridge, MA

    MATH  Google Scholar 

  • Brams SJ, Fishburn PC (1984) A careful look at another look at approval voting. Polity 17(1):135–143

    Google Scholar 

  • Brams SJ, Fishburn PC (1985) Comment on the problem of strategic voting under approval voting; Rejoinder to Niemi. Am Polit Sci Rev 79(3):816–819

    Google Scholar 

  • Brams SJ, Fishburn PC (1988) Does approval voting elect the lowest common denominator? PS Polit Sci Polit 21(2):277–284

    Google Scholar 

  • Brams SJ, Fishburn PC (1992a) Approval voting in scientific and engineering societies. Group Decis Negot 1:41–55

    Article  Google Scholar 

  • Brams SJ, Fishburn PC (1992b) Coalition voting. Math Comput Model (Formal Theory of Politics II: Mathematical Modelling in Political Science) 16:15–26

    MATH  MathSciNet  Google Scholar 

  • Brams SJ, Fishburn PC (2001) A nail-biting election. Soc Choice Welf 18(3):409–414

    Article  MATH  MathSciNet  Google Scholar 

  • Brams SJ, Fishburn PC (2002) Voting procedures. In: Arrow K, Sen A, Suzumura K (eds) Handbook of social choice and welfare. Elsevier Science, Amsterdam, pp 175–236

    Google Scholar 

  • Brams SJ, Herschbach DR (2001a) Response to Richie, Bouricius, and Macklin. Science 294:305–306

    CAS  Google Scholar 

  • Brams SJ, Herschbach DR (2001b) The science of elections. Science 292:1449

    Article  PubMed  CAS  Google Scholar 

  • Brams SJ, Nagel JH (1991) Approval voting in practice. Public Choice 71(1–2):1–17

    Article  Google Scholar 

  • Brams SJ, Fishburn PC, Merrill S III (1988) The responsiveness of approval voting: comments on Saari and Van Newenhizen; Rejoinder to Saari and Van Newenhizen. Public Choice 59:121–131, 149

    Article  Google Scholar 

  • Colomer JM, McLean I (1998) Electing popes: approval balloting and qualified-majority rule. J Interdiscip Hist 29(1):1–22

    Article  Google Scholar 

  • Cox GW (1987) The Cabinet and the development of political parties in Victorian England. Cambridge University Press, New York

    Google Scholar 

  • Daverman RJ (2002) Private communication

  • Davis C (1982) Comment Not Am Math Soc 29(2):138

    Google Scholar 

  • Dummett M (1984) Voting procedures. Oxford University Press, Oxford, UK

    Google Scholar 

  • Federal Election Commission (1989) Report on the visit by the Federal Election Commission to the Soviet Union, June 1989. Federal Election Commission, Washington, DC

    Google Scholar 

  • Fishburn PC, Brams SJ (1991) Yes–no voting. Soc Choice Welf 10:35–50

    MathSciNet  Google Scholar 

  • Fishburn PC, Little JDC (1988) An experiment in approval voting. Manage Sci 34(5):555–568

    Article  Google Scholar 

  • Fossum RM (2002) Private communication

  • Gardner M (written by Lynn Arthur Steen) (1980) Mathematical games (From counting votes to making votes count: the mathematics of elections). Sci. Am. 243(4):16ff

  • Gillman L (1987) Approval voting and the coming MAA elections. Focus: the newsletter of the mathematical association of America 7, no. 2 (March-April) 2, 5

  • Gordon JP (1981) Report of the secretary. Econometrica 48(1):229–233

    Google Scholar 

  • Guterman L (2002) When votes don't add up: mathematical theory reveals problems in election procedures. Chron High Educ A18–A19

  • Hill S (2002) Fixing elections: the failure of America's winner take all politics. Routledge, New York

    Google Scholar 

  • Jarvis JJ (1984) Council—actions and issues: approval voting. OR/MS Today 11(4):16

    MathSciNet  Google Scholar 

  • Keller B (1987) In Southern Russia, a glimpse of democracy. N Y Times 1, 4

  • Keller B (1988) Moscow says changes in voting usher in many new local leaders. N Y Times A1, A7

  • Kiely T (1991) A choice, not an echo? Technol Rev 94(6):19–20

    Google Scholar 

  • Kiewiet RD (1979) Approval voting: the case of the 1968 election. Polity 12(1):528–537

    Google Scholar 

  • Klarreich E (2002) Election selection: are we using the worst voting procedure? Sci News 162(18):280–282

    Google Scholar 

  • Laslier J-F (2003a) Analysing a preference and approval profile. Soc Choice Welf 20(2):229–242

    Article  MATH  Google Scholar 

  • Laslier J-F (2003b) Spatial approval voting. Working paper 2003–001, Laboratoire d'Econométrie, Ecole Polytechnique, Paris

    Google Scholar 

  • Laslier J-F, Van der Straeten K (2003) Approval voting: an experiment during the French 2002 presidential election. Laboratoire d'Econométrie, Ecole Polytechnique, Paris

    Google Scholar 

  • Lijphart A, Grofman B (eds) (1984) Choosing an electoral system: issues and alternatives. Praeger, New York

    Google Scholar 

  • Lines M (1986) Approval voting and strategy analysis: a venetian example. Theory Decis 20:155–172

    Article  MATH  MathSciNet  Google Scholar 

  • Little J, Fishburn P (1986) TIMS tests voting method. OR/MS Today 13(5):14–15

    Google Scholar 

  • MacKenzie D (2000) May the best man lose. Discover 21(11):84–91

    Google Scholar 

  • Merrill S III (1988) Making multicandidate elections more democratic. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Nagel J (1984) A debut for approval voting. PS Polit Sci Polit 17(1):62–65

    MathSciNet  Google Scholar 

  • National Academy of Sciences (1981) Constitution and Bylaws

  • Niemi RG (1984) The problem of strategic voting under approval voting. Am Polit Sci Rev 78(4):952–958

    MathSciNet  Google Scholar 

  • Niemi RG (1985) Reply to Brams and Fishurn. Am Polit Sci Rev 79(3):818–819

    Google Scholar 

  • Nurmi H (1987) Comparing voting systems. D. Reidel, Dordrecht, Holland

    Google Scholar 

  • Potthoff RF, Brams SJ (1998) Proportional representation: broadening the options. J Theor Polit 10(2):147–178

    Google Scholar 

  • Regenwetter M, Grofman B (1998) Approval voting, Borda winners, and Condorcet winners: evidence from seven elections. Manage Sci 44(4):520–533

    MATH  Google Scholar 

  • Reilly B (2002) Social choice in the south seas: electoral innovation and the Borda Count in the Pacific Island countries. Int Polit Sci Rev 23(4):355–372

    Google Scholar 

  • Richie R, Bouricius T, Macklin P (2001) Candidate number 1: instant runoff voting. Science 294:303–304

    Article  PubMed  CAS  Google Scholar 

  • Saari DG (2001a) Analyzing a nail-biting election. Soc Choice Welf 18(3):415–430

    Article  MATH  MathSciNet  Google Scholar 

  • Saari DG (2001b) Chaotic elections! a mathematician looks at voting. American Mathematical Society, Providence, RI

    MATH  Google Scholar 

  • Saari DG, Van Newenhizen Jill (1988) The problem of indeterminacy in approval, multiple, and truncated voting systems; Is approval voting an ‘unmitigated evil’?: a response to Brams, Fishburn, and Merrill. Public Choice 59:101–120, 133–147

    Article  Google Scholar 

  • Shabad T (1987) Soviets to begin multi-candidate election experiment in June. N Y Times A6

  • Steen LA (1985) Private communication

  • Tullock G (1979) Comment on Brams and Fishburn and Balinski and Young. Am Polit Sci Rev 73(2):552–553

    Google Scholar 

  • Weber RJ (1995) Approval voting. J Econ Perspect 9(1):39–49

    Google Scholar 

  • White S (1989) Reforming the electoral system [USSR]. J Communist Stud 4:1–17

    MATH  Google Scholar 

  • Wright J (1990) School funding reform options unpopular. Register-Guard (Eugene, OR):1C, 3C

Download references

Acknowledgements

We thank Richard F. Potthoff for valuable comments. Brams gratefully acknowledges the support of the C.V. Starr Center for Applied Economics at New York University.

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Authors and Affiliations

  1. Department of Politics, New York University, New York, NY, 10003, USA

    Steven J. Brams

  2. AT&T Shannon Laboratory, Information Sciences Research Center, Florham Park, NJ, 07932, USA

    Peter C. Fishburn

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  1. Steven J. Brams
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  2. Peter C. Fishburn
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Correspondence to Steven J. Brams.

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Prepared for delivery at the 2003 Annual Meeting of the American Political Science Association, August 28–August 31, 2003. Copyright by the American Political Science Association.

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Brams, S.J., Fishburn, P.C. Going from theory to practice: the mixed success of approval voting. Soc Choice Welfare 25, 457–474 (2005). https://doi.org/10.1007/s00355-005-0013-y

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