Strategic voting under conditions of uncertainty: A re-evaluation of Duverger's law

British Journal of Political Science

Volumn 37, Issue 2, 2007, Pages 313-332

  Clough, Emily ^a  

^a UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947655909     PISSN: 00071234     EISSN: 14692112     Source Type: Journal    
DOI: 10.1017/S0007123407000154     Document Type: Article

References (60)

1. Maurice Duverger, Political Parties (New York: Wiley, 1954).
2. E.g. Douglas W. Rae, The Political Consequences of Electoral Laws (New Haven, Conn.: Yale University Press, 1971).
3. E.g. Seymour M. Lipset and Stein Rokkan, Party Systems and Voter Alignments: Cross-National Perspective (New York: The Free Press, 1967).
4. Duverger, Political Parties;
5. Gary Cox, 'Strategic Voting Equilibria Under the Single Non-Transferable Vote', American Political Science Review, 88 (1994), 608-21;
6. Gary Cox, Making Votes Count (New York: Cambridge University Press, 1997).
7. A single-member plurality system is one in which each electoral district elects only one representative and that representative is chosen by receiving a plurality of the vote.
8. Cox, Making Votes Count, p. 79.
9. Cox, 'Strategic Voting Equilibria under the Single Non-transferable Vote'; and Cox, Making Votes Count.
10. Duverger, Political Parties.
11. Duverger, Political Parties, p. 226.
12. John Sprague, 'On Duverger's Sociological Law: The Connection Between Electoral Laws and Party Systems' (St. Louis: Washington University, Political Science Paper No. 48, 1980).
13. While game theorists have become interested in strategic voting in the last fifteen years, a number of decision theorists tackled the issue somewhat earlier. Important works include Richard McKelvey and Peter Ordeshook, 'A General Theory of the Calculus of Voting', in J. F. Herndon and J. L. Bernd, Mathematical Applications in Political Science, 6 (1972), pp. 32-78;
14. and Dale T. Hoffman, 'A Model for Strategic Voting', SIAM Journal of Applied Mathematics, 42 (1982), 751-61.
15. Gary Cox, 'Duverger's Law and Strategic Voting' (unpublished, University of Texas, 1987);
16. Thomas Palfrey, 'A Mathematical Proof of Duverger's Law', in Peter C. Ordeshook, ed., Models of Strategic Choice in Politics (Ann Arbor: University of Michigan Press, 1989), pp. 69-91.
17. Cox, 'Strategic Voting Equilibria under the Single Non-transferable Vote'; Cox, Making Votes Count.
18. For instance, Mark Fey's ('Stability and Coordination in Duverger's Law: A Formal Model of Preelection Polls and Strategic Voting', American Political Science Review, 91 (1997), 135-47)
19. treatment of Roger Meyerson and Robert Weber's ('A Theory of Voting Equilibria', American Political Science Review, 87 (1993), 102-14) model showed how polling could eliminate non-Duvergerian equilibria.
20. James Sundquist, Dynamics of the Party System (Washingon, D.C.: The Brookings Institution, 1986).
21. Pradeep K. Chhibber and Ken Kollman, The Formation of National Party Systems (Princeton, N.J.: Princeton University Press, 2004).
22. Rajeeva L. Karandikar, Clive Payne and Yogendra Yadav, 'Predicting the 1998 Indian Parliamentary Election', Electoral Studies, 21 (2002), 69-89.
23. Cox, Making Votes Count, p. 79.
24. Paul R. Abramson, John H. Aldrich, Phil Paolino and David W. Rohde, 'Sophisticated Voting in the 1988 Presidential Primaries', American Political Science Review, 86 (1992), 55-69.
25. Jerome Black, 'The Multicandidate Calculus of Voting: Applications to Canadian Federal Elections', American Journal of Political Science, 22 (1978), 609-38.
26. Robert Forsythe et al., 'An Experiment on Coordination in Multicandidate Elections: The Importance of Polls and Election Histories', Social Choice and Welfare, 10 (1993), 223-47.
27. Recently David P. Myatt and Stephen D. Fisher, 'Tactical Coordination in Plurality Electoral Systems', Oxford Review of Economic Policy, 18 (2002), 504-22;
28. and David P. Myatt, 'A New Theory of Strategic Voting', Oxford Working Paper, no. 12 (2002), used the concept of a global game to look at strategic voting without common knowledge. Global games are games that alter the assumption of common knowledge by having each player observe a noisy signal from the true state of things. While the system generating the noise is common knowledge, the underlying state is not. This approach does allow the authors to move further from the common knowledge assumption.
29. Thomas Schelling, Micromotives and Macrobehavior (New York: W.W. Norton, 1978).
30. Cox, Making Votes Count.
31. Kenneth Kollman, John Miller and Scott Page, 'Adaptive Parties in Spatial Elections', American Political Science Review, 86 (1992), 929-37.
32. Given the simple nature of the model and the way utilities are calculated, multiple policy dimensions should have no effect in this model. However, it is possible that multi-dimensional preferences would affect where individuals acquire information. Voters may acquire information about different policy areas from different parts of their social networks. One interesting variation on the relatively simple model here would be to have individuals collecting information about different dimensions from different individuals.
33. Cox, Making Votes Count;
34. Palfrey, 'A Mathematical Proof of Duverger's Law'.
35. Cox, Making Votes Count, p. 97.
36. Amos Tversky and Daniel Kahneman, 'Judgement Under Uncertainty', Science, 185 (1974), 1124-31.
37. Cox, Making Votes Count;
38. Palfrey, 'A Mathematical Proof of Duverger's Law', p. 76.
39. Prospective ratings were first used by Myerson and Weber, 'A Theory of Equilibria'.
40. Duverger, Political Parties.
41. Cox, Making Votes Count.
42. The model was run on a Macintosh G5 computer with 1.25 GB of memory.
43. A torus is a shape in which the bottom and the top meet and the sides meet with one another; essentially, it looks like a doughnut.
44. Lars-Erik Cederman, Emergent Actors in World Politics: How States and Nations Develop and Dissolve (Princeton, N.J.: Princeton University Press, 1997);
45. and Joshua M. Epstein and Robert Axtell, Growing Artificial Societies: Social Science from the Bottom Up (Washington, D.C.: The Brookings Institution, 1996).
46. Roger Myerson and Robert Weber, 'A Theory of Voting Equilibria', American Political Review, 87 (1993), 102-14.
47. Introduced in Cox, Making Votes Count.
48. Kenneth Janda, Political Parties: A Cross-National Survey (New York: The Free Press, 1980).
49. Myatt, 'A New Theory of Strategic Voting'.
50. In order to test the effects of size of the grid on the results presented, the 8-168 neighbour versions of the model were run on a 25 × 25 grid. The increased size of the grid made it impossible to run results for larger neighbourhood sizes, especially the full information version of the model. While not precisely the same, the results were very similar, and the basic relationships between the relevant variables still held. This strongly suggests that the results hold for larger grid sizes (and hence larger populations).
51. Cox, Making Votes Count.
52. Using a two-tailed difference of proportions test, these differences were found to be significant at the 0.01 level.
53. Once again, these differences are significant at the 0.01 level.
54. Once again, these differences are significant at the 0.01 level.
55. When neighbourhood size is 168, voters are talking to the whole community.
56. In each case the histogram for the SF ratio distribution has a large spike at 0. In addition, the median SF ratio is 0 for each of these conditions and the average SF ratio is below 0.05.
57. These intervals are calculated using a finite population correction, and the standard errors were estimated using a proportion of 0.5.
58. Michael Huelshoff and Marc Rosenblum, 'Determinants of Party Systems: Comparing Established and New Democracies', paper presented at the Midwest Political Science Association Annual Meeting, April 2005.
59. Chhibber and Kollman, The Formation of National Party Systems.
60. James Sundquist, Dynamics of the Party System: Alignment and Realignment of Political Parties in the United States (Washington, D.C.: The Brookings Institution, 1986).