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Empirical and Formal Models of the United States Presidential Elections in 2000 and 2004

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Political Economy of Institutions, Democracy and Voting

Abstract

This chapter develops a general stochastic model of elections in which the electoral response is affected by the valence (or quality) of the candidates. In an attempt to explain non-convergence of candidate positions in the 2000 and 2004 Presidential elections, a formal spatial stochastic model, based on intrinsic valence, is presented. A pure spatial model of the election is constructed. It is shown that the equilibria, under vote maximization, do indeed lie at the electoral origin. Other work on Presidential elections in the United States has suggested that a superior empirical model should incorporate the electoral perceptions of the candidate character traits. The chapter then considers a joint model with sociodemographic valences as well as electoral perception of traits and shows by simulation that the vote maximizing equilibrium positions were close to, but not precisely at, the electoral origin. This model used electoral estimates of the candidates.positions. These differed substantially from the estimated equilibria of the traits model. To account for this difference, a more general formal model is then considered where the valence differences between the candidates were due to resources that were contributed to the candidates by party activists. The trade off between activist and electoral support is given by a (first order) balance condition involving, called the centrifugal marginal activist pull. Survey information on party activists, who contributed resources to the candidates, was obtained. It is argued that the difference between the equilibrium obtained from the spatial model with traits, and the estimated candidate positions, is compatible with the location of these activists. The final model is one where the activist resources are used by candidates to target individual voters or groups of voters. The balance condition in this case involves a complex constrained optimization problem, that captures the essence of modern electoral politics.

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Notes

  1. 1.

    See the earlier work by Enelow and Hinich (1982, 1989), Erikson and Romero (1990) and more recent work by Duggan (2006), McKelvey and Patty (2006) and Patty et al. (2009).

  2. 2.

    Ansolabehere and Snyder (2000), Groseclose (2001), Aragones and Palfrey (2002, 2005), Adams and Merrill (2002, 2005), Banks and Duggan (2005), Ashworth and Bueno de Mesquita (2009), Jessee (2009, 2010), Zakharov (2009), Serra (2010).

  3. 3.

    The empirical analyses were based on the 2000 and 2004 American National Election Surveys (ANES).

  4. 4.

    See also Clarke et al. (2005). Jesee (2009, 2010) has also examined partisan bias in the 2004 and 2008 Presidential elections.

  5. 5.

    We focus on local equilibria because we consider that candidates will only be able to make small adjustments to their policy statements as the election nears.

  6. 6.

    We focus on vote maximizing rather than maximizing the probability of winning because the former model is linear and would seem to more closely characterize the likely behavior of candidates adapting to electoral information obtained from polls and the like. As Patty (2002, 2007) has shown, these two classes of models differ in the equilibria.

  7. 7.

    For convenience, it is assumed that μ(z j ) is only dependent on z j , and not on z k , \( k\, \ne \,j \), but this is not a cucial assumption.

  8. 8.

    We mean by this that the appropriate Hessians have negative eigenvalues of sufficient magnitude.

  9. 9.

    An earlier paper by Groseclose and Snyder (1996) looked at vote buying, but in the legislature.

  10. 10.

    Snyder and Ting (2008) also consider the contracts between activists and candidates but assume that the policy space is one dimensional.

  11. 11.

    Indeed, Herrera et al. (2008) observe that spending by parties in federal campaigns went from 58 million dollars in 1976 to over 1 billion in 2004 in nominal terms.

  12. 12.

    See the works by Fiorina et al. (2005), Fiorina and Abrams (2009) and McCarty et al. (2006) on polarization in the electorate and Layman et al. (2010) on polarization among activists. Schofield et al. (2011) gives similar results for the 2008 election.

  13. 13.

    See also the earlier work by Sundquist (1973).

  14. 14.

    All models in Table 4 are given with Gore as the base, so the results give the estimations of the probability of voting for Bush.

  15. 15.

    Table 4 shows that the pure traits model has an AIC of 574.8. This compares with an AIC of 664.3 for the trait model found by Clarke et al. (2009a).

  16. 16.

    The AIC results are similar. The AIC for the pure traits model is 575, which drops to 563 when β is added and drops further to 549 with the addition of the sociodemographics.

  17. 17.

    As we show in Sect. 4.3, we can interpret these terms as policy preferences on the part of candidates, but induced from the policy preferences of activists.

  18. 18.

    Notice that the difference between the loglikihoods of the joint spatial model and that of the pure spatial model is +53. It is possible that adding further demographic variables would change the LNE of the joint model. However, since the effect of sociodemographic variables is limited, it is unlikely that there would be any substantial effect on the LNE.

  19. 19.

    Clarke et al. (2009a) obtained an AIC of 239 for a composite version of the model here called JPT. However, they used many more sociodemographic variables. The value of 297.7 for the AIC of the spatial model, JST, suggests that it is a valid model of electoral behavior.

  20. 20.

    This deal between the two opposed coalitions will have a serious effect on the overall U.S. debt.

  21. 21.

    The bill did make it more difficult to transfer detainees from Guantánamo.

  22. 22.

    We can use the model either for party leaders or candidates for office, as in the United States. In the following we shall use the term agents to mean either one.

  23. 23.

    For refining the model, and for empirical analysis, we could adapt the model so that parties choose positions to maximize their seat shares, relative to a given constituency structure. We adopt the simplifying vote share assumption in order to present the essential structure of the formal model.

  24. 24.

    See Clarke et al. (2009a) for the same empirical procedure.

  25. 25.

    We keep to strict equilibria to avoid non-generic problems when one eigenvalue is zero.

  26. 26.

    For example, presidential candidates may attempt to maximize total electoral votes, so voters can be weighted by the relative electoral college seats of the state they reside in.

  27. 27.

    By this we mean that the eigenvalues of the activist functions are negative and of sufficient magnitude everywhere. That is to say, there exists α < 0, such that all eigenvalues < α is sufficient to guarantee existence of a PNE.

  28. 28.

    It is worth observing that if we use just distance rather than distance squared then the first order condition is essentially a counting rule, giving a median position of the candidates as equilibrium.

  29. 29.

    This can be done using the gradient equation given below.

  30. 30.

    Strictly speaking, the condition is that the eigenvalues are non-positive. To avoid the degenerate case with a zero eigenvalue, we focus on a strict local equilibrium associated with negative eigenvalues of the Hessian.

  31. 31.

    In the usual way, the condition for an LNE is that the eigenvalues are negative semidefinite.

  32. 32.

    Indeed, we found the same result for the 2008 election reported in Schofield et al. (2011).

  33. 33.

    Stokes (2005) make a somewhat similar inference, discussing clientist models of politics, where m ij is simply a monetary bribe to i. Obviously the marginal benefit to a poor voter is greater than to a wealthy voter, under the usual assumption of decreasing marginal utility for money. Dal Bo (2007) also considers a model of bribery but does not consider income effect per se.

  34. 34.

    It is reasonable to assume that the resource distributions lie in a compact ball, namely \( {{\mathbb{B}}^{n \times p}} \).

  35. 35.

    See Coram (2010) and Duggan and Kalandrakis (2011) for dynamical versions of bargaining models. Acemoglu and Robinson (2008) also develop a model based on Markov Perfect Equilibrium where the elite, the activists, have different preferences for the public good, in X and contribute to the de facto power, or political strength, of the political leader. However, they do not assume competing political leaders.

  36. 36.

    The “matching” model proposed by Jackson and Watts (2010) embeds the Nash equilibrium within a coalition game, and would allow the principals to switch from one agent coalition to another.

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Acknowledgments

This chapter is based on work supported by NSF grant 0715929. This version was completed while Schofield was the Glenn Campbell and Rita Ricardo-Campbell National Fellow at the Hoover Institution, Stanford, 2010. A version was presented at the International Conference on the Political Economy of Democratic Institutions, Baiona, Spain, June 14–16, 2010. We thank Jon Eguia for very helpful comments.

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Authors and Affiliations

  1. Washington University in Saint Louis, St. Louis, MO, USA

    Norman Schofield, Christopher Claassen, Maria Gallego & Ugur Ozdemir

  2. Department of Economics, Wilfrid Laurier University, Waterloo, ON, Canada

    Maria Gallego

Authors
  1. Norman Schofield
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  2. Christopher Claassen
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  3. Maria Gallego
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  4. Ugur Ozdemir
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Correspondence to Norman Schofield .

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Editors and Affiliations

  1. Center in Political Economy, Washington University in St.-Louis, Brookings Drive 1, Saint Louis, 63130, Missouri, USA

    Norman Schofield

  2. , Faculty of Economics, University of Vigo, Lagoas Marcosende, Vigo, 36310, Spain

    Gonzalo Caballero

Data Appendix

Data Appendix

Question Wordings for the American National Election Surveys, for 2000 and 2004.

  1. 1.

    We need a strong government to handle today’s complex economic problems [1]; or the free market can handle these problems without government being involved [3].

  2. 2.

    Should federal spending on welfare programs be increased [1], decreased [3], or kept about the same? [2].

  3. 3.

    This country would be better if we worried less about how equal people are. Do you agree strongly [5], agree somewhat [4], neither agree nor disagree [3], disagree somewhat [2], or disagree strongly [1] with this statement?

  4. 4.

    Many minorities overcame prejudice and worked their way up. African Americans should do the same without any special favors. Do you agree strongly [5], agree somewhat [4], neither agree nor disagree [3], disagree somewhat [2], or disagree strongly [1] with this statement?

  5. 5.

    Do you think the number of immigrants from foreign countries who are permitted to come to the United States to live should be increased a lot [1], increased a little [2], left the same as it is now [3], decreased a little [4], or decreased a lot [5]?

  6. 6.

    We hear a lot of talk these days about liberals and conservatives. Here is a three-point scale on which the political views that people might hold are arranged from extremely liberal to extremely conservative. liberal = [1], moderate = [2], all conservative = [3].

  7. 7.

    Do you think the federal government should make it more difficult [1] for people to buy a gun than it is now, make it easier [3] for people, or keep the rules the same [2].

  8. 8.

    Which one of the opinions on this page best agrees with your view [on abortion]? By law, abortion should never be permitted [3]; The law should permit abortion only in case of rape, incest, or when the woman’s life is in danger [2]; The law should permit abortion for reasons other than rape, incest, or danger to the woman’s life, but only after the need for the abortion has been clearly established [2]; By law, a woman should always be able to obtain an abortion as a matter of personal choice [1].

  9. 9.

    Do you think gay or lesbian couples, in other words, homosexual couples, should be legally permitted to adopt children? Yes [1], No [3].

  10. 10.

    This country would have many fewer problems if there were more emphasis on traditional family ties. Do you agree strongly [5], agree somewhat [4], neither agree nor disagree [3], disagree somewhat [2], or disagree strongly [1] with this statement?

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Schofield, N., Claassen, C., Gallego, M., Ozdemir, U. (2011). Empirical and Formal Models of the United States Presidential Elections in 2000 and 2004. In: Schofield, N., Caballero, G. (eds) Political Economy of Institutions, Democracy and Voting. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19519-8_10

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