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Identifying the bandwagon effect in two-round elections

Abstract

We propose a new method to test for the existence of the bandwagon effect, the notion that voters are more likely to vote for a given candidate if they expect the candidate to win. Two-round election systems with a large number of single-member districts offer an ideal testing ground because results from the first round provide a better benchmark for voter expectations than any possible alternative measure. Using data from the 2002 and 2006 general elections in Hungary, we find that the lead of a candidate in the first round is magnified by about 10 percent in the second round, controlling for country-wide swings of the electorate between the two rounds and for the behavior of voters of smaller parties. A separate exercise suggests that at least part of the effect is caused by the lower probability of individuals voting in the second round if their preferred candidate is likely to lose by a large margin.

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Fig. 1

Notes

  1. The few recent theoretical studies include Hong and Konrad (1998) and Callander (2007). In contexts other than elections, social psychologists and economists have analyzed related phenomena. Psychological research dates back to the well-known conformity experiments by Asch (1951, 1955). The concept of bandwagon effect in the microeconomics of consumption was introduced by Leibenstein (1950). Recent research looks at the causes and consequences of the bandwagon effect in social networks (Golub and Jackson 2010).

  2. Bartels (1985), Skalaban (1988) and McAllister and Studlar (1991) all address this problem of reverse causality and try to control for it in different ways. See also Krizan et al. (2010) for a recent analysis focusing on the projection effect.

  3. This link between the West Coast and bandwagon effects has been made by Hodgson and Maloney (2013).

  4. Lott (2005) found evidence for a similar effect in the 2000 presidential election in Florida. Turnout was reduced in 10 counties of the Western ‘Panhandle’ where, due to the different time zone from the rest of the state, polls closed later. The low turnout was apparently due to the fact that television networks called the Florida race early (and, as it turned out, wrongly).

  5. Separately, we are also able to test whether the national leader enjoys a boost in runoff elections but we find no evidence for this. The only year when there seems to be a large swing between both rounds in our data is 2002, and the swing benefits the losing side.

  6. Two-round elections have been used to identify the effect of the closeness of an election on turnout (Fauvelle-Aymar and Francois 2006; Simonovits 2012). We are not aware of any study using two-round elections to identify the bandwagon effect.

  7. In a previous version of the paper, these districts were not removed; the results remain qualitatively, as well as quantitatively, very similar if these districts are included in the analysis.

  8. The official results of Hungarian elections are publicly available on the website of the Hungarian Election Committee, www.valasztas.hu. The data are also available, in a more easily usable form, on the website www.vokscentrum.hu (accessed in September 2012).

  9. For a thorough treatment on strategic voting, see Cox (1997).

  10. In a complementary project, Kiss (2012) analyses strategic voting in Hungarian general elections in the period 1990–2010, focusing on three-candidate runoff contests.

  11. An earlier version of the paper included another alternative specification in which vote shares were defined not as percentages of valid votes but as votes cast as a percentage of the number of eligible voters. That definition is, however, inferior to our main specification because a uniform increase in the participation rate between both rounds biases the bandwagon coefficient upwards (and vice versa). Overall, results from this alternative specification are similar to our baseline results, although, as predicted, the estimated bandwagon effect is larger in 2002 (when participation increased between both rounds) and lower and statistically not significant in 2006 (when participation declined between both rounds).

  12. While Ashworth et al. (2006) do not refer to the literature on the bandwagon effect, some aspects of their analysis can be seen as related to it. Analyzing a cross section of Belgian municipal elections, they find a non-linear relationship between closeness and turnout: turnout falls with the margin of victory to a point, but starts to rise again for very lopsided races.

  13. We would like to thank an anonymous referee for suggesting the analysis of possible nonlinearity.

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Acknowledgements

This research had been conducted before Áron Kiss started working at the European Commission. Opinions expressed in this paper are those of the authors and do not reflect the views of their past or present institutions. The authors would like to thank Ivo Bischoff, Benny Geys, Kai Konrad, Balázs Muraközy, Christian Pfeil, Gábor Tóka, Balázs Váradi, participants of the PolBeRG seminar at Central European University (Budapest), the Meeting of the Hungarian Association for Economics in 2011, and the European Public Choice Society Meeting 2013 (Zürich), as well as four anonymous referees and the Editor in Chief, for useful comments and suggestions. Any remaining error or omission is our responsibility.

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Appendix: Analysis of the 1998 election

Appendix: Analysis of the 1998 election

In 1998 there were 88 districts where the candidates of Fidesz and the Socialist Party received the most votes in the first round, and subsequently competed in a two-way runoff election. Table 6 details what happened in the other districts. The third row of the table shows that there were 35 districts in which turnout was less than 50 % in the first round. According to the electoral law, all candidates qualified for the first-past-the post second round in these districts, because of which we excluded them from the sample.

Table 6 Deriving the sample of districts in the 1998 election

The districts with two-candidate races came about as a result of endorsements. Fidesz and the Democratic Forum had many joint candidates already in the first round. But in those districts where Forum ran separately, Forum endorsed Fidesz before the second round. In addition, the Smallholders’ Party withdrew many of their third-place candidates unilaterally ahead of the second round and endorsed Fidesz. The Socialists and Free Democrats agreed to withdraw their weaker candidates in most, but not all, districts. As part of the deal, the Socialists withdrew three of their second-place candidates and endorsed a third-place Free Democrat (see row 7 in Table 1).

Table 7 shows summary statistics for the election contests in our sample. The participation rate was similar in both rounds: 58 % in the first and 58.6 % in the second.

Table 7 Summary statistics

The table confirms that both major parties had a far lower vote share in the first round than in either 2002 or 2006: Socialist candidates received, on average, 31 % of the first-round vote, while Fidesz’s candidates received 28 %. The table also details the vote shares of third-party candidates in the first round. It is testimony of the gradually increasing concentration of the party landscape that there were more third-party candidates in 1998 than in later elections.

The results of the regression analysis (see Table 8) show that in the 1998 election, unlike in 2002 and 2006, it makes a difference whether we take party alliances into account. The first three columns of Table 8 repeat our baseline analysis for 1998 without regard to alliances. While the bivariate regression shows a bandwagon coefficient similar in magnitude to our main analysis, the coefficient is not statistically significantly different from one (column 1). Controlling for the vote share of third parties in the first round makes the bandwagon effect disappear completely (columns 2 and 3): according to the estimation a one-percent Fidesz lead in the first round translates into a lead of the same size in the second.

Table 8 Regression analysis of the bandwagon effect in the 1998 election

The bandwagon effect reappears, however, if we take into account party alliances. The support of the Democratic Forum and the Smallholders’ Party manifested itself not only in the endorsement decision of party leaders. Voters of these parties also gave their full support to candidates of Fidesz (see columns 2 and 3 of Table 8). These parties came to form the new government after the elections.

On the political left, while the Socialists entered into an electoral alliance with their coalition partners the Free Democrats, it appears that the voters of this party supported Socialist candidates to a much lesser degree than in subsequent elections. It is estimated in column 2 and 3 that Socialist candidates received only about 30 % of Free Democratic support in the runoff. In contrast, Workers’ Party voters appear to have given their full support to the Socialist candidate in the second round.

Based on these observations, the exercise was repeated to reflect functioning party alliances. The alliance of Fidesz was assumed to include the Forum and the Smallholders’ Party, while the alliance of the Socialists was assumed to include the Workers’ Party. We decided against including the Free Democrats in the Socialists’ coalition (and the Christian Democrats in that of Fidesz) because it is estimated that less than half of their voters supported the respective major party candidate in the second round.

The results of the ‘Alliance specification’ are shown in columns (4) to (6) of Table 8. The bivariate regression shows a bandwagon coefficient of 1.13, statistically significantly above 1. Taking into account the vote share of third parties makes the coefficient become smaller (about 1.085), but still statistically significantly higher than 1 at the 5 % level. The coefficients of the other parties remain very close to the ‘No alliance’ estimates.

In sum, the analysis finds evidence for the bandwagon effect in the 1998 election, comparable in magnitude to our analysis of 2002 and 2006, but only once party alliances are taken into account. These findings make sense since the major parties received only about 30 % of the vote each in the first round, a much smaller share than in 2002 and 2006. As the voters of 1998 seem to have done, the researcher must look into the results of other parties to find out ‘who was in the lead’ in a given district after the first round.

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Kiss, Á., Simonovits, G. Identifying the bandwagon effect in two-round elections. Public Choice 160, 327–344 (2014). https://doi.org/10.1007/s11127-013-0146-y

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Keywords

  • Bandwagon effect
  • Underdog effect
  • Two-round elections
  • Runoff
  • Turnout
  • West Coast effect

JEL Classification

  • D72
  • D80