Majority cycles in national elections

Transcription

1 Majority cycles in national elections Bodo Knoll, Joan Serra 1 University of Bochum Abstract This paper provides information on cycle probabilities for 147 national elections and tests if a high level of political information reduces the empirical probability of Condorcet cycles. We construct preference ratings for parties and party leaders from the Comparative Study of Electoral Systems survey database, and we identify three cyclical group preferences for parties and three cyclical preferences for party leaders in 147 elections studied. Only one of these cycles affects the winner and, therefore, no best alternative exists. A bootstrapping exercise shows that the probability of a majority cycle in none of these six cases exceeds 40%. Our results suggest, therefore, that Condorcet cycles in national elections are rare. We compare subsamples of well and less informed citizens to test if the absence of cycles is caused by a similar assessment of parties and leaders of large groups of politically informed voters. We find some evidence for this hypothesis as cycles are more likely in the sample of less sophisticated voters. Keywords: Majority cycle, Condorcet Paradox, Comparative Study of Electoral Systems 1. Introduction Majority cycles, also known as Condorcet cycles or the voting paradox, have attracted a large amount of interest in the public choice literature. Theoretical papers have focused on analyzing which characteristics of preference profiles 1 Bodo Knoll, Joan Serra, University of Bochum, Department of Economics, Chair of Public Finance and Economic Policy, Universitätsstr. 150, Bochum Preprint submitted to 24th World Congress of Political Science July 23-28, 2016, Pozna, PolandJuly 1, 2016

2 make majority cycles more likely. Single-peaked preferences over onedimensional alternatives (e.g. ranked on a left-right scale) exclude majority cycles (Black, 1958). With equiprobable preference profiles, the likelihood of cycles rises with the number of alternatives and the number of voters (see e.g. Gehrlein (1983)). In actual large elections cycles have been searched so far only in a casuistic manner. They have been detected rarely; only two emirical studies find cycles in national elections to the best of our knowledge. 2 Kurrild-Klitgaard (2001) shows a cycle for a sample of 1994 Danish national election voters and Smith (2009) makes use of several polls and actual election outcomes to show a cycle in the 2009 Romanian presidential election. The purpose of the present paper is to look for Condorcet cycles in a large sample of national elections and to empirically assess their likelihood. We study electoral surveys from 147 national parliamentary elections in 62 different countries from 1996 to We take advantage of the richness of the surveys to look for cycles both among parties and among party leaders. Furthermore, the paper accounts for the fact that only samples of about 1000 to 2000 voters per election are included in the surveys. Cycles found in the sample of voters who participated in the election survey do not necessarily indicate a cycle in the entire population (see Regenwetter et al., 2002). Therefore, we bootstrap the cycle search procedure for each election and calculate probabilities that cycles occur in the actual electorate. A reason for the failure to observe electoral cycles in national elections may be that these electorates have largely onedimensional electoral preferences, for example along the left-right dimension. In a classic empirical study, Converse (1964) shows that the level of structure in the political preferences is higher among voters with higher levels of information about politics and with higher levels of education. Following this observation, we complete our analysis by splitting the national samples into several subsamples: We compare respon- 2 See Van Deemen (2014) for a good recent overview of the empirical search for majority cycles. 2

3 35 dents with high and low levels of education and likewise groups of politically well informed and less informed citizens to test whether education and political information reduce the probability of cycles. 2. Data and methodology The data comes from the Comparative Study of Electoral Systems (CSES) database (modules 1-4) which collects surveys of post-election studies from 147 elections in 62 countries from 1996 to It includes information on political opinions of voters. Participants of the election studies in our dataset are asked to indicate if they like or dislike political parties and party leaders on a scale from 0 to 10. Following the procedure described in Van Deemen & Vergunst (1998),we interpret these two questions as ordinal preferences for parties and party leaders respectively and identify majority cycles. In a second step we bootstrap the cycle search procedure. For each election and both the party preferences and the party leader preferences we draw bootstrap samples and construct the skew-symmetric matrix described above in order to detect majority cycles and check the samples for the existence of a Condorcet winner. In a third step we split the sample into subgroups and calculate cycle probabilities for each subgroup in every election. This split is done according to voters level of information about politics and according to their level of education. Respondents are considered to be informed about politics if they could answer right at least two questions in a three question political information quiz. The subsample of voters with a high education level includes all respondents who completed secondary education. Both variables divide the sample into two similarly sized halves. In order to check whether the differences are significant we conduct two-sample Kolmogorov-Smirnov tests. 3

4 3. Empirical results and discussion We find six majority cycles in the survey populations, three of these cycles relate to voters party preferences, three relate to preferences for party leaders. One cycle affects the most preferred alternatives and therefore no Condorcet winner exists. Table 1 lists all cycles along with the corresponding sample sizes, the number of alternatives and the empirical cycle probability calculated in the bootstrap exercise. In no case the probability of a cycle in the actual population exceeds 40%. Table 1 about here Table 2 shows the results for subsamples of politically informed and uninformed voters respectively. Results in Table 3 are based on a split of the sample into voters with a high and a low level of education. Both comparisons demonstrate systematic differences between the subsamples. We find many more cycles in elections if the electorate is constrained to less informed or less educated voters. Most cycles that occur in groups of well informed voters apply to preferences for party leader whereas the politically uninformed would generate many cycles in their party preferences. The empirical cycle probabilities are also higher in some elections. Under the impartial culture assumption, less cycles should occur as the smaller number of voters in the subsample reduces mechanically the probability of a cycle. On the other hand, Tangian (2000) argues that cycles can be interpreted as errors in ranking candidates according to their strength or merits. In a large electorate these errors vanish and Condorcet cycles are less likely. Our results are in line with this view which may also account for the observation that most cycles do not include the top alternatives. Small parties and leaders are not well known by voters. Hence, less voters report a preference for these alternatives. And we may assume that the individual probability of errors in ranking unknown parties or party leaders is higher than in ranking well known alternatives. Both reasons explain why many of the cycles in our data are characterized by tiny majorities of few voters in pairwise comparisons 4

5 90 of small parties. Note further, that cycles in the entire survey population do not necessarily prevail in the subsamples. This is not surprising as our bootstrap exercise shows that even random draws from the survey participants would lead to cycles in at most 35% of all draws. For this reason, we focus on the empirical probability of cycles in the following. Table 2 about here Table 3 about here In order to compare our subgroups of well-informed (well-educated) and lessinformed (less-educated) voters, we consider the empirical cycle propensities as a characteristic of each election. Figure 1 shows the distribution of the estimated bootstrap probabilities for the subsamples with high and low levels of information. According to a Kolmogorov-Smirnov test the cumulative density functions differ significantly. An electorate consisting of well-informed voters is more likely to end up in an election with a low cycle probability. This pattern holds both for preferences over parties and preferences over party leaders. Figure 1 about here 105 Figure 2 shows the same exercise for a sample split based on the education levels of voters. Again, we find significant differences in the distribution of cycle probabilities among the two subgroups with p-values of 0.14% and 5.72% respectively. Figure 2 about here 4. Conclusion 110 This paper confirms that majority cycles hardly occur in any election. Empirical cycle probabilities based on preference profiles of survey respondents are low; and this result holds regardless if people are asked to vote for parties or party leaders. Having data on preferences of many voters in a large set of national elections allows to analyze potential causes of high cycle probabilities. 5

6 One strategy is to split the survey samples into artificial subgroups sharing specific characteristics. We demonstrate this strategy by addressing the research question whether low political information and low levels of education in a population raise empirical cycle probabilities. We find that the subgroup of uninformed and less educated voters observes significantly higher cycle probabilities and is closer to a random assignment of preferences. Future research may follow and extend this approach by splitting samples according to other characteristics of voters or taking into account several dimensions simultaneously. Furthermore, it is still an open question whether a large number of voters raises or reduces the empirical probability of cycles. Controlling for the size of the bootstrap samples helps to test opposing theories empirically. References Black, D. (1958). The theory of committees and elections. Cambridge: Cambridge University Press. 130 Converse, P. E. (1964). The nature of belief systems in mass publics. In D. E. Apter (Ed.), Ideology and Its Discontents (pp ). New York: Free Press. Gehrlein, W. (1983). Condorcet s paradox. Theory and Decision, 15, Kurrild-Klitgaard, P. (2001). An empirical example of the condorcet paradox of voting in a large electorate. Public Choice, 107, Regenwetter, M., Adams, J., & Grofman, B. (2002). On the (sample) condorcet efficiency of majority rule: An alternative view of majority cycles and social homogeneity. Theory and Decision, 53, Smith, W. D. (2009). The romanian 2009 presidential election featured one or more high condorcet cycles. RangeVoting. org., Center for Range Voting, Tangian, A. S. (2000). Unlikelihood of condorcets paradox in a large society. Social Choice and Welfare, 17,

7 Van Deemen, A. (2014). Public Choice, 158, On the empirical relevance of condorcets paradox. 145 Van Deemen, A., & Vergunst, N. (1998). Empirical evidence of paradoxes of voting in dutch elections. Public Choice, 97,

8 5. Tables Table 1: List of Cycles Country Year Unit Voters Alternatives Top Cycle Bootstrap Switzerland 1999 Party Philippines 2004 Party Spain 2008 Party Peru 2000 Leader Czech Republic 2006 Leader Denmark 2007 Leader x

9 Table 2: Cycles by Level of Information Country Year Unit Voters Alternatives Top Cycle Bootstrap High Information Switzerland 2011 Party Romania 1996 Leader x Finland 2011 Leader New Zealand 2008 Leader Thailand 2011 Leader Low Information Albania 2005 Party France 2002 Party Italy 2006 Party Netherlands 2002 Party Norway 2001 Party Germany 2009 Party South Korea 2008 Party Philippines 2010 Party Switzerland 2011 Party Spain 2008 Leader x

10 Table 3: Cycles by Level of Education Country Year Unit Voters Alternatives Top Cycle Bootstrap High Education Lithuania 1997 Party x Russian Federation 1999 Party Great Britain 2005 Party Italy 2006 Party Chile 2009 Party Denmark 2007 Leader x Finland 2007 Leader Montenegro 2012 Leader Low Education Republic Of Korea 2000 Party Bulgaria 2001 Party Denmark 2001 Party Finland 2003 Party Kyrgyzstan 2005 Party Philippines 2004 Party Belarus 2008 Party Switzerland 2007 Party Germany 2009 Party Finland 2011 Party Hong Kong 2008 Party Israel 2006 Party Switzerland 2011 Party France 2012 Party Thailand 2011 Party Peru 2001 Leader Belarus 2008 Leader

11 Spain 2008 Leader Slovenia 2008 Leader

12 6. Figures Figure 1: Cycles and Information Party Cycle Probabilities by Information Leader Cycle Probabilities by Information Cumulative Probability High Information Voters Low Information Voters K S test: p value: Cumulative Probability High Information Voters Low Information Voters K S test: p value: Probability of Cycles Parties Probability of Cycles Leaders 12

13 Figure 2: Cycles and Education Party Cycle Probabilities by Education Leader Cycle Probabilities by Education Cumulative Probability High Education Voters Low Education Voters K S test: p value: Cumulative Probability High Education Voters Low Education Voters K S test: p value: Probability of Cycles Parties Probability of Cycles Leaders 13