nach oben

Erschienen in:

2016 | OriginalPaper | Buchkapitel

Comparison of Voting Procedures Using Models of Electoral Competition with Endogenous Candidacy

verfasst von : Damien Bol, Arnaud Dellis, Mandar Oak

Erschienen in: The Political Economy of Social Choices

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This article surveys the latest advances in the literature on the comparative properties of different voting procedures in the context of political elections. In particular, we focus on the various attempts at understanding how different voting procedures affect the number of candidates and the positions they adopt. In public debate as well as academic scholarship, the comparative properties of different voting procedures has been a topic of enduring interest. This interest dates as far back as the late eighteenth century French philosopher-mathematicians Condorcet and Borda (and even earlier with the works of Lull and Cusanus), building up to the classic works of Arrow, May and Gibbard-Satthertwaite in the mid-twentieth century. The work in this tradition is largely confined to a rather abstract treatment of voting procedures, over an exogenously given set of alternatives.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Autocratic Health Versus Democratic Health: Different Outcome Variables for Health as a Factor Versus Health as a Right

Nächstes Kapitel Negative Advertising During Mexico’s 2012 Presidential Campaign

See Hotelling (1929), Downs (1957).

See Duverger (1954).

Under the plurality rule, each voter votes for one candidate and the candidate who gets the most votes is elected.

The plurality runoff rule takes several forms. In a standard form, each voter votes for one candidate. If a candidate gets a majority of votes, he is elected. Otherwise, all but the top two vote-getters are eliminated, and voters are invited to vote for one of the two candidates still standing. The one of these two candidates who then gets a majority of votes is elected.

There is a small literature on models of endogenous candidacy in multi-member district elections which we briefly refer to in the concluding section.

The numbers presented below are based on our own calculations on data from the comparative manifesto dataset (Volkens et al. 2015). The dataset can be accessed at https://manifestoproject.wzb.eu/

Australia uses the alternative vote rule, an example of instant runoff rule, in elections held to elect members of the House of Representatives; France uses the plurality runoff rule in its Presidential elections and in elections held to elect members of the Assemblée Nationale.

We use manually coded data from the comparative manifesto dataset (Volkens et al. 2015). In this dataset, each sentence is coded according to its theme, in particular, a left-wing theme (e.g., a sentence in favor of multiculturalism) and a right-wing theme (e.g., a sentence in favor of maintaining law and order). The left-right position of each party is calculated by taking the difference between the number of left and right sentences, and dividing this difference by the sum of left and right sentences altogether. This measure of the left-right position varies between − 1 (extreme left) to + 1 (extreme right).

For instance, even in the most moderate case of the US, the polarization index of 0.08 means that party manifestos have, on average, an imbalance of about 28 % of sentences towards left or right compared to the “center of gravity” of the party system.

Depending on the family of models, the set of potential candidates is disjoint from the set of voters (\(\mathcal{M}\cap \mathcal{N} =\emptyset\)) or is a subset of the set of voters (\(\mathcal{M}\subset \mathcal{N}\)).

Keep in mind that policy-motivation does not exclude the possibility that a Partisan is also office-motivated, i.e., cares about the policy outcome as well as the rent he can extract when holding office.

Cox (1990) follows a similar approach but extends the analysis to elections for multi-member districts, including the proportional representation system. For the purpose of our survey we focus only on single office elections. Hence, it is Cox (1987) that is immediately relevant for us.

That the set of feasible actions for each candidate is X and not X ∪{∅} means there is no option to not be part of the race. This is a common feature of the exogenous candidacy models. Alternatively, one could model the set of feasible actions as X ∪{∅} but then set δ(∅) > 0 and δ(x) = 0 for x ∈ X. This ensures that no candidate chooses action ∅.

Cox also considers the possibility that the candidates have a more complicated objective which he calls complete plurality maximization, meaning a candidate, for a given margin of victory, seeks to maximize the plurality relative to other candidate(s). Cox’s results generally do not depend on which of the objectives described above are candidates’ objectives, hence he collectively refers to them as “admissible candidate objectives”.

The normalization is without loss of generality.

They define formally a voting procedure as a function \(V: 2^{\mathcal{M}}\setminus \left \{\emptyset \right \}\times \mathcal{P}\rightarrow \mathcal{M}\), where \(\mathcal{P}\) is the set of all profiles of strict preference relations in which a candidate finds himself most preferred, such that for all \(\mathcal{C}\in 2^{\mathcal{M}}\setminus \left \{\emptyset \right \}\) and \(P \in \mathcal{P}\):

\(V \left (\mathcal{C},P\right ) \in \mathcal{C}\),

\(V \left (\mathcal{C},P\right ) = V \left (\mathcal{C},P^{{\prime}}\right )\) for all \(P^{{\prime}}\in \mathcal{P}\) such that P _n = P _n ^′ for every \(n \in \mathcal{N}\), where P _n is a strict preference relation for voter n, and

\(V \left (\mathcal{C},P\right ) = V \left (\mathcal{C},P^{{\prime}}\right )\) for all \(P^{{\prime}}\in \mathcal{P}\) such that \(P\mid _{\mathcal{C}} = P^{{\prime}}\mid _{\mathcal{C}}\), where \(P\mid _{\mathcal{C}}\) is the profile of strict preference relations P restricted to a non-empty set of candidates \(\mathcal{C}\).

In words, a voting procedure chooses a candidate from the non-empty set of candidates \(\mathcal{C}\subseteq \mathcal{M}\) (condition 1), is determined only by voters’ preferences (condition 2), and depends only on the preferences over the set of candidates \(\mathcal{C}\) (condition 3).

Formally, a voting procedure V is unanimous if \(V \left (\mathcal{C},P\right ) = b\) for any \(\mathcal{C}\subset \mathcal{M}\), \(P \in \mathcal{P}\), and \(b \in \mathcal{C}\) such that bP _n c for all \(c \in \mathcal{C}\setminus \left \{b\right \}\) and every voter \(n \in \mathcal{N}\).

Formally, a voting procedure V is candidate stable if \(V \left (\mathcal{M},P\right ) = V \left (\mathcal{M}\setminus \left \{a\right \},P\right )\) or \(V \left (\mathcal{M},P\right )P_{a}V \left (\mathcal{M}\setminus \left \{a\right \},P\right )\) for every \(a \in \mathcal{M}\) and \(P \in \mathcal{P}\).

Formally, a voting procedure V is dictatorial if there is a voter \(n \in \mathcal{N}\) such that \(V \left (\mathcal{M},P\right ) = top\left (\mathcal{M},P_{n}\right )\) and \(V \left (\mathcal{M}\setminus \left \{a\right \},P\right ) = top\left (\mathcal{M}\setminus \left \{a\right \},P_{n}\right )\) for all \(P \in \mathcal{P}\) and \(a \in \mathcal{M}\), where \(top\left (\mathcal{C},P_{n}\right )\) is voter n’s most preferred candidate in candidate set \(\mathcal{C}\).

Dutta et al. (2001) and Eraslan and McLennan (2004) examine the robustness of the above result to relaxing each of the following three assumptions: (1) the set of candidates is disjoint from the set of voters; (2) preferences are strict; and (3) ties are broken deterministically.

See Bol et al. (Forthcoming) for an attempt at using laboratory experiments to evaluate the contributions of strategic voting behavior and strategic candidacy behavior in explaining Duverger’s law.

Cahan and Slinko (2012) provides an attempt at characterizing non-symmetric (pure-strategy) equilibria in scoring rule elections.

Contributions in this family differ in the assumptions they make on the entry cost and on candidates’ objectives. Palfrey (1984) and Weber (1992) consider settings where there is no entry cost, with all potential candidates standing for election and seeking to maximize their vote share. Weber (1997) considers a setting in which candidates seek to maximize their vote share and a potential candidate contests the election if and only if he expects to receive at least a fraction \(q \in \left [0, 1\right ]\) of the votes. Finally, Callander (2005a,b) and Callander and Wilson (2007) consider settings in which candidates seek to maximize their winning probability and a potential candidate contests the election if and only if he anticipates to win with positive probability.

To simplify exposition, in this survey we consider the case where there are only two established candidates. Weber (1997) and Callander (2005a,b) consider a version of the model with an arbitrary finite number M ≥ 2 of established candidates.

To simplify exposition, we follow Callander (2005b) and assume that the density of voters’ ideal policies f is single-peaked and symmetric around the median voter’s ideal policy m.

For example, the alternative vote rule used for elections to the Australian House of Representatives requires every voter to cast a single ballot, in which she rank-orders all the candidates, from first to last. If one candidate is ranked first by a majority of voters, he is elected. Otherwise, the candidate who is ranked last on the greatest number of ballots is eliminated. Votes are then recounted using transformed ballots from which the eliminated candidate has been removed. A candidate is elected if he is ranked first on a majority of the transformed ballots. Otherwise, a second candidate is eliminated and votes are recounted using newly transformed ballots. The counting process is repeated until a candidate is elected.

It is important to keep in mind that this analysis provides a possible explanation for the stability of a two-party system under a runoff rule. There are other possible explanations such as ethnic composition (e.g., Ordeshook and Shvetsova 1994) or the specificities of each runoff rule. Discriminating between these different possible explanations is an important question which is not addressed in this analysis.

At the same time, there cannot be more than two candidates standing at x since one of them could then win outright by deviating and adopting a position on the left flank or on the right flank of x. Indeed, the deviator would then capture essentially half of the votes that were going to the candidates at x, instead of receiving only one third or less of these votes. Since all candidates must be tying for first place, the deviator would then win outright, implying that the deviation is beneficial and contradicting that we are at an equilibrium.

Bol et al. (2015) discusses alternative approaches that have been taken in order to ensure the existence of a pure-strategy Nash equilibrium under the plurality rule. To give an example, Feddersen et al. (1990) shows that when the voting behavior is assumed to be strategic, instead of sincere, an equilibrium exists under the plurality rule, in which all candidates standing for election adopt the position preferred by the median voter.

Moreover, no other potential candidate wants to enter the race at another position, for the same reasons that neither of the four candidates wants to deviate. And no other potential candidate wants to enter at x _L or x _R since he would split the votes with the other two candidates at this position, implying these three candidates would be eliminated at the first round and the two candidates at the other position would be moving to the second round.

The equilibrium concept is here a refinement of pure-strategy Nash equilibrium. We refer the interested reader to Xefteris (2016) for more details on this and on the concept of genericity.

To be sure, this example is not rigorous; its only purpose is to illustrate the mechanism underlying the difference between the plurality rule and the other multiple vote rules. The interested reader can consult the formal proofs in Xefteris (2016).

Intuitively, the restriction that no potential entrant, upon entry, can be among the top two voter-getters is a stronger restriction than that such entrant be the top vote-getter.

I.e., suppose that there is one citizen at each of the locations 0, 1∕N, 2∕N, ⋯ , 1 for some large integer N.

Under the plurality rule, voting for any candidate except the least preferred candidate is a weakly undominated strategy.

It can be verified that at δ ∈ [1∕9, 1∕3] no candidate located in between 1∕6 and 5∕6 would want to enter, nor either of the incumbent candidates would want to step down.

In the citizen-candidate model, there exists only the extensive margin for candidate behavior, i.e., each candidate either chooses to run at his ideal policy or not be in the race. In this family of models the system as a whole exhibits centrifugal, or centripetal, tendencies in the sense that it induces candidates located at symmetric, and therefore mutually balancing, positions around the median to stand for election, where their positions are further apart from, or closer to, the median.

Alesina, A. (1988). Credibility and policy convergence in a two-party system with rational voters. American Economic Review, 78(4), 796–805.

Ansolabehere, S., James, S. Jr., & Charles, S. III. (2001). Candidate positioning in U.S. house elections.American Journal of Political Science, 45(1), 136–159.CrossRef

Besley, T., & Stephen C. (1997). An economic model of representative democracy. Quarterly Journal of Economics, 112(1), 85–114.CrossRef

Bol, D., André B., & Simon L. S.-V (forthcoming). Which matters most: Party strategic exit or voter strategic voting? A laboratory experiment. Political Science Research and Methods.

Bol, D., Arnaud D., & Mandar, O. (2015). Endogenous Candidacy in Electoral Competition: A Survey on the Number of Candidates and their Polarization. Working paper.

Brusco, S., Marcin D., & Jaideep, R. (2012). The hotelling-downs model with runoff voting. Games and Economic Behavior, 74(2), 447–469.CrossRef

Cahan, D., & Arkadii, S. (2015). Nonconvergent Electoral Equilibria Under Scoring Rules: Beyond Plurality. Working paper.

Callander, S. (2005a). Electoral competition in heterogenous districts. Journal of Political Economy, 113(5), 1116–1145.CrossRef

Callander, S. (2005b). Duverger’s hypothesis, the run-off rule, and electoral competition. Political Analysis, 13(3), 209–232.CrossRef

Callander, S. (2008). Political motivations. Review of Economic Studies, 75(3), 671–697.CrossRef

Callander, S., & Catherine, W. (2007). Turnout, polarization, and Duverger’s law. Journal of Politics, 69(4), 1047–1056.CrossRef

Caselli, F., & Massimo, M. (2004). Bad politicians. Journal of Public Economics, 88(3–4), 759–782.CrossRef

Cox, G. (1987). Electoral equilibrium under alternative voting institutions. American Journal of Political Science, 31(1), 82–108.CrossRef

Cox, G. (1990). Centripetal and centrifugal incentives in electoral systems. American Journal of Political Science, 34(4), 903–935.CrossRef

Dalton, R. J. (2008). The quantity and the quality of party systems: Party system polarization, its measurement, and its consequences. Comparative Political Studies, 41(7), 899–920.CrossRef

De Sinopoli, F. (2004). A note on forward induction in a model of representative democracy. Games and Economic Behavior, 46(1), 41–54.CrossRef

De Sinopoli, F., & Alessandro, T. (2002). A remark on voters’ rationality in a model of representative democracy. Journal of Public Economic Theory, 4(2), 163–170.CrossRef

De Sinopoli, F., & Giovanna, I. (2007). A spatial voting model where proportional rule leads to two-party equilibria. International Journal of Game Theory, 35(2), 267–286.CrossRef

Dellis, A. (2009). Would letting people vote for multiple candidates yield policy moderation? Journal of Economic Theory, 144(2), 772–801.CrossRef

Dellis, A. (2013). The two-party system under alternative voting procedures. Social Choice and Welfare, 40(1), 263–284.CrossRef

Dellis, A., & Mandar, O. (2006). Approval voting with endogenous candidates. Games and Economic Behavior, 54(1), 47–76.CrossRef

Dellis, A., & Mandar, O. (2007). Policy convergence under approval and plurality voting: The role of policy commitment. Social Choice and Welfare, 29(2), 229–245.CrossRef

Dellis, A., & Mandar, O. (2016). Multiple votes, multiple candidacies and polarization. Social Choice and Welfare, 46(1), 1–38.CrossRef

Dellis, A., Alexandre G.-B., & Mandar, O. (2016). Policy Polarization and Strategic Candidacy in Elections Under the Alternative Vote Rule. Working paper.

Dhillon, A., & Ben, L. (2002). Multiple equilibria in the citizen-candidate model of representative democracy. Journal of Public Economic Theory, 4(2), 171–184.CrossRef

Downs, A. (1957). An economic theory of democracy. New York: Harper.

Duggan, J. (2006). Candidate objectives and electoral equilibrium. In B. Weingast, & D. Wittman (Eds.), The Oxford handbook of political economy. Oxford: Oxford University Press.

Dutta, B., Matthew, J., & Michel L. B. (2001). Strategic candidacy and voting procedures. Econometrica, 69(4), 1013–1037.CrossRef

Duverger, M. (1954). Political parties: Their organization and activity in the modern state. New York: Wiley.

Dziubiński, Marcin, and Jaideep, R. (2013). Hotelling-downs competition with free entry when voters have an option to contest. Journal of Public Economic Theory, 15(4), 620–653.CrossRef

Eguia, J. (2007). Citizen candidates under uncertainty. Social Choice and Welfare, 29(2), 317–331.CrossRef

Eraslan, H., & Andrew, M. (2004). Strategic candidacy for multivalued voting procedures. Journal of Economic Theory, 117(1), 29–54.CrossRef

Farrell, D. (2001). Electoral systems. A comparative introduction. New York: Palgrave.

Feddersen, T., Itai, S., & Stephen, W. (1990). Rational voting and candidate entry under plurality rule. American Journal of Political Science, 34(4), 1005–1016.CrossRef

Grosser, J., & Thomas, P. (2014). Candidate entry and political polarization: An antimedian voter theorem. American Journal of Political Science, 58(1), 127–143.CrossRef

Hotelling, H. (1929). Stability in competition. Economic Journal, 39(153), 41–57.CrossRef

Iaryczower, M., & Andrea, M. (2013). On the nature of competition in alternative electoral systems. Journal of Politics, 75(3), 743–756.CrossRef

Laakso, M., & Rein, T. (1979). Effective number of parties: A measure with application to West Europe. Comparative Political Studies, 12, 3–27.

Lee, D., Enrico, M., & Matthew, B. (2004). Do voters affect or elect policies? Evidence from the U.S. house. Quarterly Journal of Economics, 119(3), 807–859.CrossRef

Levy, G. (2004). A model of political parties. Journal of Economic Theory, 115(2), 250–277.CrossRef

Lupu, N. (2015). Party polarization and mass partisanship: A comparative perspective. Political Behavior, 37, 331–356.CrossRef

Mattozzi, A., & Antonio, M. (2008). Political careers or career politicians? Journal of Public Economics, 92(3–4), 597–608.CrossRef

Messner, M., & Mattias, P. (2004). Paying politicians. Journal of Public Economics, 88(12), 2423–2445.CrossRef

Morelli, M. (2004). Party formation and policy outcomes under different electoral systems. Review of Economic Studies, 71(3), 829–853.CrossRef

Myerson, R. (1999). Theoretical comparisons of electoral systems. European Economic Review, 43(4–6), 671–697.CrossRef

Myerson, R. (2002). Comparison of scoring rules in poisson voting games. Journal of Economic Theory, 103(1), 219–251.CrossRef

Myerson, R., & Robert, W. (1993). A theory of voting equilibria. American Political Science Review, 87(1), 102–114.CrossRef

Ordeshook, P., & Olga, S. (1994). Ethnic heterogeneity, district magnitude, and the number of parties. American Journal of Political Science, 38(1), 100–123.CrossRef

Osborne, M. (1993). Candidate positioning and entry in a political competition. Games and Economic Behavior, 5(1), 133–151.CrossRef

Osborne, M., & Al, S. (1996). A model of political competition with citizen-candidates. Quarterly Journal of Economics, 111(1), 65–96.CrossRef

Palfrey, T. (1984). Spatial equilibrium with entry. Review of Economic Studies, 51(1), 139–156.CrossRef

Palfrey, T. (1989). A mathematical proof of Duverger’s law. In P. Ordeshook (Ed.), Models of strategic choice in politics. Ann Arbor: University of Michigan Press.

Riker, W. (1982). The two-party system and Duverger’s law: An essay on the history of political science. American Political Science Review, 76(4), 753–68.CrossRef

Roemer, J. E. (2003). Indeterminacy of citizen-candidate equilibrium. Cowles foundation discussion paper no. 1410.

Roemer, J. E. (2006). Book reviews. [Review of the book Positive Political Theory II: Strategy and Structure by David Austen-Smith and Jeffrey S. Banks.] Journal of Economic Literature, 44(2), 421–425.

Sartori, G. (1976). Parties and party systems: A framework for analysis (Vol. 1). Cambridge: Cambridge University Press.

Volkens, A., Pola, L., Theres, M., Nicolas, M., Sven, R., & Annika, W. (2015). The manifesto data collection. Manifesto Project (MRG/CMP/MARPOR). Version 2015a. Berlin: Wissenschaftszentrum Berlin für Sozialforschung (WZB).

Weber, S. (1992). On hierarchical spatial competition. Review of Economic Studies, 59(2), 407–425.CrossRef

Weber, S. (1997). Entry deterrence in electoral spatial competition. Social Choice and Welfare, 15(1), 31–56.CrossRef

Xefteris, D. (2016). Stability in electoral competition: A case for multiple votes. Journal of Economic Theory, 161, 76–102.CrossRef

Titel: Comparison of Voting Procedures Using Models of Electoral Competition with Endogenous Candidacy
verfasst von: Damien Bol
Arnaud Dellis
Mandar Oak
Verlag: Springer International Publishing
Buch: The Political Economy of Social Choices
Print ISBN: 978-3-319-40116-4

Electronic ISBN: 978-3-319-40118-8

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-319-40118-8_2