¹ Cameron, David R., ‘The Stalemate in the Constitutional IGC over the Definition of a Qualified Majority’, European Union Politics, 5 (2004), 373–91 CrossRefGoogle Scholar

Garrett, Geoffrey, ‘International Cooperation and Institutional Choice: The European Community's Internal Market’, International Organization, 46 (1992), 533–60 CrossRefGoogle Scholar

Moberg, Axel, ‘The Nice Treaty and Voting Rules in the Council’, Journal of Common Market Studies, 40 (2002), 259–82 CrossRefGoogle Scholar

² Mattila, Mikko and Lane, Jan-Erik, ‘Why Unanimity in the Council? A Roll Call Analysis of Council Voting’, European Union Politics, 2 (2001), 31–52 CrossRefGoogle Scholar

Hayes-Renshaw, FionaAken, Wim Van and Wallace, Helen, ‘When and Why the EU Council of Ministers Votes Explicitly’, Journal of Common Market Studies, 44 (2006), 161–94 CrossRefGoogle Scholar

Heisenberg, Dorothee, ‘The Institution of “Consensus” in the European Union: Formal Versus Informal Decision-Making in the Council’, European Journal of Political Research, 44 (2005), 65–90 CrossRefGoogle Scholar

Hagemann, Sara and Clerck-Sachsse, Julia De, ‘Old Rules, New Game: Decision-Making in the Council of Ministers after the 2004 Enlargement’, CEPS Annual Conference, Brussels, 2007; Mikko Mattila, ‘Roll Call Analysis of Voting in the European Union Council of Ministers after the 2004 Enlargement’, European Journal of Political Research, 48 (2009), 840–57 Google Scholar

³ Tsebelis, George and Yataganas, Xenophon, ‘Veto Players and Decision-Making in the EU after Nice’, Journal of Common Market Studies, 40 (2002), 283–307 CrossRefGoogle Scholar

König, Thomas and Bräuninger, Thomas, ‘Accession and Reform of the European Union: A Game-Theoretical Analysis of Eastern Enlargement and the Constitutional Reform’, European Union Politics, 5 (2004), 419–39 CrossRefGoogle Scholar

Zimmer, ChristinaSchneider, Gerald and Dobbins, Michael, ‘The Contested Council: Conflict Dimensions of an Intergovernmental EU Institution’, Political Studies, 53 (2005), 403–22 CrossRefGoogle Scholar

⁴ Hayes-Renshaw et al., ‘When and Why the EU Council of Ministers Votes Explicitly’; Heisenberg, ‘The Institution of “Consensus” in the European Union’Google Scholar

⁵ Gigerenzer, Gerd and Goldstein, Daniel G., ‘Reasoning the Fast and Frugal Way: Models of Bounded Rationality’, Psychological Review, 103 (1996), 650–69 CrossRefGoogle Scholar

Simon, Herbert A., Models of Bounded Rationality (Cambridge, Mass.: MIT Press, 1982)Google Scholar

⁶ Laver, Michael and Sergenti, Ernest, Party Competition: An Agent-Based Model (Princeton, N.J.: Princeton University Press, 2012)Google Scholar

Bryson, Joanna J.Ando, Yasushi and Lehmann, Hagen, ‘Agent-Based Modelling as Scientific Method: A Case Study Analysing Primate Social Behaviour’, Philosophical Transactions of the Royal Society B: Biological Sciences, 362 (2007), 1685–99 CrossRefGoogle Scholar

Marchi, Scott de, Computational and Mathematical Modeling in the Social Sciences (Cambridge: Cambridge University Press, 2005)CrossRefGoogle Scholar

Miller, John H. and Page, Scott E., Complex Adaptive Systems: An Introduction to Computational Models of Social Life (Princeton, N.J.: Princeton University Press, 2007)Google Scholar

Railsback, Steven F. and Grimm, Volker, Agent-Based and Individual-Based Modeling: A Practical Introduction (Princeton, N.J.: Princeton University Press, 2012)Google Scholar

⁷ Mattila and Lane, ‘Why Unanimity in the Council?’; Hayes-Renshaw et al., ‘When and Why the EU Council of Ministers Votes Explicitly’; Heisenberg, ‘The Institution of “Consensus” in the European Union’; Hagemann and De Clerck-Sachsse, ‘Short Old Rules, New Game’; Mattila, ‘Roll Call Analysis of Voting in the European Union Council of Ministers after the 2004 Enlargement’. Note that, under the qualified majority voting rule, abstentions have the same effect as negative votes.

⁸ Hayes-Renshaw et al., ‘When and Why the EU Council of Ministers Votes Explicitly’, pp. 180–1Google Scholar

⁹ The data for the years from 1994 to 2002 are taken from Table 1a of Heisenberg, ‘The Institution of “Consensus” in the European Union: Formal Versus Informal Decision-Making in the Council’, p. 72; the data for the years from 2003 to 2006 are taken from Table 3 of Hagemann and De Clerck-Sachsse, ‘Short Old Rules, New Game’, p. 13. The consensus rates are based on contested votes only (i.e. negative votes or abstentions). Member states also have the opportunity to attach formal statements to the minutes of the meeting in which an act is adopted. Member states who voted in favour of the adoption of the act sometimes use such statements to voice their discontent with aspects of the act. This study is interested in explaining why member states do not outvote each other even though the formal rules allow for the adoption of acts by majority vote. Thus, the appropriate dependent variable is member states’ voting behaviour. Whether or not member states also choose to comment on their voting behaviour through formal statements is not relevant for answering this question.

¹⁰ The time-period covered does not include the latest accessions of Romania and Bulgaria in 2007.

¹¹ Tsebelis and Yataganas, ‘Veto Players and Decision-Making in the EU after Nice’; König and Bräuninger, ‘Accession and Reform of the European Union: A Game-Theoretical Analysis of Eastern Enlargement and the Constitutional Reform’; Zimmer et al., ‘The Contested Council’.

¹² If anything, the consensus rate increases somewhat over time.

¹³ Steunenberg, Bernard, ‘Decision Making under Different Institutional Arrangements: Legislation by the European Community’, Journal of Institutional and Theoretical Economics, 150 (1994), 642–69 Google Scholar

¹⁴ König, ThomasLuetgert, Brooke and Dannwolf, Tanja, ‘Quantifying European Legislative Research: Using Celex and Prelex in EU Legislative Studies’, European Union Politics, 7 (2006), 553–74 CrossRefGoogle Scholar

Häge, Frank M., ‘The European Union Policy-Making Dataset’, European Union Politics, 12 (2011), 455–77 CrossRefGoogle Scholar

¹⁵ The argument also holds if the Presidency, or any other member state, is considered to be the agenda-setter inside the Council.

¹⁶ Mattila and Lane, ‘Why Unanimity in the Council?’, p. 37.

¹⁷ Situations in which such Pareto-improving policy changes are possible might be quite common in the EU. For example, Scharpf argues that decision making on product-related regulations exhibits the strategic structure of a coordination game, in which member states agree that a uniform EU standard is preferable to the existing plethora of national standards. Although a distributional conflict about exactly what type of uniform standard to implement still exists, all member states are better off with some uniform standard than none. See Fritz W. Scharpf, ‘Negative and Positive Integration in the Political Economy of European Welfare States’, in Gary Marks, Fritz W. Scharpf, Philippe C. Schmitter and Wolfgang Streeck, eds, Governance in the European Union (London: Sage, 1996), pp. 15–39.

¹⁸ Falkner, Gerda, Hartlapp, MiriamLeiber, Simone and Treib, Oliver, ‘Non-Compliance with EU Directives in the Member States: Opposition through the Backdoor?’ West European Politics, 27 (2004), 452–73 CrossRefGoogle Scholar

¹⁹ Hayes-Renshaw et al., ‘When and Why the EU Council of Ministers Votes Explicitly’; Giovanni Maggi and Massimo Morelli, ‘Self-Enforcing Voting in International Organizations’, American Economic Review, 96 (2006), 1137–58 Google Scholar

Rittberger, Volker and Zangl, Bernhard, International Organization: Polity, Politics and Policies (Basingstoke: Palgrave Macmillan, 2006)Google Scholar

²⁰ Carruba, Clifford J. and Volden, Craig, ‘Explaining Institutional Change in the European Union: What Determines the Voting Rule in the Council of Ministers?’ European Union Politics, 2 (2001), 5–30 Google Scholar

König, Thomas and Junge, Dirk, ‘Why Don't Veto Players Use Their Power?’ European Union Politics, 10 (2009), 507–34 CrossRefGoogle Scholar

²¹ Lewis, Jeffrey, ‘The Janus Face of Brussels: Socialization and Everyday Decision Making in the European Union’, International Organization, 59 (2005), 937–71 CrossRefGoogle Scholar

Lewis, Jeffrey, ‘The Methods of Community in EU Decision-Making and Administrative Rivalry in the Council's Infrastructure’, Journal of European Public Policy, 7 (2000), 261–89 CrossRefGoogle Scholar

²² Aus, Jonathan P., ‘The Mechanism of Consensus: Coming to Agreement on Community Asylum Policy’, in Daniel Naurin and Helen Wallace, eds, Unveiling the Council of the European Union (Basingstoke, Hants.: Palgrave Macmillan, 2008)Google Scholar

²³ Whether or not logrolling is a competing or complementary explanation depends largely on the negotiation stage at which it is supposed to take place. The computational model developed below is agnostic about the precise mechanisms through which the compromise agreement between blocking coalitions at the final stage of negotiations is reached. Log-rolling across issues within a proposal could surely be one of those mechanisms. Forming blocking coalitions reduces the effective number of actors and policy positions and, therefore, the cognitive demands on negotiators, making successful vote trading more likely. From this point of view, the two explanations potentially complement each other and could be combined in a sequential manner. The conclusion briefly discusses how a competitive empirical test could look if the two theories are considered as alternatives.

²⁴ This informal comparison of different theories cannot replace a more rigorous empirical test. However, the discussion points to potential shortcomings of existing accounts and justifies the consideration of new alternatives.

²⁵ Häge, Frank M., Bureaucrats as Law-Makers: Committee Decision-Making in the EU Council of Ministers (London: Routledge, 2012)Google Scholar

²⁶ Information on member state positions was derived from various internal Council documents. All documents are available from the public register of Council documents (http://www.consilium.europa.eu/showPage.aspx?id=1279&lang=en). Four interviews with Commission, Council, and member state officials in May and June 2007 yielded additional insights into the negotiation process.

²⁷ Hayes-Renshaw, Fiona and Wallace, Helen, The Council of Ministers (Basingstoke, Hants.: Palgrave Macmillan, 2006)CrossRefGoogle Scholar

²⁸ Commission (2003): Proposal for a Directive of the European Parliament and of the Council on batteries and accumulators and spent batteries and accumulators. 21 November 2003, COM/2003/723.

²⁹ Council (2004): Report of the meeting on 8 June 2004 of the Working Party on Environment. 22 June 2004, 10743/04.

³⁰ Council (2004): Dutch Presidency: Provisional agendas for Council meetings prepared by Coreper (Part 1). 30 June 2004, 11014/04, p. 25.

³¹ Council (2004): Report of the meeting on 10 November 2004 of the Working Party on Environment. 12 November 2004, 14228/1/04; Council (2004): Report of the meeting on 18 November 2004 of the Working Party on Environment. 19 November 2004, 14941/04.

³² Council (2004): Meeting document for the meeting on 10 November 2004 of the Working Party on Environment: French impact assessment. 4 November 2004, DS 742/04.

³³ Council (2004): Report of the meeting on 25 November 2004 of the Working Party on Environment. 26 November 2004, 15204/04 ADD 1.

³⁴ Council (2004): Report of the meeting on 8 December 2004 of the Working Party on Environment. 10 December 2004, 15537/1/04.

³⁵ Council (2005): Draft minutes of the 2632nd meeting of the Council of the European Union (Environment), held in Brussels on 20 December 2004. 25 February 2005, 16275/1/04.

³⁶ Council (2005): Draft minutes of the 2632nd meeting of the Council of the European Union (Environment), held in Brussels on 20 December 2004. 25 February 2005, 16275/04 COR. 1; Council (2005): Draft minutes of the 2632nd meeting of the Council of the European Union (Environment), held in Brussels on 20 December 2004. 25 February 2005, 16275/04 COR. 2.

³⁷ In this respect, the approach taken here is in no way different from more classical mathematical modelling, which usually aims to capture some empirical regularity or stylized fact about a political phenomenon. The model is implemented in NetLogo 4.1, see Uri Wilensky, Netlogo, Version 4.1 (Evanston, Ill.: Center for Connected Learning and Computer-Based Modeling, Northwestern University, 1999), available from http://ccl.northwestern.edu/netlogo/. The simplified NetLogo code is provided in the appendix and the entire simulation model is available for download from www.frankhaege.eu.

³⁸ Mesterton-Gibbons, Mike, Gavrilets, SergeyGravner, Janko and Akçay, Erol, ‘Models of Coalition or Alliance Formation’, Journal of Theoretical Biology, 274 (2011), 187–204 CrossRefGoogle ScholarPubMed

³⁹ Simon, Models of Bounded Rationality.

⁴⁰ See for example, Gigerenzer and Goldstein, ‘Reasoning the Fast and Frugal Way: Models of Bounded Rationality’.

⁴¹ Susanne K. Schmidt, ‘Only an Agenda Setter?’, European Union Politics, 1 (2000), 37–61.

⁴² Mark Neuman, Asaf Bitton and Stanton Glantz, ‘Tobacco Industry Strategies for Influencing European Community Tobacco Advertising Legislation’, Lancet, 359 (2002), 1323.

⁴³ Tallberg, Jonas, ‘The Power of the Chair: Formal Leadership in International Cooperation’, International Studies Quarterly, 54 (2010), 241–65 CrossRefGoogle Scholar

⁴⁴ Novak, Stephanie, ‘Decision Rules, Social Norms and the Expression of Disagreement: The Case of Qualified-Majority Voting in the Council of the European Union’, Social Science Information, 49 (2010), 83–97 CrossRefGoogle Scholar

⁴⁵ Mateo, Gemma, ‘Bargaining Power and Negotiation Tactics: The Negotiations on the EU's Financial Perspective, 2007–2013’, Journal of Common Market Studies, 48 (2010), 557–78 Google Scholar

⁴⁶ Westlake, Martin and Galloway, David eds, The Council of the European Union (London: John Harper, 2004)Google Scholar

⁴⁷ Computational experiments perform the same theoretical function as comparative statics analysis in mathematical modelling, i.e. the derivation of additional predictions.

⁴⁸ Kellstedt, Paul M. and Whitten, Guy D., The Fundamentals of Political Science Research (Cambridge: Cambridge University Press, 2008)CrossRefGoogle Scholar

King, GaryKeohane, Robert O. and Verba, Sidney, Designing Social Inquiry. Scientific Inference in Qualitative Research (Princeton, N.J.: Princeton University Press, 1994)Google Scholar

⁴⁹ Still, it is of course instructive to investigate how sensitive the model predictions are to the inclusion of real-world voting weights and multiple voting thresholds. The online appendix of this paper includes the results of replication analyses based on such models. With the exception of the model specification with Nice treaty rules and twenty-five member states, which results in a predicted consensus rate that is up to 9 per cent higher than the prediction of the base model, the predictions of the modified models generally lie within 6 percentage points of the predictions of the base model, and often considerably closer (see Table A2 in the online appendix). None of the qualitative results of this article is dependent on the exclusion of voting weights from the model.

⁵⁰ Achen, Christopher H., ‘Evaluating Political Decision-Making Models’, in Robert Thomson, Frans Stokman, Christopher H. Achen and Thomas König, eds, The European Union Decides (Cambridge: Cambridge University Press, 2006), pp. 264–98 Google Scholar

Thomson, Robert, Resolving Controversy in the European Union (Cambridge: Cambridge University Press, 2011)CrossRefGoogle Scholar

⁵¹ The online appendix presents replication results of models in which the sequence of moves is ordered according to voting weights and member states with smaller weights move before member states with larger ones. The predicted consensus rates change only marginally from those of the base model (i.e. by no more than three percentage points, see Table A2 in the online appendix).

⁵² In principle, the formation of a blocking minority could also result in a rejection of the proposal. In reality, Commission proposals are hardly ever rejected in their entirety. Empirical data indicate that 90 to 95 per cent of all proposals are eventually adopted; see König et al., ‘Quantifying European Legislative Research’, p. 563; Häge, ‘The European Union Policy-Making Dataset’, p. 470. Thus, the overwhelming majority of actually observed legislative proposals seem to lead to efficiency-improving negotiation outcomes. A selection effect seems to operate here, in that the Commission refrains from submitting unpopular proposals in anticipation of their rejection by the Council; see König and Junge, ‘Why Don't Veto Players Use Their Power?’ The model could be modified to include at the end of the negotiation process an evaluation of the potential compromise outcome against a reversion point. However, the location of this reversion point could easily be calibrated to make sure that the model output corresponds to a 5–10 per cent rejection rate. While making the model arguably more realistic, such an extension would yield little additional theoretical insight.

⁵³ Schneider, GeraldSteunenberg, Bernard and Widgrén, Mika, ‘Evidence with Insight: What Models Contribute to EU Research’, in Robert Thomson, Frans N. Stokman, Christopher H. Achen and Thomas König, eds, The European Union Decides (Cambridge: Cambridge University Press, 2006), pp. 407–30 Google Scholar

⁵⁴ Figure 1 presents the same consensus rate data in the form of a time-series. Unfortunately, no voting records are available for the period prior to 1994.

⁵⁵ The actual percentage voting threshold applied in the Council varied slightly during the observed time period. However, these small changes in the formal voting threshold do not affect the effective voting threshold in terms of the number of member states required to form a winning coalition.

⁵⁶ Taking real-world voting weights and multiple voting thresholds into account considerably improves the predictive accuracy in the case of twelve member states but reduces it somewhat in the case of twenty-five member states (but never below a PRE value of 91 per cent). The total PRE value for the entire sample period is hardly affected by these modifications, always ranging between 94 and 96 per cent (see Table A1 and Figures A1–A8 in the online appendix).

⁵⁷ A voting threshold of 100 per cent is not considered in the simulation because the results would be trivial. Under unanimity rule, each individual member state constitutes a blocking minority and therefore does not engage in coalition building. Threshold values between 90 and 100 per cent are also less interesting, as they do not occur in most real-world decision-making systems.

⁵⁸ Koenker, Roger and Hallock, Kevin F., ‘Quantile Regression’, Journal of Economic Perspectives, 15 (2001), 143–56 CrossRefGoogle Scholar

⁵⁹ Hao and Naiman, Quantile Regression, p. 33.

⁶⁰ The prediction of a stark decline in the consensus rate under the Lisbon Treaty rules is not sensitive to the simplifying assumption of equal voting weights with a single majority threshold. See Table A2 and Figures A9 and A10 in the online appendix for a comparison with model predictions based on real-world voting systems.

⁶¹ Naurin, Daniel and Lindahl, Rutger, ‘Out in the Cold? Flexible Integration and the Political Status of Euro Opt-Outs’, European Union Politics, 11 (2010), 485–509 CrossRefGoogle Scholar

Beyers, Jan and Dierickx, Guido, ‘The Working Groups of the Council of the European Union: Supranational or Intergovernmental Negotiations?’ Journal of Common Market Studies, 36 (1998), 289–317 CrossRefGoogle Scholar

⁶² Mattila, Mikko, ‘Contested Decisions: Empirical Analysis of Voting in the European Union Council of Ministers’, European Journal of Political Research, 43 (2004), 29–50 CrossRefGoogle Scholar

⁶³ Ehlermann, Claus-Dieter and Ehring, Lothar, ‘Decision-Making in the World Trade Organization’, Journal of International Economic Law, 8 (2005), 51–75 CrossRefGoogle Scholar

Woods, Ngaire, ‘Good Governance in International Organizations’, Global Governance, 5 (1999), 39–61 Google Scholar

Kahler, Miles, ‘Multilateralism with Small and Large Numbers’, International Organization, 46 (1992), 681–708 CrossRefGoogle Scholar

Steinberg, Richard H., ‘In the Shadow of Law or Power? Consensus-Based Bargaining and Outcomes in the Gatt/WTO’, International Organization, 56 (2002), 339–74 CrossRefGoogle Scholar

White, Nigel D., ‘Decision-Making’, in Jan Klabbers and Åsa Wallendahl, eds, Research Handbook on the Law of International Organizations (Cheltenham: Edward Elgar, 2011), pp. 225–50 Google Scholar

Churchill, Robin R. and Ulfstein, Geir, ‘Autonomous Institutional Arrangements in Multilateral Environmental Agreements: A Little-Noticed Phenomenon in International Law’, American Journal of International Law, 94 (2000), 623–59 CrossRefGoogle Scholar