¹ Parties in polarized systems are more reluctant to initiate political crises – due to ideological or other reasons – for fear of breaking up a coalition. This is so because they see no alternative to the present coalition except early elections.

² A proto-coalition is defined as a coalition that could potentially form given the ideological positions of its members and their seat proportions.

³ Lupia, Arthur and Strøm, Kaare, ‘Coalition Termination and the Strategic Timing of Parliamentary Elections’, American Political Science Review, 89 (1995), 648–665CrossRefGoogle Scholar; Nyblade, Benjamin, ‘Reconsidering Ideological Diversity and Government Survival’ (paper presented at the Annual Meeting of the American Political Science Association, Chicago, 2004)Google Scholar; Warwick, Paul V., Policy Horizons and Parliamentary Government (New York: Palgrave Macmillan, 2006), p. 7CrossRefGoogle Scholar.

⁴ One may argue that the two hypotheses are, in fact, identical because cabinet duration is correlated with the number of cabinets in a given electoral cycle. While this may be true in principle, the actual correlation in our data between these two measures of political stability is moderate but not as high as one would expect. We discuss this below.

⁵ Warwick, Paul V., ‘The Durability of Coalition Governments in Parliamentary Democracies’, Comparative Political Studies, 11 (1979), 465–498CrossRefGoogle Scholar.

⁶ See, e.g. Lupia and Strøm, ‘Coalition Termination and the Strategic Timing of Parliamentary Elections’; Diermeier, Daniel and Stevenson, Randy T., ‘Cabinet Survival and Competing Risks’, American Journal of Political Science, 43 (1999), 1051–1068CrossRefGoogle Scholar; Diermeier, Daniel and Stevenson, Randy T., ‘Cabinet Terminations and Critical Events’, American Political Science Review 94 (2000), 627–640CrossRefGoogle Scholar.

⁷ Diermeier, Daniel, Eraslan, Hulya and Merlo, Antonio, ‘A Structural Model of Government Formation’, Econometrica, 71 (2003), 27–70CrossRefGoogle Scholar.

⁸ Powell, G. Bingham Jr, Contemporary Democracies: Participation, Stability, and Violence (Cambridge, Mass.: Harvard University Press, 1982)Google Scholar. King et al. (King, Gary, Alt, James E., Elizabeth Burns, Nancy and Laver, Michael, ‘A Unified Model of Cabinet Duration in Parliamentary Democracies’, American Journal of Political Science, 34 (1990), 846–871CrossRefGoogle Scholar) and Warwick (‘The Durability of Coalition Governments in Parliamentary Democracies’) also use this measure of political polarization in their analyses.

⁹ Warwick, Paul V., Government Survival in Parliamentary Democracies (Cambridge: Cambridge University Press, 1994)Google Scholar.

¹⁰ Gross, Donald A. and Sigelman, Lee, ‘Comparing Party Systems: A Multidimensional Approach’, Comparative Politics, 16 (1984), 463–479CrossRefGoogle Scholar.

¹¹ Yves Duclos, Jean, Esteban, Joan and Ray, Debraj, ‘Polarization: Concepts, Measurement, Estimation’, Econometrica, 72 (2004), 1737–1772CrossRefGoogle Scholar; Esteban, Joan-Maria and Ray, Debraj, ‘On the Measurement of Polarization’, Econometrica, 62 (1994), 819–851CrossRefGoogle Scholar.

¹² Rehm, Philipp and Reilly, Timothy, ‘United We Stand: Constituency Homogeneity and Comparative Party Polarization’, Electoral Studies, 29 (2010), 40–53CrossRefGoogle Scholar.

¹³ Maoz, Zeev, ‘Network Polarization’ unpublished paper, University of California, Davis (2009)Google Scholar.

¹⁴ Additional measures of polarization are based on the ideological difference between the largest parties in the system (Ware, Alan, Political Parties and Party Systems (Oxford: Oxford University Press, 1996)Google Scholar), the standardized left–right policy differences between all pairs of parties (Klingemann, Hans-Dieter and Wessels, Bernhard, ‘Sincere Voting in Different Electoral Systems’ (unpublished manuscript, Wissenschaftzentrum Berlin fur Sozialforschung, 2002Google Scholar), or on the ideological compactness of the system using both the ideological diversity of voters and the issue distances between each pair of parties (Alvarez, Michael R. and Nagler, Jonathan, ‘Party System Compactness: Measurement and Consequences’, Political Analysis, 12 (2004), 46–62CrossRefGoogle Scholar).

¹⁵ p_i is a monotonically increasing function of s_i., and in our case p_i is the seat shares of clique i.

¹⁶ See Wasserman, Stanley and Faust, Katherine, Social Network Analysis (New York: Cambridge University Press, 1997), pp. 3–17Google Scholar; and Pattison, Philippa, Algebraic Models for Social Networks (New York: Cambridge University Press, 1993), pp. 14–20CrossRefGoogle Scholar.

¹⁷ These figures are drawn using the twenty-six issues from the CMP dataset. These data are discussed below.

¹⁸ See Maoz (Maoz, Zeev, ‘Systemic Polarization, Interdependence, and International Conflict, 1816–2002’, Journal of Peace Research, 43 (2006), 391–411CrossRefGoogle Scholar; and ‘Network Polarization’) for more details on the measurement of this polarization index. The index presented here offers a slight variation (and a number of extensions) on Maoz (‘Systemic Polarization, Interdependence, and International Conflict, 1816–2002’, pp. 395–7). An elaborate explanation and derivation of this index is given in Maoz, ‘Network Polarization’.

¹⁹ In our analyses, we use three different cut-off points to designate cliques. See the discussion in the text.

²⁰ The maximum value of COI asymptotically approaches 1 as k becomes sufficiently large. Maoz (‘Network Polarization’) provides more details on the properties of this index.

²¹ The software for developing this polarization measure using social network analysis is available from Zeev Maoz’s website at: http://psfaculty.ucdavis.edu/zmaoz/networks/netsoftware.html.

²² Maoz, ‘Network Polarization’; Ducols et al., ‘Polarization’.

²³ The countries included in the dataset are Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain and Sweden.

²⁴ See Wolfgang C. Müller and Kaare Strøm, Parliamentary Democracy Data Archive http://www.pol.umu.se/ccpd/, 2006; Müller, Wolfgang C. and Strøm, Kaare, Coalition Governments in Western Europe (Oxford: Oxford University Press, 2003)Google Scholar; Warwick, Survival Dataset, http://www.sfu.ca/~warwick/datasets/, 1992; Budge, Ian, Klingemann, Hans-Dieter, Volkens, Andrea, Tannenbaum, Eric and Bara, Judith, Mapping Policy Preferences: Estimates for Parties, Electors, and Governments 1945–1998 (Oxford: Oxford University Press, 2001)Google Scholar.

²⁵ These measures generally correlate with other widely used measures on party positioning like expert surveys, party placements of election survey respondents and other word-scoring techniques. See, e.g., Hearl, Derek, ‘Checking the Party Policy Estimates: Reliability’, in Ian Budge, Hans-Dieter Klingemann, Andrea Volkens, Eric Tannenbaum and Judith Bara, eds, Mapping Policy Preferences: Estimates for Parties, Electors, and Governments 1945–1998 (Oxford: Oxford University Press, 2001), pp. 111–125Google Scholar; McDonald, Michael and Mendes, Sylvia, ‘Checking the Party Policy Estimates: Convergent Validity’, in Budge et al., eds., Mapping Policy Preferences, pp. 127–141Google Scholar; Laver, Michael, Benoit, Kenneth and Garry, John, ‘Extracting Policy Positions from Political Texts Using Words as Data’, American Political Science Review, 97 (2003), 311–331CrossRefGoogle Scholar.

²⁶ Harmel, Robert, Janda, Kenneth and Tan, Alexander, ‘Substance vs. Packaging: An Empirical Analysis of Parties’ Issue Profiles’ (presented at the Annual Meeting of the American Political Science Association, Chicago, 1995)Google Scholar.

²⁷ See Budge et al., Mapping Policy Preferences, for the details of measurement for the specific issues we used.

²⁸ The data for this research and additional supplementary analyses are available at Zeev Maoz’s web-site at: http://psfaculty.ucdavis.edu/zmaoz/datasets.htm.

²⁹ This cut-off point may seem arbitrary. Thus, we used two additional cut-off points. The first was the median of the distribution of overlap figures (which was sometimes higher and sometimes lower than the mean, for different elections and for different countries). The second was the two-third percentile (67 percentile) level of overlap. We label this as NPI(p67). This cut-off point created a significantly smaller set of proto-coalitions than did the other two cut-off points. The results of this sensitivity variation were a set of three different measures of NPI which differed quite significantly from each other. The substantive results are retained, however. The results of these additional analyses can be found on our web-page at http://psfaculty.ucdavis.edu/zmaoz/datasets.htm. From this point on, we proceed to measure NPI in the manner described in the previous section.

³⁰ This also allows for a different measurement of the network. Instead of using party position overlap as the measure of the strength of ideological ties between parties, we defined the entries of the socio-matrix as: where max|LR| is the width of the ideological range for this electoral cycle. Thus, s_ij is in the [0,1] range and higher values indicate strong ideological affinity between parties.

³¹ See Appendix Table for descriptive statistics. One important point to note is that the variation of NPI over the range of possible values is much larger than the variation of other polarization indices over their possible ranges.

³² See Appendix for more details on these control variables.

³³ In our data, the relationship between the status of a cabinet (minority or majority) and the number of parties in the cabinet is highly significant: Chi-Square = 324.24; Yule’s Q = 0.841; Tau-b = 0.541.

³⁴ Warwick, Government Survival in Parliamentary Democracies.

³⁵ Average duration of minority governments in our sample was 852 days (N = 73; SD = 439.88); the average duration of majority governments was 1,161 days (N = 139; SD = 458.97). The difference is statistically significant (t = −4.625, p < 0.0001).

³⁶ The drawback of this set of measures is that it is based on interpolated left–right positions of parties, not on their positions as reflected in their actual party manifestos. This interpolation is based on the assumption of linear position change over time of political parties (between two points of actual left–right measurement).

³⁷ This is a relatively simple test, but it is theoretically trivial, as all other indices attempt to capture different aspects of the same thing.

³⁸ Taylor, Michael and Herman, V. M., ‘Party Systems and Government Stability’, American Political Science Review, 65 (1971), 28–37CrossRefGoogle Scholar.

³⁹ Duclos, et al. , ‘Polarization: Concepts, Measurement, Estimation’Google Scholar.

⁴⁰ Rehm, and Reilly, , ‘United We Stand’Google Scholar.

⁴¹ The following tables report only a fraction of the analyses we performed with various combinations of control variables. We dropped the parliamentary fragmentation index due to its high correlation with the effective number of parties. We also dropped the electoral system dummies due to their high correlation with measures of disproportionality. Generally speaking, neither of these dropped controls exhibited any significant effect on the dependent variables when included in the analyses, and nor did their introduction change significantly the results reported herein.

⁴² Here too, we ran the full equations with all polarization indices (including NPI), and – with the exception of the significant impact of NPI on the average duration of cabinets (and the significant negative impact of NPI on the number of cabinets in an electoral cycle) – none of the results reported here has changed dramatically.

⁴³ See Grofman and van Roozeendaal (Grofman, Bernard and van Roozendaal, Peter, ‘Modeling Cabinet Durability and Termination’, British Journal of Political Science, 27 (1997), 419–451CrossRefGoogle Scholar, and Nyblade, ‘Reconsidering Ideological Diversity and Government Survival’.

⁴⁴ See Dodd (Dodd, Lawrence C., ‘Party Coalitions in Multiparty Parliaments: A Game-Theoretic Analysis’, American Political Science Review, 68 (1974), 1093–1117CrossRefGoogle Scholar) for more details.

⁴⁵ Laver, Michael and Schofield, Norman, Multiparty Government: The Politics of Coalition in Europe (New York: Oxford University Press, 1990)Google Scholar.

⁴⁶ Gallagher, Michael, ‘Proportionality, Disproportionality, and Electoral Systems’, Electoral Studies, 10 (1991), 33–51CrossRefGoogle Scholar; Lijphart, Arend, Patterns of Democracy (New Haven, Conn.: Yale University Press, 1999)Google Scholar.

⁴⁷ See Warwick, , Government Survival in Parliamentary Democracies, p. 157Google Scholar.

⁴⁸ See King et al., ‘A Unified Model of Cabinet Duration in Parliamentary Democracies’; and Strøm et al. (Strøm, Kaare, Müller, Wolfgang C. and Bergman, Torbjörn, Accountability in Parliamentary Democracies (Oxford: Oxford University Press, 2006)Google Scholar).

⁴⁹ Warwick, , Government Survival in Parliamentary Democracies.Google Scholar

⁵⁰ Laasko, Markku and Taagepera, Rein, ‘Effective Number of Parties: A Measure with Applications to Western Europe’, Comparative Political Studies, 12 (1979), 3–27Google Scholar.

⁵¹ It is important to note that the NPI incorporates the ideological cohesion of parties in proto-coalitions. However, for any given cabinet, proto-coalitions might be different from actual coalitions, so these reflect two different things.