Fission and Fusion in a Party System

Existing work on party systems typically involves essentially static models and pays little attention to the dynamics of party splits and fusions. Our approach explores these dynamics by setting out a simple model of legislative behavior in a parliament responsible for making and breaking governments. This model abandons the unitary actor assumption about political parties models individual legislators as utility-maximizing agents tempted to defect to other parties if this would increase their expected payoffs. We first set out a dynamic model of party fission and fusion couched in these terms and discuss this analytically. We then explore unanswered questions computationally by generating a novel type of “metadata” set, comprising the entire universe of possible legislative party systems in parliaments with up to 10 parties, generating a total of 6,292,018 theoretically possible non-equivalent legislatures. Using this metadata set and building on analytic results, we set out to characterize what makes certain parties “attractive” to legislators from other parties in a dynamic system. The results reveal an inherent instability in party systems and identify legislative configurations more prone to fission and fusion. They also strikingly highlight the role of the largest party, regardless of it size, as being attractive to potential defectors from other parties. Finally, they highlight the relatively weak position of the second-largest party. This provides an intriguing new interpretation of the potential for intense competition between the largest two parties for the role of the largest party, in a generalization to multiparty systems of the “all or nothing” competition endemic in twoparty systems. † Department of Political Science, Trinity College, Dublin 2, Ireland. E-mail: [email protected] and [email protected]. FISSION AND FUSION IN A PARTY SYSTEM Tables / PAGE 1 P1 (min. legisl only) P2 (min. legisl only) P3 (min. legisl only) No. of parties No. of different party configs (NEDs) No. of different expectation vectors Min Max Min Max Min Max 1 1 1 . . . . . . 2 50 1 . . . . . . 3 833 3 35 50 26 49 1 32 4 7,153 7 27 50 18 48 1 32 5 38,225 20 22 50 14 48 1 31 6 143,247 113 19 50 11 47 1 31 7 407,254 1,209 16 50 10 47 1 31 8 930,912 49,493 15 50 8 46 1 30 9 1,786,528 587,758 13 50 8 46 1 30 10 2,977,866 1,865,672 12 50 7 45 1 30 Table 1: Non-equivalent divisions and unique expectation vectors for generic 100seat legislatures. Last 6 columns are for minority legislatures only, excluding ties between any of P1, P2, or P3. FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 1 Figure 1a. Expectation-to-weight ratios by proportion of seats, first, second, and third parties, when a dominant party exists, 4-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 2 Figure 1b. Expectation-to-weight ratios by proportion of seats, first, second, and third parties, when no dominant party exists, 4-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 3 Figure 1c. Expectation-to-weight ratios by proportion of seats, first, second, and third parties, when a dominant party exists, 5-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 4 Figure 1d. Expectation-to-weight ratios by proportion of seats, first, second, and third parties, when no dominant party exists, 5-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 5 Figure 1e. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when a dominant party exists, 6-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 6 Figure 1e. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when no dominant party exists, 6-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 7 Figure 1f. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when a dominant party exists, 7-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 8 Figure 1g. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when no dominant party exists, 7-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 9 Figure 1h. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when a dominant party exists, 8-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 10 Figure 1i. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when no dominant party exists, 8-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 11 Figure 1j. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when a dominant party exists, 9-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 12 Figure 1k. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when no dominant party exists, 9-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 13 Figure 1l. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when a dominant party exists, 10-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 14 Figure 1m. Expectation-to-weight ratios by proportion of seats, First, second, and third parties, when no dominant party exists, 10-party legislature FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 15 Figure 2. Expectation-to-weight ratios by proportion of seats, all other parties, 7-party legislature. Note: Excludes all ties between P4, P5, P6, and P7. FISSION AND FUSION IN A PARTY SYSTEM Figures / PAGE 16 Figure 3. The incidence of dominant parties, by size of largest party, in the universes of 3 – 8 party legislatures. (minority legislatures only, with p1=p1, p2=p3, p1=p2=p3 ties excluded) FISSION AND FUSION IN A PARTY SYSTEM Tables / PAGE 2 Table 2. Proportions of relevant cases for which one party in the system is attractive to members of another. All data is for minority legislatures only and excludes any ties between P1, P2, and P3. Potential Attractor Largest Party Dominant? P1 P2 P3 P4 P5 P6 P7 Dominant -.97 .63 .61 .61 --Not -.00 .19 .83 .71 --Dominant .03 -.02 .25 .45 --Not 1.00 -.22 .87 .76 --Dominant .37 .98 -.36 .57 --Not .81 .76 -.67 .67 --Dominant .39 .75 .55 -.39 --Not .17 .13 .23 -.00 --Dominant .39 .55 .42 .50 ---Not .29 .24 .32 .28 ---Dominant -.95 .69 .75 .73 .66 -Not -.20 .37 .79 .60 .78 -Dominant .05 -.12 .36 .45 .46 -Not .80 -.30 .74 .57 .75 -Dominant .31 .88 -.44 .58 .58 -Not .63 .70 -.59 .54 .77 -Dominant .25 .64 .44 -.36 .49 -Not .21 .26 .25 -.05 .34 -Dominant .27 .54 .40 .48 -.30 -Not .40 .43 .43 .46 -.36 -Dominant .34 .54 .42 .49 .44 --Not .22 .25 .23 .29 .20 --Dominant -.95 .74 .84 .81 .77 .74 Not -.46 .59 .82 .63 .79 .74 Dominant .05 -.19 .41 .47 .47 .50 Not .54 -.45 .73 .53 .72 .71 Dominant .26 .81 -.50 .61 .61 .63 Not .41 .55 -.54 .48 .70 .67 Dominant .16 .58 .36 -.37 .47 .52 Not .18 .27 .25 -.15 .43 .47 Dominant .19 .53 .37 .44 -.32 .46 Not .37 .47 .48 .52 -.46 .53 Dominant .23 .53 .39 .49 .41 -.32 Not .21 .28 .30 .38 .23 -.30 Dominant .26 .50 .37 .47 .46 .36 -Not .26 .29 .33 .37 .29 .34 -P7 n =7 P6 n =6