Proportional Representation and Political Conflict
Proportional Representation and Political Conflict
Daniel Kselman
dmk10@duke.edu
Working Paper, Duke University Department of Political Science(
ABSTRACT:
Authors in a variety of settings have argued that proportional representation electoral institutions help to reduce political conflict in tense political situations. Such studies generally rest on two implicit assumptions, namely that elections are party-centered and that the political-cleavage structures which define electoral campaigns are relatively fixed and predictable. This paper develops a game theoretic framework which endogenizes a country’s mode of accountability, demonstrating that the party-centered competition implicit in previous research emerges only under closed-list proportional representation. Furthermore, we argue that this very party-centrism has potentially deleterious consequences in country’s whose political-cleavage structures are subject to short-term variation, and propose a particular from of open-list proportional representation as the most suitable institutional alternative for peace and stability in fluid political environments. Historical evidence detailing parallel cycles of party system concentration and political conflict in Turkey provide a suggestive narrative in support of the paper’s basic claims.
I. Literature Review
Over the past three decades theoretical studies in both political science and economics have investigated the consequences of formal electoral institutions for various aspects of political-economic life. Most such studies address the ‘classical’ distinction between majoritarian (MAJ) elections and proportional representation (PR). The most common MAJ system employs ‘winner-take-all’ contests in single-member districts, while in multi-member PR systems a district’s numerous legislative seats are allocated to political party lists in rough proportion to the parties’ district-level vote shares. Authors in a variety of settings have argued that, in potentially divisive political contexts, PR systems generate a less confrontational form of political competition than their MAJ counterparts.[1] The primary mechanism linking majoritarianism to political conflict is its tendency to exclude important social minorities from governance.[2] Faced with this perpetual political exclusion, minority groups are more likely to pursue their interests in extra- or quasi-legal ways, resulting in social unrest and at times devastating violence.
In contrast, scholarship grounded in West European political history has highlighted PR’s stabilizing influence on political competition in ethnically divided societies (Lijphart 1977): in PR systems a minority comprising 20% of a country’s population should receive roughly 20% of its legislative seats, rather than the parliamentary exclusion characteristic of MAJ elections. In guaranteeing a parliamentary presence for members of ethnic minorities, PR was foundational for a form of coalitional politics known as consociationalism, whose central feature is the collective adherence to a mutually beneficial ‘social pact’ presided over by a disciplined political elite.[3]
As well, recent work on the comparative political economy of advanced industrial democracies identifies PR’s role in generating left-leaning coalition governments with substantial representation of organized labor (Iversen and Soskice 2006). This foothold in government, which is absent in MAJ systems,[4] provides labor movements the capacity to pursue workers’ interests in the parliamentary rather than the industrial arena, which in turn generates less conflictual capital-labor relations.[5] By fostering labor movement participation in the governmental process, PR has played an important role in sustaining what some have recently labeled cross-class coalitions in most Northern European democracies,[6] coalitions which bear analytic similarity to cross-ethnic consociational pacts. These coalitions have not formed in MAJ democracies, which since WWII have tended to experience higher levels of industrial conflict (Korpi and Shalev 1979).[7]
II. Theoretical Framework
In both cases the mechanism linking proportionality to conflict reduction is coalition politics, which provides ethnic minorities the chance to participate in multi-party governments, and helps to constrain the expropriating tendencies of working-class parties. The following paper argues that, while making invaluable contributions to our understanding of electoral institutions’ political consequences, this coalition-driven literature rests on a series of implicit assumptions as to the nature of political party competition in PR systems. Firstly, the above reviewed research characterizes elections as party-centered. In such contexts, voter choice tends to be governed by citizens’ national-level preferences for a country’s various competing political parties, and has little to do with the local reputation of individual legislators from within these party organizations. Partly as a consequence political parties tend to be highly disciplined, such that executive leaders can count on the support of their members of parliament (MP’s) who form a loyal legislative voting bloc.[8]
Sections III, IV, and V below develop a game theoretic model which moves a step beyond the ‘classical’ MAJ-PR dichotomy; and in so doing identifies the institutional conditions under which this party-centered political competition should in fact emerge. More particularly, they investigate the importance of an institutional distinction within PR systems: that between closed-list and open-list proportional representation (CLPR and OLPR respectively). In CLPR systems, candidates’ chances of securing re-election are largely dependent on intra-party processes which unfold prior to the general election, and which govern their eventual position on party lists. In equilibrium, this leads to a situation in which individual candidates have almost no incentive to invest effort in developing a personal following in specific regions or localities. On the other hand, in OLPR systems a candidate’s electoral fortunes depend on both: a.) her party’s aggregate success, and b.) the success of her own voter mobilization efforts vis à vis those of her list-mates. This combination of inter- and intra-party incentives leads to a cartel-like situation in which all candidates devote just enough effort to voter mobilization so as secure one another’s mutual re-election. Put shortly, in OLPR systems incumbent legislators ‘collude’ on Mutually Assured Re-election Nash Equilibria.
As a consequence of these equilibrium properties the party-centered electoral competition required for ‘consociational pacts’ or ‘cross-class coalitions’ should emerge in CLPR but not OLPR systems. However, this is not to say that OLPR will fail as a mediating device in all potentially conflictual situations; nor conversely that CLPR generates universally salutary political outcomes. To understand their respective strengths and weaknesses we must address a second assumption implicit in the above reviewed work, namely that a country’s political cleavage structure is more or less fixed and predictable. Political cleavages are the cultural and socio-economic divisions which become salient in political campaigns. The most oft-noted cleavage-structure distinction is that between ‘one-dimensional’ environments, as found in elections structured by a single ‘left-right’ political-economic dimension; and the multi-dimensional environments found, for example, in Belgium and the Netherlands where religious divisions combine with social class distinctions to complicate political space.
This paper emphasizes a different distinction: that between fixed cleavage environments in which the social identity dimensions which define political campaigns are relatively stable over time;[9] and fluid cleavage environments in which these competitive dimensions are subject to greater short-term variation.[10] Section VI argues that the very party-centeredness which forms the basis of past arguments relating PR to conflict mediation is potentially destabilizing in countries with less predictable dimensions of political cleavage. The analysis thus suggests that CLPR may under certain circumstances aggravate ethno-political tensions and instigate the very social violence it was designed to avert. Furthermore, it demonstrates that OLPR institutions contain a number of analytic properties absent in nearly all previously proposed institutions for conflict mediation (Reilly 2004 discusses ‘hybrid’ alternatives to PR), and may represent the best alternative for peace and stability in complex political environments. Historical evidence detailing parallel cycles of party system concentration and political conflict in Turkey provide a suggestive narrative in support of the paper’s basic claims.
Table 1 summarizes this discussion. The columns and rows capture a country’s extant electoral rule and the stability of its cleavage environment respectively, yielding a 2 X 3 typology with 6 basic system configurations. Past research on PR and conflict mediation applies most accurately to the comparison of cells 1 and 2, amounting to the argument that CLPR outperforms MAJ competition in relatively fixed political contexts. The current paper demonstrates the importance of distinguishing between CLPR and OLPR, arguing that the latter may generate a less conflictual form of politics in countries with less stable lines of political cleavage (cells 5 and 6). We thus identify the potential pitfalls of exporting an institution (CLPR) whose salutary consequences in one context may in fact represent the mirror-image of its deleterious consequences elsewhere.
(Table 1 here)
III. The Model
While the model is robust to multi-party situations, a simple two-party game is sufficient to identify the fundamental distinction between CLPR and OLPR competition.[11] Consider a country comprised of M evenly sized regions identified by the marker[pic], in which two political parties [pic] compete for office. Furthermore, let the country’s Legislature contain M incumbent legislators, each of which belongs to one of the two competing political parties. Assume that each individual incumbent has the option of developing a personal voting bloc in exactly one of a country’s M evenly-sized regions, and that no two incumbents have this option in the same region.[12] More specifically, all [pic] incumbents possess 1 unit of effort which they divide exhaustively between: a.) developing a personal reputation in their particular region (denoted[pic]);[13] and b.) developing an organizational reputation among key intra-party actors, for example their party’s executive leaders and national convention delegates (denoted [pic]). In the following game, all M legislators simultaneously make decisions as to how to allocate their 1 unit of effort between [pic] and[pic], after which point an election is held and citizens choose between parties A and B.
Effort devoted to [pic] appears to regional constituents in the form of targeted fiscal transfers (i.e. pork-barrel projects), ombudsman services, local visits and public appearances, etc. The provision of such goods and services allows individual candidates to develop regional voting constituencies whose choice at election time has little to do with issues of national level public policy, and much more to do with their allegiance to a local politician with a reputation for constituency service. Behaviors associated with [pic] include supporting one’s party in legislative votes and bargaining, aiding in the development and implementation of a party’s public policy initiatives, attending a party’s national-level social events and fundraisers, etc. This effort allows legislators to curry favor with powerful intra-party actors in control of both material resources and opportunities for career advancement within the organization.[14]
In specifying incumbent utility functions, we will make the natural assumption that legislators gain some measure of satisfaction from the material and professional rewards accrued by courting a party’s executive and organizational leaders. Formally, legislators’ utility will be increasing in the amount of effort they devote to [pic]. On the other hand, constituents in region [pic] control a distinct resource of value to incumbent legislators: votes. Office-minded legislators may thus benefit from effort devoted to [pic] insofar as the consequent increased regional vote-shares might increase their chances of re-election. Define f ≡[pic] as the strategy vector containing constituency effort levels chosen by all incumbent legislators from both parties.[15] Then define [pic]{ f } as the probability that the incumbent affiliated with region j will gain re-election to the legislature (which will be a function of f ). Finally, let R denote the fixed utility associated with gaining re-election.[16] One can then write the incumbent affiliated with region j’s utility as follows:
[pic] = [pic]f } · R ] . (1)
After incumbents make their effort allocation decisions, voters will evaluate both a political party’s national-level public policies as well as the regional performance of its individual legislators. Most basically, assume a voter from region[pic]’s utility increases in[pic], the effort invested by one of party P’s legislative incumbents in providing region-specific goods and services. As well, let [pic] denote voter [pic] in region[pic]’s relative satisfaction with party A’s national-level policy positions as compared to those adopted by party B, where higher (lower) values of [pic] correspond to higher preferences for party A’s (B’s) policy positions as compared those of party B (A). For the moment, assume these partisan preferences in region j vary according to a uniform distribution over the support set [pic], such that [pic]< 0 ([pic]> 0) represents the bias of the voter in region[pic] who is least (most) inclined to vote for A.[17]
Voters’ attitudes towards A and B’s respective national-level policies will be determined not only by the relative ‘satisfaction’ captured in [pic], but also by their expectations as to the parties’ relative emphasis on implementing nationally oriented as opposed to locally oriented public policy programs. Consider the following utility functions for voter [pic] in region j over parties A and B respectively:[18]
[pic] = [pic] + [[pic]] and [pic] = [pic] – [[pic]]. (2)
The function w(·) is a weighting function whose value will be determined by the average effort devoted by P’s legislative incumbents to supporting their party organization’s campaign and policy strategies, denoted [pic]. If one defines [pic] as the total number of seats P currently has in the legislature, then this average effort is written as:
[pic]= [pic]. (3)
By definition, when all incumbents from P choose [pic]= 1 this average effort will be [pic]= 0; and when they all choose [pic]= 1 it will be [pic]= 1.
We will assume throughout that w(0) = 0, w(1) = 1, and w(·) is weakly increasing (i.e. non-decreasing) in [pic]. In words, the less effort that P’s incumbents devote to organizational campaign and policy strategies, the more voters will ‘discount’ P’s national-level policy positions. Conversely, the more P’s incumbents pursue the interests of regional constituencies rather than the goals of their party organization, the less consideration will be given to P’s national-level policies at election time. Political parties whose legislators maintain independent local reputations will tend to be less disciplined, more factionalized, and less ideologically consistent than parties whose legislators are oriented primarily to pursuing organizational goals. While often neglected in formal political theory, these intra-party dynamics occupy center-stage to voters in electoral campaigns. The assumption that w(·) weakly increases in [pic] states that voters use a party’s cohesion as one of many heuristics with which to evaluate its likely success in implementing public policy.[19] The results below require no further assumptions as to w(·)’s functional form, i.e. the rate at which w(·) increases with a given increase in [pic].
Turning to the model of electoral choice, note that (by construction) citizens in regions whose affiliated incumbents are from party A (B) receive constituency-level goods and services only from this party’s representative and never from a representative of B (A).[20] It is thus convenient to model voter choice as the decision to ‘accept’ or ‘reject’ the party of one’s regional incumbent after observing the effort allocation[pic].[21] The notion of a reservation utility provides a useful mechanism for capturing this dynamic. Define the reservation utility [pic] as the satisfaction level at which voters feel sufficiently pleased with the party of their incumbent legislator to choose that party in the ensuing election. Voters from a region[pic] whose incumbent legislator is from party A will thus choose A if[pic]; otherwise they will choose B. Similarly, voters from regions whose affiliated incumbent is from B will choose B if [pic] and A otherwise.
With the simple calculus of uniform distributions, we can then derive the total support for party P in region j given any strategy vector f of incumbent effort allocations. Using as an example a region j whose affiliated incumbent is from party A, algebraic rearrangement (Appendix A) demonstrates that A’s total vote share in region j is:
[pic]( f ) [pic]. (4)
As shown in figure 1, [pic] represents the ‘height’ of [pic] in j. B’s vote share in the same region will simply be [pic]( f ).[22] The same process can be undertaken to derive [pic]( f ) and 1–[pic]( f ), B and A’s respective vote shares in regions where the affiliated incumbent is from party B. These vote share functions capture a tradeoff faced by all incumbent legislators: while effort devoted to [pic] increases P’s vote share in region j, it also shrinks[pic], which in turn costs party P votes in regions outside of [pic]. The relative rates at which these counteracting dynamics occur, along with the institutional mechanisms defining the role of personal voting constituencies in securing re-election, will dictate legislators’ equilibrium effort allocations.
(Figure 1 here)
To model proportional representation in its purest form, let the entire electorate (i.e. voters from all regions) reside in a single national electoral district with M seats, as is the case in countries such as the Netherlands and Israel.[23] We then employ a simple quota and largest remainder rule to model the proportional allocation of seats to A and B. Define q =[pic] as the electoral quota needed to earn an individual legislative seat; in elections jargon this is the Droop quota. Consider the case in which [pic] (i.e. the national district contains 10 seats), such that q=10%. If party A wins 58% of the aggregate vote (i.e. votes summed across all regions) and party B wins 42%, then party A’s vote share contains 5 full quotas and party B’s vote share 4, implying that in a first allocation they will receive 5 and 4 seats respectively. As for the final seat, it will go to A because her remainder of 8%, the vote share left over after her 5 quotas are subtracted, is larger than B’s remainder of 2%. As such, in a final tally A will win 6 seats and B will win 4. If both parties have identical remainders of 5%, the final seat will be allocated with a non-biased coin-flip.
IV. Legislative Equilibrium under Closed-List Proportional Representation
At election time both parties present a list of M candidates to the electorate. Among these M candidates are the[pic] legislative incumbents from party P and [pic] challenger candidates. In this model, challengers are not endowed with a strategic move, though as Section V demonstrates their mere presence has an important impact on intra-party competition in OLPR systems.[24] If a party wins some number [pic] legislative seats, these seats are subsequently allocated to the top X candidates on the party’s list. Under CLPR competition candidates’ list positions are fixed prior to the general election according to their respective parties’ internal candidate nomination procedures. This paper treats these intra-party processes as exogenous, and simply assumes that incumbents are aware of their list position when choosing effort allocations.[25]
As a result, while effort devoted to[pic] may increase P’s aggregate vote share thus indirectly increasing [pic]{ f }, it will not affect one’s pre-determined position on the party list. High list positions will thus be a valuable commodity in CLPR systems: parties can generally count on some minimum number of safe seats, such that candidates high on their party’s list will almost certainly be elected regardless of the particular instantiation of f. On the other hand, candidates low on a party’s list can do little to ensure their own victory as they will be dependent on the party’s aggregate success and thus, at least in part, on the vote-seeking efforts of their co-partisans.
The equilibrium consequences of this closed-list dynamic are easiest to present for the case in which incumbent legislators from both parties A and B occupy higher list positions than their respective parties’ challengers (Appendix B contains the general analysis). If incumbents find themselves ahead of challenger candidates on party lists it is straight-forward to show that, given any electoral outcome, either party A or party B will have all of its incumbents re-elected. For example, consider the situation in which A and B currently have 7 and 3 seats respectively. If some f is played such that A wins 4 legislative seats and B the remaining 6, than all of B’s incumbents and 3 of its challengers secure re-election, while only 4 of A’s incumbents are re-elected. We can now characterize the Equilibrium of the following CLPR game when incumbents occupy more favorable list positions than challengers:
|The CLPR Game |
| |
|Stage 1: all incumbents simultaneously choose an effort allocation subject to the effort constraint [pic]; |
|Stage 2: elections are held in which voters choose according to the reservation utility rule; |
|Stage 3: A and B’s respective vote shares are aggregated across all regions, and the Droop quota/largest remainder rule is |
|employed to determine how many seats each party receives; |
|Stage 4: a party’s X seats go to the top X candidates on that party’s list. |
Define f *=[pic] as a Nash Equilibrium strategy vector, and label f o = [pic] as the full-partisanship strategy vector, that in which all incumbents choose [pic]= 1 and devote no effort to personal vote-seeking. Let [pic]([pic]) denote the party whose incumbents are (are not) all re-elected when the full-partisanship vector f o is played. While by definition all [pic] incumbents from [pic] are re-elected given f o, only some number [pic] < [pic] incumbents from [pic] are re-elected, where [pic] denotes the number of ‘safe seats’ held by [pic].
Recalling the utility function specified in (1) above, no incumbent who secures re-election given the full-partisanship electoral outcome has any incentive alter his or her effort allocation: they secure re-election despite having chosen [pic], and any deviation would represent a needless transfer of effort away from the pursuit of valuable material and professional rewards. What about the decision facing an incumbent from [pic] at list position S+1, i.e. the highest position not to receive one of the party’s safe seats? In order to secure re-election this marginal candidate must devote just enough effort to constituency mobilization such that [pic]’s aggregate vote share is sufficient to receive [pic] rather than S seats. Define [pic] as this critical level of constituency service, and [pic] as the marginal candidate’s equilibrium choice. Theorem 1 demonstrates that, under CLPR competition, only the marginal candidate from [pic] ever devotes any effort to personal vote seeking:
| |
|* Theorem 1: The vector f *=[pic] is the unique Nash Equilibrium |
|of the CLPR game, where [pic] depends on the game’s exogenous parameters. |
Under CLPR competition, at most one incumbent ever devotes effort to constituency service. Appendix B contains the general proofs of both Existence and Uniqueness; the following discussion presents the intuition.
Returning to the example in which A and B have 7 and 3 seats respectively, consider the case in which the electoral outcome associated with f o leaves party A with 40% of the vote and party B the remaining 60%. The marginal candidate is thus the incumbent at list position 5 from the current majority party A. When all other incumbents play[pic]= 0, to be re-elected this marginal incumbent must add just over 5% to A’s vote share: when A’s vote share just exceeds 45%, by the largest remainder the party wins a 5th legislative seat, which will go to the candidate from A at list position 5 (i.e. the marginal candidate). Depending on the functional form of [pic] and the size of R, securing this additional 5% may or may not be possible and/or desirable.
Firstly, with every incremental increase in constituency service effort exerted by the marginal candidate, party A wins votes in this incumbent’s region but loses votes in other regions due to the accompanying drop in [pic] (Appendix A). If the latter dynamic occurs more rapidly than the former, the marginal candidate will be unable to secure the necessary additional 5%, and the full-partisanship vector f o itself is the CLPR game’s unique Nash Equilibrium. Secondly, this same vector will be the game’s Nash Equilibrium when the opportunity cost of choosing [pic] and securing the additional 5% outweighs the benefit to doing so R. If securing the needed 5% is both possible and desirable for the marginal candidate, then [pic] and the marginal candidate develops the political system’s lone personal voting constituency.
While the proof of Existence (i.e. the proof that f * from Theorem 1 is indeed a Nash Equilibrium) presented in Appendix B is crucial, it is the proof of Uniqueness which uncovers a hybrid collective action problem in CLPR systems. Continuing with the now familiar example in which A and B have 7 and 3 incumbent respectively, consider a strategy vector f in which each incumbent devotes enough effort to constituency service so as to secure 100% of the votes in their respective regions. Given such an outcome A receives 70% of the aggregate vote share, B receives the remaining 30%, and all incumbents from both parties secure re-election. However, those incumbents with high list positions will have the incentive to defect. For example, the incumbent who occupies party A’s first list position only needs A to receive 1 seat in order to secure re-election. When all other incumbents secure 100% of votes in their respective regions, even if the incumbent at list position 1 defects to [pic], her party will receive more than enough votes to secure this 1 necessary seat. The incumbent at list position 1 will thus defect, and secure re-election by free-riding on the effort of her co-partisans.
But this defection will likely drop A’s aggregate vote share to below 65%, such that A will no longer have the electoral support necessary to garner 7 seats. As such, despite exerting enough constituency effort to secure 100% of her region’s voters, A’s incumbent at list position 7 does not re-gain her legislative seat: this constituency-level voter support goes to re-electing her defecting co-partisan at list position 1. Since even maximal constituency effort is insufficient to secure re-election, the incumbent at list position 7 has every incentive to defect to [pic], which maximizes her utility when re-election is impossible. The proof of Uniqueness in Appendix B demonstrates that, at any other vector aside from f * in Theorem 1, either incumbents high on the list will defect so as to free-ride on their co-partisans’ mobilizing efforts; or incumbents low on the list will defect to avoid having their efforts usurped by those with more favorable list positions.
The near complete absence of personal vote-seeking has important consequences for political party competition under CLPR. Equilibrium party cohesion [pic] will equal roughly 1 for each party, which implies that voter choice is almost completely determined by the parties’ respective national-level policy positions.[26] This in turn makes incumbent legislators almost completely dependent on high list positions to secure re-election. Access to these safe list positions is controlled by the intra-party leader or group responsible for candidate nomination procedures. As such, CLPR competition strengthens the hand of a party’s organizational leaders and/or activists when dealing with their groups in Parliament. This nationalized political competition with disciplined parliamentary factions constitutes the very party-centered dynamic required to sustain consociational and/or cross-class bargains.[27]
IV. Legislative Equilibrium under Open-List Proportional Representation
When turning out to vote in OLPR systems, voters simultaneously choose a political party and a particular candidate from within that party’s list. To model this process, we will let [pic] represent not only the percentage of votes from region j which accrue to party P’s aggregate total, but also the number of candidate votes received by the region’s incumbent. Aside from the 4th and final stage, the OLPR game proceeds identically to the CLPR game outlined on page 14. In this final stage, after P wins some number [pic] legislative seats, these seats are allocated to the candidates on P’s list with the highest X candidate vote totals in their respective regions. As such, devoting effort to [pic] and increasing [pic] not only increases the number of seats P wins, but also the likelihood that one of these seats will be allocated to the incumbent in question. Rather than being fixed prior to the general election, the ‘order’ of electoral lists in OLPR systems is thus crucially dependent on incumbents’ constituency mobilization efforts.
In the CLPR context, the regional affiliation of challenger candidates is irrelevant, as votes cast against the party of one’s regional incumbent transfer directly to the opposing party’s aggregate total. By definition, in OLPR systems votes cast against one’s regional incumbent serve not only to increase the opposing party’s aggregate vote share, but also as candidate votes for one of the individual challengers on the opposing party’s list. In keeping with the game’s basic set-up, assume that each of P’s challengers accrue candidate votes in exactly one of the [pic] regions currently held by an opposing party incumbent, and that no challenger candidate accrues such votes in more than one region (see ftn 14). As such, while [pic] ([pic]) represents the number of candidate votes received in region j by an incumbent from A (B), [pic] ([pic]) represents the number of candidate votes accrued by a single regional challenger from the opposing party B (A). Although as above challengers have no strategic move, their mere presence on electoral lists in OLPR systems has a profound impact on intra- and inter- party competition between legislative incumbents.
Define [pic]as the percentage of party loyalists in region j: voters whose value of [pic]is such that they will choose the party of their incumbent legislator even if this incumbent chooses [pic]= 0. To communicate the model’s intuition, investigate a stylized situation in which party A and B have 6 and 4 current incumbents respectively, and [pic] in all regions. If the full-partisanship strategy vector f o is played, by aggregating the parties’ vote shares across regions we see that A receives roughly 40% of votes (4 seats) while B receives the remaining 60% (6 seats).[28] Furthermore, legislative seats are allocated almost exclusively to challenger rather than incumbent candidates: at f o all incumbents choose [pic] and receive only [pic] preference votes; this in turn implies that all challengers receive [pic] preference votes. Since challengers receive more preference votes than incumbents, in the OLPR game’s final stage the 6 seats B receives will be allocated to 6 of its challengers, and the 4 seats A receives will be allocated to its 3 challengers and 1 of its incumbents.
Unlike the CLPR game f o will thus never be a Nash Equilibrium. For example, given that each of A’s incumbents receives the same number of preference votes when f o is played, it is reasonable to assume that each will have a 1 in 7 probability of receiving the lone legislative seat not allocated to a challenger (i.e. preference vote ties among incumbents are broken by chance). But any one of A’s 7 incumbents could then choose [pic] ([pic], increase her preference vote total to just above that received by her fellow incumbents, and gain this individual seat with certainty. In turn, another of A’s incumbents could choose [pic] ([pic]) and herself gain the seat. But then a 3rd incumbent could do the same, and so on. Thus, the 7 incumbents from A will jockey among themselves over the single legislative seat not allocated to A’s challengers.
Although an expression of non-cooperative intra-party competition, this jockeying in fact ends up benefiting party A as a whole: each time an incumbent slightly increases her preference vote total in an attempt to best her colleagues, she also increases A’s aggregate vote share. As such, as A’s incumbents attempt to ‘outbid’ one another for this single legislative seat, A’s aggregate seat total eventually begins to climb: from 4 to 5, and then from 5 to 6, and so on. Furthermore, this jockeying simultaneously decreases the number of preference votes received by B’s challengers. Consider the point at which preference vote competition has led each of A’s incumbents to secure [pic]. At this point, any of B’s incumbents can secure re-election by allocating just enough effort to [pic] such that [pic]. Thus, the more intense the intra-party competition among A’s incumbent candidates, the easier it becomes for incumbents from B to reach the preference vote totals registered by their party’s challengers.
Under most circumstances the vote jockeying characteristic of OLPR competition will continue until a mutually assured re-election Nash Equilibrium (MARNE) is reached. At MARNE outcomes incumbents from both parties simultaneously devote just enough effort to constituency mobilization so as to secure the entire Legislature’s re-election. Continuing with stylized case in which [pic] is identical across all, define [pic] ([pic]) as the number of seats held by the current majority (minority) party. Theorem 2 employs the condition [pic]+ 1)[pic], which ensures that incumbents’ preferences for re-election are strong enough so as to support the entire range of possible MARNE. Appendix C investigates the model in situations with regional heterogeneity in levels of party loyalty and lower levels of R; neither complication alters Theorem 2’s basic implications.[29]
| |
|* Theorem 2: Under OLPR competition with [pic]+ 1)[pic], any Nash Equilibrium f *=[pic] must satisfy the following conditions, and|
|any vector satisfying these conditions must be a Nash Equilibrium: |
| |
|all incumbents gain re-election; |
|all incumbents from the same majority (minority) party receive identical vote shares [pic] ( [pic]) in their respective districts;|
|[pic]. |
Consider the case in which A and B have 6 and 4 current incumbents respectively. Then, one strategy vector which meets Theorem 2’s requirements is that at which all of A’s incumbents receive [pic]= 60% and all of B’s incumbents receive [pic]= 40%: at this outcome A and B win back their 6 and 4 seats by the quota/remainder rule, and condition (c) from Theorem 2 is satisfied. Another strategy vector which meets these requirements is that at which [pic]= 64% and [pic]= 36% for all incumbents from A and B respectively. In fact, Theorem 2 allows for any outcome in which: a.) [pic] and [pic] are identical for all incumbents from parties A and B respectively, b.) 65% < [pic][pic] 75% and 25% [pic] [pic]< 35%, and c.) [pic].
(Figure 2 here)
No incumbent wishes to deviate from any such strategy vector: since each incumbent secures re-election devoting more effort to [pic] and receiving more candidate votes is unnecessary; but devoting less effort to [pic] would upset her re-election by dropping her preference vote total to just below that received by her party’s challengers (by condition (c) in Theorem 2). Though arising in a non-cooperative environment, MARNE contain fundamentally collusive properties. At the level of intra-party competition, the mutual jockeying for preference votes between incumbents of the same legislative group leads each to receive identical preference vote totals, thus dividing evenly the constituency service required to secure mutual re-election. At the level of inter-party competition, condition (c) in Theorem 2 guarantees that incumbents from the opposing party secure just enough constituency support to keep the challengers from one’s own party at bay.[30]
The incentive for incumbents to develop personal voting constituencies in OLPR systems dwarfs that of their counterparts under CLPR competition, leading to much lower levels of equilibrium party cohesion [pic]. Voters thus discount more heavily a party’s national-level policies, and show less responsiveness to shifts in the national-level programs announced by party organizations. As a result, office-minded political party leaders find themselves to a large extent dependent on the personal vote-seeking of their respective parliamentary factions at election time. Under OLPR competition the intra-party balance of power between a party’s organizational leaders/activists and its parliamentary faction should thus be tilted in favor of the latter. In some sense, the collusion between legislative incumbents from opposing parties under OLPR competition uncovered in Theorem 2 is thus two-fold. Not only does constituency effort exerted by the opposing party’s incumbents keep one’s own challengers at bay; it contributes more generally to securing the intra-party ascendancy of parliamentary groups over their respective organizational machines. In the upcoming argument, incumbent legislators’ shared interest (both within and across parties) in ensuring one another’s ability to develop personal voting constituencies serves as the key theoretical mechanism linking OLPR to conflict reduction in newly democratizing societies.
VI. Proportional Representation in Fluid Environments
In CLPR systems, the ability of incumbents with favorable list positions to free-ride on the constituency service of co-partisans lower on the list leads to a highly party-centered from of competition in which parliamentary groups are largely subservient to their respective party organizations. Candidate voting under OLPR competition serves as an inter-legislator commitment mechanism, allowing legislators from all parties a shared confidence in one another’s constituency building effort, which in turn fosters the independence of parliamentary groups from their party organizations. While party-centered competition lies at the heart of most past research relating proportionality to conflict reduction, CLPR and the accompanying intra-party ascendancy of organizational machines over parliamentary groups may in fact have destabilizing consequences in many of the world’s newer and/or soon to be democratic states.
Recall that voters under CLPR competition make voting decisions based almost exclusively on their preferences for parties’ national level policies ([pic]). To understand the consequences of CLPR competition, one must thus understand the processes by which party organizations adopt national-level campaign platforms. Elsewhere (Kselman 2008) we argue that control over these platforms emerges as a function of bargaining between a party’s activists and its executive leaders. While ceteris paribus office-seeking party leaders will naturally prefer winning to losing in general elections, they must first secure enough activist support so as to maintain their intra-party ascendancy to the organization’s top executive post.[31] Party activists must also strike a balance, that between their incentives to choose electable organizational leaders and their interest in maintaining the party’s ideological or organizational ‘purity’. This interest in purity may result from any number of sociological, psychological, or material factors (Panebianco 1988). Suffice it to say that history is replete with examples of entrenched activists restraining the office-seeking tendencies of party leaders despite incurring significant electoral costs as a result (Kitschelt 1995). That said, neither is history short of examples in which a party’s activist cadre delegates nearly full decision-making authority to its executive leaders. While clearly a multi-faceted issue, voters’ elasticity to alternative campaign appeals serves as a key mechanism in explaining the relative centralization or decentralization of organizational power in CLPR systems.
Elasticity is high when voters who currently prefer one party are nonetheless responsive to alternative appeals from competing party organizations. In many established democracies, this responsiveness has been dampened by a series of historical processes, not the least of which are centuries-long processes of state formation and economic industrialization.[32] Indeed, the very fact that a democracy is long-standing might correlate with voter elasticity insofar as strong ‘party identification’ is only acquired over time as a consequence of repeated political experiences.[33] In less economically developed countries with shorter national and democratic histories, voters will tend to be responsive to a multiplicity of political appeals. Consider the situation faced by a Turkish laborer living in 1965 Istanbul. This individual would likely have voted for the Justice Party (JP) in the 1965 general election, which at that time had a near monopoly presence at the grass-roots level in Istanbul’s lower income neighborhoods (Sherwood 1967). In 1969 this same individual might very well have transferred his general election vote to the opposing Republican People’s Party (RPP) which, after its defeat at the JP’s hands in 1965 election, had re-branded itself as ‘Social Democratic’ and become a viable competitor for lower class voter support (Sayarı 1975). Finally, in 1977 he might have moved to the far right Nationalist Action Party (NAP), which had begun to secure strong support in lower class areas as a response to the rapidly accelerating social unrest of the 1970’s (Ahmad 1993).
In no way do we mean to criticize such behavior. Indeed, without a strong attachment to individual political parties it is only natural to alter one’s vote choice in response to the appearance of new issues in political campaigns. However, this responsiveness does lend potential fluidity to a country’s political cleavage structures. Indeed, while in established democracies the ethnic and/or socio-economic identity dimensions which define political campaigns have remained relatively constant over time (Lipset and Rokkan 1967), in the Turkish Second and Third Republics (1960-1980 and 1983-present respectively) large scale political ‘realignments’ have happened in relatively short-order from election campaign to election campaign.
Why might voter elasticity and the accompanying potential for short-term political realignment condition the relative centralization or decentralization of party organizations? More particularly, under what conditions will a party’s activist cadre allow party leaders to choose vote-maximizing campaign strategies which nonetheless violate the party’s past ideological or organizational commitments? Consider first a case in which voter elasticity is low. In such cases, the electoral payoff to deviating from a party’s traditional positions will by definition be minimal, as the number of voters susceptible to alternative campaign appeals is minimal. Not only do activists in one party recognize this relative absence of electioneering incentives; more importantly, they also know that activists in other parties recognize the absence of elasticity, and that these competing activists know that they know, and so on. In equilibrium, when low voter elasticity is common knowledge, activists from all parties can thus count on one another’s incentives to constrain the electioneering incentives of opportunistic party leaders.
When the electoral payoff to deviating from a party’s traditional positions is relatively more pronounced, activists become slightly more likely to tolerate such deviations. Furthermore, once one party organization deviates even slightly from its previous policy positions for the sake of vote-maximization, activists in other parties are faced with the choice between: a.) losing the election with a significantly higher probability; and b.) allowing their own organizational leaders to effect similar vote-maximizing deviations. The afore-mentioned paper (Kselman ibid) demonstrates that, if voter elasticity surpasses some critical threshold T, activist cadres from a party system’s various organizations can no longer count on one another to constrain their respective executive leaders. The result is a spiraling situation of mutually-reinforcing abdication by activist cadres from competing parties of their organizational powers. This centralizing tendency has been especially pronounced in Turkish democratic history, where political parties often assume the form of personal fiefdoms at the near total disposal of power leadership personalities (Gallagher 1988, Özbudun 2000).
As reviewed in Section 1, coalition government constitutes the key mechanism linking proportionality to conflict reduction in previous research. Coalition governments emerge most frequently in party systems with more than two political parties. The key to understanding the potential dangers of CLPR is recognizing the fundamentally ‘dualistic’ pressure that activist abdication exerts on party systems in fluid cleavage environments. Figure 3 plots the Effective Number of Parliamentary Parties (ENPP) in the Turkish Grand National Assembly from 1961 to 2007.[34] The trend is patently cyclical. Each intervening decade begins in a state of relative party system fragmentation, but trends towards concentration near its end.[35] In the 1960’s and 1970’s the two primary beneficiaries of this party system concentration were the afore-mentioned JP and RPP. In the late 1990’s and early 21st century, legislative seats became nearly completely monopolized by the RPP and the Justice and Development Party (JDP). Importantly, the governments characteristic of these more concentrated periods have been either majority single party governments (1969 and 2002) or minority governments supported by a small number of independent legislators (1977-1980).
(Figure 3 here)
The sequence of events which underlies the move from fragmentation to concentration demonstrates strong parallels from one decade to the next. The (disequilibrium…) state of fragmentation persists, whether for one election as in the 1970’s or 3 elections as in the 1990’s, until the electioneering permitted of powerful party leaders allows two parties to establish some measure of ascendancy over their competitors. Though this initial ascendancy may be minimal, in fluid environments it becomes self-perpetuating in no small part due to the phenomenon of party-hopping in the Turkish legislature (Sayarı 2002).[36] Indeed, the absence of ‘party identification’ may be even more striking among Turkish members of Parliament than among Turkish voters themselves. Without long-standing organic ties to individual party machines, legislators jump ship in between elections at a striking rate, joining one of the two relatively larger parties’ parliamentary groups in exchange for the promise of favorable list positions in subsequent rounds of electoral competition.
The outcome of these party system dynamics is a highly unstable form of two-party competition which has acquired a number of conceptual labels: ‘basic dualism’ (Sayarı 1975), ‘amoral majoritarianism’ (Kalaycioğlu 1988), etc. It is suggestive that each of Turkey’s spikes in party system concentration has been coterminous with periods of social and political instability. In both 1971 and 1980 the Turkish military was forced to intervene in civilian politics in response to outbreaks of intense social unrest and violence. In 2006-2007 tensions between the ruling JDP and the opposition RPP simmered, resulting in what is now an ongoing period of constitutional crisis. This newest period of instability has been punctuated by secularist/nationalist protests of over 1 million people in the streets of Ankara and Istanbul (May 2007) and crackdowns against ‘May-Day’ labor rallies in Istanbul’s Taksım Square (2007 and 2008). More recently the Turkish Constitutional Court (traditionally allied with the Turkish military) has initiated a legal process in favor of dismantling the JDP, which it claims constitutes a threat to Turkish secularism. While the current period of instability has not yet resulted in levels of violence comparable to those of the 1960’s and 1970’s, one cannot help but wonder as to the civil consequences of shutting down a political party (the JDP) which won nearly 50% of the vote in Turkey’s most recent 2007 election, and avails itself of a large and highly organized grass-roots following.
Though not all two-party competition need have deleterious consequences, that which appears in fluid CLPR contexts is plagued by a marked centrifugalism which often results in violent social conflict. At the root of this centrifugalism is the fact that the electioneering characteristic of fluid CLPR systems leads to the creation of highly heterogeneous political parties whose supporters have diverging preferences as to the ideal nature and level of public good provision (Kselman ibid). When in office and faced with the task of satisfying this heterogeneous constituency, a party leader’s only recourse is the provision of targeted material benefits, as any strategy for public good provision will by definition alienate some portion of a party’s supporters and threaten leaders’ intra-party positions. Thus, economic policy in fluid CLPR systems tends to become more and more particularistic as party system concentration increases. Furthermore, the near complete absence of constituency service incentives characteristic of all CLPR systems makes this particularism highly exclusionary: unable to count on the individual efforts of their local representatives, voters understand that targeted benefits will only be forthcoming if their national-level party choice wins office. This combination of particularism and exclusion lends a strong zero-sum flavor to politics. Indeed the ‘amoral majoritarianism’ descried here may be no less destabilizing than the majoritarianism generated by MAJ systems themselves. The Concluding Section argues that OLPR may provide a form of inclusive particularism which outperforms both CLPR and MAJ systems in generating peace and stability in fluid political environments.
VII. Conclusion
This paper argues that the party-centrism characteristic of past research on proportionality and conflict mediation emerges in CLPR but not OLPR systems; and that this very party-centrism may have destructive consequences in newly emerging democracies. Of course, the historical narrative and aggregate data presented in Section VI do not by any means constitute a definitive empirical ‘test’ of the argument. Such a test would require the collection of data over a much larger set of cases, and might help to identify intervening parameters in Turkish society which render CLPR especially destabilizing. However, Turkey is certainly not the only case in which CLPR has failed to generate civil order. For example, in a sequence of parliamentary elections (1992) post-communist Yugoslavia experienced patterns of organizational centralization, mutually reinforcing radicalism, and political violence with significant parallels to those described above in the Turkish case. As well, the recent post-conflict election in Iraq employed CLPR in a single national district in the hopes of mediating pent up ethnic tensions; the infamous results need little description here.
It is also interesting that, to my knowledge, no parliamentary regime employing OLPR elections has witnessed the social violence and democratic instability which comprise shared experiences in Turkey, Serbia, and Iraq.[37] Although used much less frequently than either CLPR or MAJ institutions, one can identify a number of new and ethnically-divided democracies in which OLPR electoral rules may have played some roll in preventing the onset of large scale civil disorder. For example, the Baltic Republics of Lithuania, Latvia, and Estonia have all employed OLPR in parliamentary elections since the fall of communism, and have avoided large scale social violence despite being divided between native populations restless after decades of Soviet hegemony and large ethnic Russian minorities. As well, the recent post-conflict legislative elections in Afghanistan were held under the Single-Non-Transferable-Vote, an electoral rule whose theoretical properties overlap in significant ways with OLPR. While remnants of the Taliban continue to stage destructive raids from Pakistan, Afghanistan has not experienced blood-letting between its Uzbek, Turkmen, and Pashtun communities, nor between its Sunni and Shia sects, of the severity witnessed in Iraq.
Without subscribing to an institutional reductionism, why might OLPR contribute the maintenance of civil order? The answer lies in the inclusive consequences of candidate voting and legislator collusion captured in Theorem 2. Consider a majority party which competes with a smaller opposition party. Legislators in this majority party have every incentive to allow their opposition counterparts some access to public resources: it is these very opposition legislators whose constituency service efforts help to keep both the majority party’s challengers and the majority party’s leaders at bay. Voters thus need not rely on the executive incumbency of their local legislators’ party to partake in the ‘public pie’. The shared incentives fostered by OLPR thus significantly deflate the zero-sum nature of politics characteristic of CLPR elections in fluid environments, leading to a more geographically balanced distribution of resources (recall Figure 2). Some might object that the decentralization resulting from OLPR elections will lead to a ‘lesser’ form of democratic accountability, characterized by high levels of pork-barreling and policy capture by geographically defined special interest groups. However, while not generating ‘universalistic’ public goods, OLPR may serve as a ‘second-best’ temporary option for averting violence in societies whose particular socio-political dynamics are in any case unlikely to generate a short-term political emphasis on public good provision.
Beginning with Horowitz (1985) an important body of research advocates hybrid preferential voting systems as outperforming traditional forms of PR in mediating social conflict (Reilly ibid). This important and consequential body of work, to which the current paper owes a substantial intellectual debt, criticizes the assumption in past consociational studies that party leaders will naturally cooperate once in Parliament. In turn, it proposes that electoral systems which allow voters to rank order candidates will stimulate party leaders to form cross-ethnic pacts and shared ‘communicative spaces’ prior to the post-election period of coalition bargaining itself. While a full exposition is beyond our current scope, we believe that the key to stimulating civil order in fluid political in environments is to never rely on the cooperative instincts of party leaders at the helm of centralized party organizations; not before voting takes place, and not after. As such, it is our contention that the decentralization and geographic inclusiveness fostered by OLPR represents the best hope for conflict mediation in many new democracies. We look forward to a collaborative polemic with proponents of preferential voting in future research.
Table 1: the Theoretical Framework
| | → Current Domain |
| | → Previous Research |
| | | | |
| |MAJ |CLPR |OLPR |
| | | | |
|Fixed |1 |2 |3 |
| | | | |
|Fluid |4 |5 |6 |
Figure 1: Party Choice in Region j
[pic]
* This shaded area represents the subset of all voter types who choose party A given some effort allocation by that party’s incumbent in the region. All voter types from the non-shaded area thus choose B.
Figure 2: MARNE under OLPR Competition
Example (a): [pic] and [pic]
[pic]
Example (b): [pic] and [pic]
[pic]
* Regions with dashed lines moving up (down) diagonally from left to right are those whose current incumbent is affiliated with party A (B). Party A (B) is presented as currently holding regions 1 through 6 (7 through 10) for the purposes of visual ease; the ordering could just as easily be staggered.
Figure 3: Turkey’s ENPP, 1961-2007
[pic]
YEAR |1961 |1965 |1969 |1973 |1977 |1991 |1995 |1999 |2002 | |ENPP |3.23 |2.62 |2.35 |3.32 |2.47 |3.58 |4.40 |4.87 |1.85 | |
* Data collected from the website of the Turkish Grand National Assembly
Appendix A: Regional Vote Shares
• Define [pic] as the swing voter in region j given some allocation [pic], i.e. the voter whose utility exactly reaches the reservation level needed to choose re-election. In other words,
[pic]. (A1)
• The utility of voters in region j with [pic] will thus surpass the reservation level, and they will vote for the regional incumbent. As demonstrated visually in Figure 1, the following captures the portion of voters from whom [pic]:
[pic] (A2)
• By the definition of uniform distributions [pic]. Substituting into A2 using this fact and A1 yields (2) in the text. Since [pic] cannot be greater than 1, any value of [pic] such that (A2) is greater than 1 implies a vote share 1. ■
• [pic] captures the responsiveness of voters in region j to marginal increases in [pic]. The results derived in Appendices B and C assume that [pic] is large enough such that voters are at least minimally responsive to constituency effort. Without this assumption the game is trivial: legislators have no incentive to engage in constituency service if it has no electoral impact.
Appendix B: the CLPR Nash Equilibrium
I.) Theorem 1: Proof of Existence
• Begin by proving the Theorem under the assumption that all incumbents assume higher list positions than challenger candidates.
• Naturally, none of the incumbents from[pic] defect from f * in Theorem 1, as they secure re-election costlessly on the basis of loyalist support alone. The same is true of the top S incumbents from [pic].
• The marginal incumbent needs her party’s aggregate vote share to reach the following level in order to gain an additional legislative seat:
[pic], [pic]. (B1)
At this level, her party’s remainder just outpaces that of the opposing party, thus securing [pic] an additional seat.
• Define [pic] as the number of current seats held by[pic]. As well, define A(f o) as the aggregate vote share received by [pic] at the full-shirking vector as A(f o). Finally, define [pic] as the number of loyalists in the marginal incumbent’s region, those voters who choose [pic] even if the marginal candidate devotes no effort to constituency service.
• If A(f o) +[pic] < (B1), then there are not enough undecided voters in the marginal incumbent’s region to secure [pic] an additional legislative seat, so the marginal incumbent has no incentive to defect from f o. Furthermore, if [pic] drops rapidly enough with marginal decreases in [pic], then the marginal incumbent will be unable to secure her party an additional seat with constituency service, and will have no incentive to defect from f o.
• When A(f o) +[pic] > (B1) and [pic] does not decrease too rapidly with decreases in [pic], we can define [pic] as the constituency service necessary to push [pic]’s vote total to (B1). In such cases, the marginal incumbent will defect from f o and choose [pic] as long as [pic] < R.
• The final step in proving Existence is demonstrating that none of [pic]’s candidates at list positions lower than S+1 wish to defect. The following expression captures the aggregate vote share [pic] needs to gain S+2 legislative seats:
[pic], [pic]. (B2)
• Define [pic] as the number of party loyalists in incumbent S+2’s region. Regardless of the marginal candidate’s choice [pic], it is straight-forward to show (algebra omitted) that the aggregate vote share at the vector presented in Theorem 1 will not be high enough for incumbent S+2 to secure an additional seat, even if she wins the support of every voter in her district: A(f *) + [pic] < (B2). Why? Any ‘vote surplus’ remaining after [pic] receives its S safe seats is usurped by the marginal candidate, such that there will not be enough floating voters in candidate S+2’s region to secure an additional electoral quota, and deviating is not optimal.
• This in turn implies the identical condition for candidates S+3, S+4, and so on. As such, no candidate higher than S+1 ever wishes to defect from f * as stipulated in Theorem 1. ■
II.) Theorem 1: Proof of Uniqueness
• Lemma 1: Any policy vector f in which at least one incumbent sets [pic] but does not gain reelection is not a Nash Equilibrium (henceforth NE). If [pic] but the incumbent in question does not secure reelection, then she has the incentive to deviate by either: a.) increasing [pic] so as to secure her party an additional legislative seat; or b.) decreasing [pic] to 0 so as to gain utility [pic]
• Consider a strategy vector in which some number [pic] incumbents from [pic] choose [pic]. At any such vector either: a.) all N gain re-election; or b.) at least one of the N does not gain re-election. If (a), then those incumbents from among the N with higher list positions can defect by decreasing [pic] without losing re-election: they can free-ride on the constituency mobilization of those among the N at lower positions. If (b), at least one incumbent has the incentive to defect by Lemma 1. As such, no strategy vector in which [pic] incumbents from [pic] choose [pic]can be a NE.
• Among incumbents from [pic], choosing [pic] is necessary for re-election if and only if some fixed number [pic] incumbents from [pic] choose [pic], since by definition all incumbents from [pic] are re-elected when [pic] incumbents from [pic] choose [pic]. But since we know that no strategy vector at which [pic] incumbents from [pic] choose [pic]can be a NE, no strategy vector at which incumbents from [pic] choose [pic]can be a NE.
• As such, in equilibrium only one incumbent from [pic] ever chooses [pic]. This will never be an incumbent at list position Q < S+1: they receive safe seats due to the fact that [pic] for all incumbents from [pic]. As well, this will never be an incumbent at list position Q > S+1: they would be choosing [pic] without gaining re-election, which is ruled out by Lemma 1. ■
III.) Multi-Party Competition, Voter Abstention, and Challengers with Safe Seats
• We now provide a sketch of equilibrium in elections with 3 political parties and/or voter abstention; all results are generalizable to [pic] (Kselman 2007). The CLPR outcome with 3 parties can be assigned to one of three basic categories. The first and most basic is that in which two of three parties gain surplus seats at f o while the remaining party does not have all of its incumbents re-elected (parties receive surplus seats if all of their incumbents and at least one of their challengers is re-elected). In this case, the marginal candidate comes from the party whose incumbents are not all re-elected, and the unique NE is identical to that presented in Theorem 1 above.
• A second possibility is that two of three parties have all of their incumbents re-elected at f o, but at least one of these two has only just enough seats to re-elect all her incumbent legislators (i.e. has no surplus). In this case the marginal candidate is once again the incumbent from the 3rd party at list position S+1. In most cases, the unique equilibrium will be identical to that from Theorem 1. However, consider the situation in which the marginal candidate chooses to secure her party an additional seat, and in so doing wrests a seat from the party without a seat surplus, thus upsetting a fellow incumbent’s re-election. The incumbent whose seat was taken will in turn have the incentive to regain her lost legislative seat by increasing her own constituency service; which in turn leads the original marginal candidate to once again alter her effort level, and so on ad infinitum. In other words, in this particular situation the CLPR game has no NE.
• In the third CLPR situation to consider, that in which one party wins a seat surplus while the other two at least one incumbent does not gain re-election, there are in fact two marginal candidates, those at list positions S+1 from each of the two latter parties. In many cases at least 1 of the marginal candidates has no incentive to defect from f o, and the game’s unique equilibrium is identical to Theorem 1; in some cases the two marginal candidates engage in a never-ending back and forth of the type described above, such that no equilibrium exists.
• Finally, what about the case in which some number of challenger candidates find themselves above incumbent candidates on parties’ lists? Put shortly, as with the above cases this may under certain situations upset the NE due to a never-ending back and forth between two marginal incumbents.
Appendix C: MARNE and quasi-MARNE under OLPR
I.) Theorem 2: Proofs of Sufficiency and Necessity
• Appendix C assumes that candidate vote ties between incumbents and challengers are broken in favor of incumbents to eliminate the open-set problem which supervenes when actors can make infinitesimal moves.
• Begin by proving sufficiency: as long as [pic]+ 1)[pic], no incumbent has the incentive to deviate from any vector strategy f * which satisfies (a), (b), and (c). Since all incumbents at any such strategy vector already gain re-election, choosing a greater level of [pic] represents an unnecessary diversion of effort from [pic], and is thus a strictly dominated strategy. Furthermore, choosing any level of [pic] lower than that stipulated by f * would imply losing re-election: it would drop the defecting incumbent’s preference vote total below that of his or her party’s challengers. [pic]+ 1)[pic] guarantees that no such deviation is optimal: for any of the MARNE specified in Theorem 2, incumbents prefer expending the effort necessary for re-election to choosing [pic]= 0. ■
• Having proven that all vectors stipulated in Theorem 2 are NE, we now prove necessity, i.e. that no strategy vector which violates (a), (b), or (c) can be a NE. At any vector which does not satisfy conditions (a), (b), and (c), one of two things (and often both) must occur: either at least one incumbent who gains re-election does so with a surplus of preference votes; or at least one incumbent does not gain re-election due to her lack of sufficient preference votes. If the former, the incumbent with excessive support will have the incentive to defect by decreasing [pic]; if the latter the non-elected incumbent will have the incentive to increase [pic] until just surpassing the preference vote total of her party’s last elected legislator. In either case at least one incumbent has the incentive to defect. ■
II.) Quasi-Marne at lower levels of R
• As ([pic]) drops below [pic]+ 1)[pic], two things occur: a.) the model’s predictions become more precise without losing Theorem 2’s basic collusive properties; and b.) eventually some subset of incumbent legislators loses their seat(s) in equilibrium (Kselman 2007).
• For instance, when A and B have 6 and 4 seats respectively and [pic], if [pic] then the OLPR game yields a unique Nash Equilibrium in weakly-dominant strategies (MARNE are in strictly-dominant strategies) where one legislators from A chooses [pic] and loses her legislative seat. However, among the remaining incumbents from A and B the fundamentally collusive nature of OLPR competition continues to obtain: the 5 (4) re-elected incumbents from A (B) receive identical vote shares in their respective regions (55% and 45% respectively); and the re-elected incumbents from the opposing party gain just enough support to keep one’s own party’s challengers at bay. We thus label these outcomes quasi-MARNE.
IV.) Regional Heterogeneity and Multi-Party Competition
• Environments in which [pic] differs across regions lead to NE which display characteristics intermediate to the MARNE and quasi-MARNE outcomes discussed above (Kselman 2007). They share with quasi-MARNE the fact that not all incumbents are re-elected; but they share with MARNE outcomes a range of Nash Equilibria in strictly dominant strategies. As well, it is exactly those incumbents with low re-election incentives who end up loosing their seats: unlike CLPR, in the OLPR case incumbents’ likelihood of gaining re-election bears a direct relationship to their preferences for re-election.
• Legislative equilibria under OLPR competition with [pic] parties demonstrate an impressive continuity with the two-party case. The following discussion provides a simple example to communicate this continuity’s intuition.
• Consider a 10 seat legislature in which parties A, B, and C, have 4, 3, and 3 seats respectively. As well, assume that [pic] in their all regions. In 3 party cases we must model the manner in which dissatisfied voters split their support between the two opposing parties. Using one intuitive approach (Kselman 2007), we can prove that there will be a unique MARNE to this OLPR game: all of B and C’s incumbents, as well as 3 of A’s 4 incumbents, choose [pic] such that [pic] by (3) above; while the final incumbent from A chooses [pic] such that [pic] ([pic]).
• Given these choices, each party wins back all of its legislative seats, and all of the 9 incumbents for whom [pic] receive exactly as many preference votes as their parties’ challengers. As well, the single incumbent from A with [pic] does not wish to defect: although she receives slightly more preference votes than her challengers, dropping constituency service to [pic] would place party A in a three-way ‘remainder-tie’ with parties B and C for the last legislative seat, such that each of A’s incumbents would face some probability of not being reelected. Since [pic]→0, this individual incumbent prefers exerting slightly higher constituency effort than her colleagues to creating a probabilistic scenario.
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( Thanks to Pablo Beramendi, Michael Brady, Herbert Kitschelt, Timur Kuran, Dan Lee, Emerson Niou, Amy Novak, Phillip Rehm, Arturas Rozenas, David Soskice, and Camber Warren for valuable feedback on earlier versions. All remaining flaws are mine.
[1] The following paper’s arguments relating electoral institutions to political conflict apply most forcefully to countries with parliamentary executives: those in which the chief executive and cabinet owe their existence and survival to parliamentary approval.
[2] Consider a stylized society comprised of 3 social groups A, B, and C, which have 20%, 30%, and 50% of the population respectively. In this context, so the argument goes, elections based on pure plurality rule will leave C the permanent ruling party; groups A and B are prevented from gaining public office by the system’s winner-take-all logic.
[3] “In terms of electoral systems, consociationalists argue that some form of proportional representation is all but essential for divided societies, as this enables all politically significant ethnic groups, including minorities, to ‘define themselves’ into ethnically based parties.” (Reilly, 2004, pg. 21)
[4] The authors argue that the coalition bargaining which characterizes PR systems provides middle class voters reassurance against expropriation by the left. In MAJ systems, the absence of coalition government impels middle class voters to side with Right parties, in turn excluding Left parties from office.
[5] “The availability of the political alternative for labour can therefore be expected to be of importance for the conflict strategies of both capital and labour.” (Korpi and Shalev 1979, pg. 170)
[6] Hall and Soskice (2000), Swenson (2002).
[7] Britain, France, New Zealand, Australia, the USA, and Canada have all seen higher levels of industrial conflict than most of their PR counterparts (see Table II in Korpi and Shalev, ibid).
[8] The ability of party leaders to deliver their parliamentary groups in confidence votes underlies the elite pacts characteristic of consociational democracies, as well as the coalition dynamics characteristic of most models of multi-party government formation (e.g. Baron and Ferejohn 1989, Iversen and Soskice ibid).
[9] Recall Lipset and Rokkan’s famous characterization of West European party systems as “frozen” (1967).
[10] The constructivist paradigm in studies of ethnic politics emphasizes that citizens have a complex repertoire of potential social identities; and that the process by which one set of identities rather than another becomes politically salient is itself worth studying (Posner 2005).
[11] Appendices B and C investigate the model in multi-party contexts.
[12] One might at first glance question a model of PR in which individual legislators are affiliated in a 1-to-1 manner with specific geographic constituencies. Indeed, individual legislators in many well-known PR systems maintain little to no personal ties with particular ‘regions’ (e.g. most of Northern Europe). That said, one can point to other examples in which individual legislators in PR systems do develop a personal presence in particular geographic strongholds (e.g. Italy pre-1993, Brazil, Finland, etc). Furthermore, note that the above specification does not assume the existence of personal voting constituencies; it allows legislators the option of forming personal relationships in a particular region. Legislators can opt out by devoting all of their effort to r, in which case the constituents in j will vote solely based on their relative preferences for the two parties’ national policies. As we will soon see, the lack of constituent-legislator ties so often attributed to the modal PR system is in fact a consequence of CLPR but not OLPR competition.
[13] Superscripts indicate a legislator’s party affiliation and subscripts his or her regional affiliation.
[14] A party’s organizational leaders might also appreciate effort devoted to f, insofar as this effort increases induces greater voter support in region j, which in turn increases the party’s aggregate vote share. However, the ‘personal’ nature of these votes provides individual legislators a credible bargaining chip in matters of intra-party politics, thus weakening party leader’s organizational control. The contours of this tradeoff will become explicit below.
[15] Drop the P superscripts inside the vector f for notational convenience.
[16] Elsewhere (Kselman 2007) we investigate a model in which the value of R varies endogenously, being higher among those legislators whose party wins enough seats to form a government. This allows us to capture the notion that legislators in parliamentary systems prefer being in the governing majority to being in the opposition. The basic equilibrium dynamics uncovered in Sections IV and V below remain largely unchanged in this more complicated theoretical environment.
[17] Sections III-V investigate legislators’ incentives to develop personal voting constituencies given some distribution of preferences for the two parties national-level po some distribution of preferences for the two parties’ national-level policy positions. Section VI discusses endogenizing of σi,j by introducing party organizations into the current framework. All results are robust to alternative distributional forms, but the simple calculus of uniform distributions greatly simplifies the analysis.
[18] The ‘–’ sign in [pic]’s utility for B captures the fact that, by construction, higher values of σi,j represent a greater preference for A’s policy positions to B’s policy positions (and vice versa).
[19] We could make voters’ evaluation of party P’s cohesion ‘noisy’ by allowing voters to have a probability distribution over all possible values of πP given incumbents’ effort allocation decisions; and allowing w(·) to be a weighting function over lotteries rather than real numbers.
[20] Of course, one might expect the parties to field challenger candidates with some capacity to compete against one another’s incumbent legislators in developing personal regional constituencies. This issue is addressed at greater length in Sections IV and V.
[21] Implicit in this rule is the assumption that voters from j are able to assess the performance of individual legislators. Again, one might object that voters in PR systems often have little personal knowledge of individual legislators, and choose among parties based solely on national-level policy platforms. In fact, this pattern of voting behavior emerges as an equilibrium consequence of CLPR but not OLPR competition. Theorem 1 below demonstrates that, even in a world in which voters are able to assess the performance of individual incumbent legislators, under CLPR rules these incumbents will devote effectively ‘0’ effort to f in equilibrium. The absence of any personal constituency-building in a theoretical environment where voters are able to reward such effort with higher constituency-level support serves as a testament to the fundamental lack of constituency service incentives in CLPR systems.
[22] In the body of the paper we thus do not consider the possibility of voter abstention. As discussed in Appendices B and C, abstention can be modeled with the same techniques used to extend the model to contexts with more than 2 political parties.
[23] One could just as easily assume that the M regions are divided into some number M/20. Thus, under CLPR competition party cohesion should generally be high, but will tend to vary inversely with the mean and/or median district magnitude.
[27] Appendix B extends the model to situations in which more than 2 parties compete, some voters abstain, and/or some challengers find themselves placed at more favorable list positions than their party’s incumbents. Under most circumstances an equilibrium identical to that in Theorem 1 emerges; but under certain circumstances these extensions lead to a cycling situation in which two or more marginal candidates from competing parties engage in a never-ending effort allocation competition, thus upsetting the game’s Nash Equilibrium. That said, even in these situations Theorem 1’s basic implication, namely that competition in CLPR systems should be heavily party-centered, continues to be obtain: despite the unpredictability of these marginal candidates’ behavior, it is still straight-forward to prove that no candidate placed higher or lower on any party’s list than the marginal candidate ever devotes any effort to constituency service. In summary, in almost all cases CLPR elections yield a result qualitatively identical to that in Theorem 1; and under no circumstances does CLPR competition yield an outcome in which more than a small minority of candidates choose f > 0.
[28] Since all voters who reject their regional incumbent by definition choose the other party, the aggregate vote share for A is {¼·(6) + ¾·(4)} / 10 = 40%. B’s vote share is thus 60%.
[29] Theorem 2 in fact relies on the assumption that, if an incumbent and a challenger receive the same number of preference votes, ties are broken in the incumbent’s favor. This assumption is only expository, as the result obtains even if incumbent-challenger ties are broken probabilistically. However, the assumption eliminates the open-set problem which supervenes when strategic actors can make infinitesimal moves, and thus greatly facilitates the presentation.
[30] When the number of parties is N>2 and voters may abstain, Theorem 2’s basic collusive properties not only persist but may in fact be enhanced: in Appendix C’s particular example, not only members of the same party, but all members of the Legislature exert nearly identical levels of constituency effort, and in so doing secure their own re-election while simultaneously keeping other parties’ challengers at bay.
[31] Formally, campaign strategies which secure a party’s victory in the general election but cost the current leader his or her position as the organizational executive will always be strictly dominated by strategies which hurt the party’s electability but allow current leaders to maintain their intra-party ascendancy.
[32] These processes have often lead to the establishment of a highly ‘organized’ civil society in which citizens form continuous affiliations with particular economic interest groups or social ‘pillars’. Historical research on both Christian Democracy (Kalyvas 1996) and Scandinavian democracy (Huber and Stephens 2000) demonstrates the importance that organized groups played in providing party organizations fixed membership pools and guaranteed electoral support.
[33] Even where the civil society affiliations described in ftn 31 are weaker, a more ‘individualistic’ brand of party identification grounded in some combination of early socialization and past voting history often greatly reduces the number of ‘floating’ voters in long-standing democracies (Fiorina 1979).
[34] ENPP is calculated by: a.) summing each party’s squared percentage of legislative seats after a particular election, and b.) dividing 1 by this aggregate sum.
[35] Figure 3 does not include the elections of 1983 and 1987: in both of these elections the Turkish party system was artificially concentrated due to a post-coup law which prevented a large portion of the Turkish political elite from participating as candidates. This law was repealed by Referendum in 1989; 1991 thus represents the first genuinely democratic election after the 1980-1983 junta relinquished power. In the most recent 2007 election the JDP again won a commanding majority with just over 60% of the legislative seats, and formed a single-party government, though the ENPP increased slightly from 1.85 to just over 2.
[36] Although at first counter-intuitive, organizational centralization and party-hopping are in fact two sides of the same coin in Turkish politics: with no intra-party recourse, legislators have little choice but to switch organizations when they become disaffected with their current party leaders.
[37] Brazil, a presidential regime, has experienced a series of democratic breakdowns despite employing OLPR in its legislative elections.
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