Party Platforms with Endogenous Party Membership

Party Platforms with Endogenous Party Membership Panu Poutvaara 1 Harvard University, Department of Economics poutvaar@fas.harvard.edu Abstract In representative democracies, the development of party platforms depends on both ideological and electoral considerations. Decisions on party membership, on the other hand, are driven by the relative desirability of party platforms. This paper analyzes the dynamic interaction between party platforms and party membership. It shows how voter mobility, membership costs and the possibility of alienation affect party membership and the ideological characteristics of party platforms. Keywords: party platforms; party membership; median voter; alienation; indifference JEL Codes: D70; D72; D79 1. Introduction In democratically governed parties, party platforms reflect both the preferences of party members and electoral considerations. Electoral considerations were presented succinctly already by Downs (1957). Without uncertainty about voter preferences, party competition leads to the same outcome as a referendum. Office-motivated parties act as middlemen converging to the position of the median voter. The same result holds also with ideologicallymotivated parties without uncertainty about the outcome of election with given platforms. With uncertainty, rational parties choose platforms in order to maximize their expected utility, which is the sum of utilities associated with each possible electoral outcome weighted by the probability of that outcome. Coleman (1971) presents a model where parties care about ideology, and engage in competition in order to win the election and to be able to carry out their policy. In his model, candidates must win the party primary before being able to compete in general election. Each party member prefers the candidate who maximizes his or her expected utility in the general election. Party members must make a compromise between platform and probability of electoral success. In primary elections, expected utility can be maximized by choosing a candidate between median member of the party and median voter. Thus, parties end up running with different platforms but converging towards the position of the median voter. Parallel to this, Wittman (1983) and Calvert (1985) prove that if policy-motivated candidates are uncertain about the position of the median voter, policy convergence is not complete. The author is indebted for useful comments to the participants of Political Economy and Rational Choice lunch series at the Department of Government in Harvard University. 1

The influence of party members on party platforms is, however, only part of the story. Membership decisions also depend on platforms offered by different parties. Thus, party membership and party platforms warrant a joint analysis. Aldrich (1983a) examines the individual decisions on party membership. In his model, individuals evaluate parties based on their current platforms. Party platform is in his model same as mean ideal point of party activists. By joining a party, individuals affect party s mean ideal point and platform, and thus may affect membership decisions at the party margins. Abstention of party membership may be based on either indifference or alienation. The two parties are in equilibrium if nobody who is outside the parties wants to join a party, and none of the current activists wants to change his or her decision. Aldrich (1983b) generalizes into N-dimensional policy space. However, in these models parties do not act strategically in their choice of electoral platform. 2 Caplin and Nalebuff (1997) provide a thorough analysis, where an institution s policy depends on its membership, and an institution s membership depends on policies chosen by all institutions. They analyze also interaction between party platforms and party membership, and prove the existence of membership-based party equilibrium, where the party platform is determined by party members. Potential members take party platforms as given when deciding whether to join or not. In Caplin and Nalebuff s model, however, party members derive utility from party platforms instead of final outcomes. If party members care about final policy instead of party platform, party platform depends not only on member preferences, but also on platforms chosen by other parties. To my knowledge, endogenous membership decisions and strategic platform choices by democratically governed parties have not yet been combined in the literature. This is surprising, because it is the interaction between these two that determines the alternatives voters can choose from. The aim of this paper is to analyze dynamic interaction between party platforms and party membership. The first question is whether there is with strategic platform choices a stable equilibrium where membership and platform decisions are unchanged, and which conditions would characterize this equilibrium. The second question is what are the effects of the change in the proportion of mobile voters. The third question is whether initial positions of parties influence the long-run equilibrium. Furthermore, this paper analyzes the effects of membership costs and possibility of alienation by extreme members on party membership and platforms. The basic structure of the model is as follows. Before an election, median members of the two parties choose platforms in order to maximize their expected utility. There is uncertainty about the position of the median voter, and thus parties do not converge completely. After both parties have chosen their platforms, election takes place. Before the next election, individuals may change their membership decisions based on party platforms. After individuals have made their membership decisions, new median members of each party choose new party platforms before next election. My model is similar to Aldrich (1983a) in the sense that in both models, individuals reoptimize their membership decisions based on platforms offered by parties. The process of the choice of party platforms is, however, different. In Aldrich s model, parties choose mechanically the mean ideal point of their current members as their platform. In this paper, median members choose platforms strategically. This paper abstracts from interest groups inside or outside of parties, from voter 2 The same result holds if parties are unable to commit to the electoral program. 2

alienation, from interest conflict between party members and elected party leaders, as well as from imperfect information about candidate position. 3 This paper analyzes two alternative criteria potential political activists may use when deciding whether to join a party closer to their ideal point or stay outside parties. With utility difference requirement, potential political activist joins party if utility difference between platforms is sufficient to outweigh membership costs. Moderate potential political activists around the centre between two platforms stay outside parties. The zone of politically independent potential activists is increasing in membership costs and in the convergence between party platforms. With proximity criterion, potential political activist joins a party if the difference between party platform and individual s ideal point does not exceed alienation threshold. When parties converge, extreme activists become alienated and abandon parties. The structure of the paper is as follows. The second section models voter behavior, party membership decisions, and the choice of party platform. It concentrates in case where only utility difference requirement is present. The third section proves the existence of a stable equilibrium where no individual wants to change his or her decision concerning party membership, and none of the parties wants to change its platform. The third section presents numerical results about the convergence of parties to this equilibrium. The third section analyzes also the effects of the proportion of mobile voters and membership costs on the sizes of parties, and on party platforms. The fourth section analyzes a model where alienation by extreme members limits party membership. The fifth section concludes. 2. The Model 2.1 Policy Space and Voter Behavior Policy space is the continuum. Parties choose platforms and are able to commit to them. Commitment can be enforced by nominating candidates whose private ideal point coincides with the party platform, ensuring that if elected, candidates are independent of the party. 4 There is a continuum of voters, whose size is normalized to unity. Each voter has a well-defined optimal policy. It is critical that the exact position of median voter is not known in advance. A proportion of voters is divided in a known manner. For simplicity, it is assumed that they are divided uniformly on policy space. voters are mobile. They are distributed uniformly to a line of length to the right of unknown starting point,. Voters are rational and vote for the party whose platform is closer to their ideal point. Hirschman (1970) suggests that more radical party members may affect disproportionately the choice of party platform for example by organizing into pressure groups inside parties. Anderson and Glomm (1992) and Aldrich (1993) analyze voter turnout. Alesina and Cukierman (1990) present a model where voters have only incomplete information about politicians preferences. Caillaud and Tirole (1999) highlight potential conflict between party leadership and the rank-and-file when the electorate does not observe the quality of the platform before the election. e Alesina (1988) discusses also case where commitment is not possible. 3

Denote party whose platform is closer to by and party whose platform is closer to by. Denote platform of by and platform of by. Cutoff point of voters is o.u. 5 Everyone to the left of cut-off point votes and everyone to the right votes. There is no abstention. Party has o.u o.u secured voters. Provided that, party captures also 5 5 o.u o.u mobile voters. If, none of the mobile voters votes party. As 5 5 party needs 4 o.u mobile voters in order to win election, the highest with which 5 5 party wins is given by The probability that is lower than the highest with which wins is also the probability that party will win elections with platforms and. This probability is denoted by Technically, random variable is independent of its previous realizations. An interesting alternative would be following random walk. With that specification, majority party would have higher probability of winning. However, as distribution of mobile voters would be better known, the situation would converge towards equilibrium without mobile voters. 2.2 Party Membership There is a continuum of potential political activists. These have known ideal points which are distributed evenly into policy space. Potential political activists derive utility from implemented policy. For potential political activist with ideal point, utility of policy is given by: 5 The main motivation for party membership is not its expected effect on final policy outcome. With a large number of party members and voters, the effect of each individual would be negligible. Party membership would be no more rational than voting, if the only motivation would be utility difference between the alternatives multiplied by the probability of being pivotal member or voter. Instead, some individuals are for ideological motivations willing to join a party if they prefer its platform sufficiently to that of another party. Justification of party membership parallels closely Riker and Ordeshook s theory of the calculus of voting (1968). 5 A potential political activist joins a party whose platform is closer to his or her ideal point if utility from this party s platform is sufficiently higher than that of another party s platform to outweigh membership cost. Membership cost is net of any ben- D For a thorough discussion on calculus of participation, see Aldrich (1983a). Paralleling Riker-Ordeshook calculus of voting, he presents a model where potential members may become alienated if the opinition of typical activist is too different from their own ideal point. 4

efits from party membership, and is the same to all potential activists. Let be a potential political activist whose preference is closer to than to. It is assumed that joins if the utility difference from parties platforms is sufficient to outweigh membership cost : 5 5 Membership cost should be small enough to ensure that parties have members, and it is assumed that they do not exceed. 6 Intuitive justification for this restriction will be provided in Appendix. Let median member of party be o and that of party be u. Marginal member of party is by definition o, and marginal member of party is u. For marginal member of party : o 5 o 5 (1) For marginal member of party : u 5 u 5 (2) (1) allows us to solve median member of party explicitly with given party platforms: o 5 5 (3) Equivalently, (2) gives as median member of party : u 5 5 (4) (3) and (4) give membership decisions after platforms have been chosen. Membership decisions are based on actual party platforms and do not take into account the effect that potential activists would have on party platform. This is in line with Aldrich (1983a). Each potential activist acts as a platform taker. This is a natural assumption with a continuum of potential activists. If there were only a small number of potential party activists, these should take into account also their own effect on party platforms. If not all voters are mobile, potential political activists are a subset of voters who are not mobile. In extreme case where all voters are mobile, one can resort to the following interpretation. Potential political activists are not taken into account when calculating the probability of winning with a certain platform because they form only a negligible percentage of voters. 2.3 Party Platforms Party platforms are chosen by party members, and party members behave strategically. This is a major difference compared with Aldrich (1983a, 1983b) where party position is determined to be the mean ideal point of party members. More specifically, this paper assume that each party chooses its platform to maximize the expected utility of its median member after the next election. Party members do not take into account the effects that party S Anderson and Glomm (1992) present a model of voter turnout that has interesting similarities with the above model of party membership. They analyze both alienation and indifference by voters. In their model, voter participates in election if and only if his or her perceived utility difference exceeds uniform participation cost. 5

platforms have on membership decisions after election. In any case, these membership decisions would not have any effect before a platform is chosen next time. It is not plausible that even rational median members would in equilibrium sacrifice maximizing expected utility in current election in order to keep his decisive position in future elections. To see this, note that in stable equilibrium this sacrifice would be repeated infinitely. Even if one party would be able to block its platform in the absence of any reaction from another party, a change in another party s platform would affect membership decisions and change the identity of median member in both parties. The expected utility from platform to median member of party is of standard form: o 5 o 5 o 5 o 5 o 5 First-order condition simplifies into: 5 o 5 o It is obvious that o u. It would be irrational for median member of to choose a more extreme platform than his or her own ideal point, because this would result in both smaller utility in case of winning election and lower probability of winning election than o u. Furthermore, and never coincide. This can be seen in the following way. If, it would be in the interest of median members of both parties to choose at least a little more extreme platform, because this would increase utility in case of electoral victory of own party, and leave utility unchanged in case of electoral victory of another party. Solving, one obtains 7 : 4.+5Ãn,+5p oãu, 6+5Ãn, +4.+5Ãn,+5p o Ãu,, 5.6+5Ãn,++5Ãn,u 5 Ã5p o (5), 6+5Ãn, The expected utility from platform to the median member of party is given by: u 5 u 5 u 5 u 5 The first-order condition can be simplified into the form: 5 u u u 5. The other root can be ruled out. It would lead to a negative program in case & ' f. This can be proved by noting that o D fd and 6, $ f2d as none of the parties has a membership of more than half of potential political activists. 6

Now is given by 8 6Ã5n.+5Ãn,+5puÃo, 6+5Ãn, +6Ã5n.+5Ãn,+5p uão,, 5 Ã6+5Ãn,+9p uã7p unã+5ãn,o 5, 6+5Ãn, 3. Results 3.1 Stable Equilibrium? In this subsection, it is proved that there exists a symmetric equilibrium where parties do not change their platforms and potential political activists do not change their membership decisions. Numerical simulations are used to study the (in)dependence of final platform positions of initial positions. The strategy is the following. First assume that there exists a stable symmetric equilibrium. In this equilibrium, party has platform and party has platform. From (3) and (4), median members are now given by: and o u (6) (7) The Appendix contains the proof of the following proposition: Proposition 1 There exists a symmetric equilibrium where parties have an equal distance from the expected position of the median voter, neither party wants to change its platform, and none of the potential political activists wants to revise his or her membership decision. Using definition 5Ãn, the equilibrium can be written as 5 5 5 5 5 (8) Note that by definition, and. To gain further insight into the equilibrium, it is useful to consider a case without membership costs. Median member of party has in that case ideal point and median member of party. Election platform chosen by median member of party is H Another root can again be excluded. If & 'f, another root would lead to a violation of condition o $ 6 o. 7

Without mobile voters, and simplifies into. With all voters being mobile, and party s platform simplifies into, which is exactly between the expected position of median voter and the ideal point of party s median member. The analysis of convergence has to be carried out numerically. Numerical analysis uses the following simplification. In each period, only one party updates its platform. The platform of the other party is unchanged. Membership decisions concerning both parties are updated after each platform update. Numerical analysis starts from a situation where initial membership in one party is taken as given, and so is the platform of another party. Numerical simulations suggest that equilibrium is stable, and that convergence to it may be very rapid. 9 3.2 Voter Mobility, Membership Costs, Party Membership, and Party Platforms This subsection provides an analysis of the effects of voter mobility and membership cost. It proves that the higher the proportion of mobile voters, the less parties converge. The intuition for this is that the more there are mobile voters, the less a move away from the platform of another party decreases probability of winning. With given membership decisions, median members choose more extreme platforms. In the presence of mobile voters, party platforms converge the more the lower the membership costs of party affiliation are. Intuitively, broader parties result in median members being closer to median voter, and thus to less extreme platforms. These results can be summarized as Proposition 2 The higher the proportion of mobile voters, the less parties converge. The higher the membership cost, the less parties converge. Not surprisingly, (6) and (7) reveal that higher membership costs lead to smaller and more extreme parties. There is an indirect partially counteracting effect through a change of. The effect of voter mobility on party membership can be found from proposition 2, and the effect of smaller in (6) and (7). Proposition 2 told us that an increase in the proportion of mobile voters leads to less convergence in party platforms. This means that increase in the proportion of mobile voters leads to a decrease in. Thus: Proposition 3 An increase in the proportion of mobile voters leads to wider party membership and less extreme parties at the same time as party platforms become more extreme. The intuition behind proposition 3 is that the more party platforms converge, the smaller the utility difference from the platforms offered by different parties. As the disutility of a policy increases more than proportionally in the distance between potential party activist s b In numerical calculations, party u was assumed to move first. In the initial situation, party u s median member and party - s platform were taken as given. Convergence was analyzed with each combination of the following sets of variables: u Mtf2cf, o MtfScf., & MtfcfcfcfDc f.c fb, S Mtfcfcf2cf. Each initial situation resulted in convergence. Some initial situations with positive S resulted in party median members being outside policy space. This can be seen as a further justification for assuming S to be very small. Naturally, a model where party members are outside of policy space is not well specified. 8

ideal point and policy, extreme members are ready to stay in the party even when more moderate members feel that utility difference between the platforms offered by two parties is not large enough to exceed membership costs. 4. Model with Alienation This section analyzes the effects of alienation in the extremes of the policy space. An additional requirement for potential political activist to join a party is that the distance between potential political activist s ideal point and party platform does not exceed. In order to be binding, has to be smaller than the distance of party platform from extreme of the policy space in equilibrium without alienation, that is,. For marginal centrist member of of party : of 5 of 5 (9) For marginal centrist member uf of party : uf 5 uf 5 (10) If there is alienation, marginal extremist members are given by: oh (11) uh (12) To find symmetric equilibrium, substitute again,. Marginal members in the direction of the center are given by and of uf (13) (14) If there is alienation, marginal extremist members are given by oh (15) uh (16) Median members are thus given by and o u (17) (18) 9

Assume first that, and the only motivation to stay outside parties is alienation. In Appendix, it is proved that Proposition 4 An increase in the proportion of mobile voters leads to wider party membership with more extreme median member at the same time as party platforms become more extreme. Comparing propositions 3 and 4 reveals how party membership depends on whether potential political activists stay outside of parties due to indifference or due to alienation. With utility difference requirement to join a party, platforms affect more strongly membership decisions of moderate potential political activists. More extreme platforms politicize the moderates as utility differences associated with alternative platforms increase. With alienation motivation to stay outside of parties, moderate potential political activists belong to parties independently of platforms. More extreme potential political activists join parties as platforms diverge. The Appendix contains also proof that an increase in, the distance between party platform and own ideal point that potential political activists are willing to accept before terminating their membership, leads to more extreme median members and to more extreme platforms. Integrating membership cost and possibility of alienation by extreme members requires a numerical analysis. Appendix contains a proof that can be solved from 5 5 5 5 5 5 5 5 5 5 6 Let,. By (8) and (6), equilibrium without alienation is, o. Next calculate and o with different alienation thresholds. With (,, o With and, equilibrium without alienation is, o. With,, o. An increase in alienation by party extremists leads in these examples to more moderate platforms and more moderate median members. 10 5. Conclusion This paper proposed one way to integrate strategic party platform choice by ideologicallymotivated parties and endogenous party membership. The median member of each party chose party platform in order to maximize the expected utility from realized policy. In choosing party platforms, median members had to balance two conflicting motivations. The utility in case of electoral victory is higher, the closer platform is to the own ideal point. When the two parties are on different sides of the expected position of the median voter, this centrifugal motivation encourages choosing more extreme platforms. The second motivation, however, pulls to the opposite direction. By converging the platform towards f Next assume S 'f, 5 '. Without alienation,, 'fds, 6, 'fs. Next assume that @ 'f Ef2. This leads into, ' fs. E, ' f.2e, 6, ' fbfe. E6, ' f2h. Again, alienation by extreme members leads to more moderate platforms and party membership. 10

the expected position of the median voter, a party can increase its probability of electoral victory. This centripetal motivation encourages convergence between parties. Not surprisingly, centrifugal motivation is increasing and centripetal motivation decreasing in the proportion of mobile voters. 11 As the proportion of voters with unknown ideal points approaches zero, platforms converge towards the expected position of median voter as Downsian model predicts. It is always rational for both parties to choose the platform between their ideal point and the other party s platform. The model suits best to analyze policies which can be changed costlessly or with only a low cost. 12 After parties have chosen their platforms, party members and potential political activists outside parties reoptimize their membership decisions. The first model assumed that any potential activist joins the party whose platform is closer to his or her ideal point, if utility difference between party platforms exceeds cost of joining a party. The cost can be interpreted as a psychological cost. With reasonably low membership costs and at least some uncertainty about the position of median voter, there exists a stable equilibrium where parties do not change their platforms, and potential political activists do not change their membership decisions. The second model assumed that any potential political activist joins preferred party if the distance between that party s platform and individual s ideal point does not exceed alienation threshold. Whether potential political activists condition joining the preferred party on a minimum utility difference from alternative platforms or on the proximity of party platform to the own ideal point, an increase in the proportion of voters whose ideal points are known leads to more complete convergence between party platforms. Two alternative membership criteria lead to empirically testable predictions. Both criteria predict smaller party membership as parties converge due to a decrease in the proportion of mobile voters, but they give opposite predictions of whether parties become more or less extreme in their membership. Without alienation, increased convergence in party platforms leads to smaller parties with more extreme members, as increasing number of more moderate potential members perceive utility difference between the party platforms to be insufficient to motivate party membership. With alienation, increased convergence leads to smaller and more moderate parties as more extreme members become alienated. One reason for alienation might be that party members derive utility not only from final policy outcomes but also from participation in political process with the like-minded. Furthermore, an increase in the propensity to withdraw from parties due to alienation implies that party members should become in average more moderate at the same time as party platforms become more moderate. Assuming that the proportion of mobile voters does not change, an increase in the membership costs in a model without alienation leads to more extreme and smaller party membership with more extreme platforms. Models that include both alienation and utility difference requirement can be solved only numerically. Numer- The proportion of mobile voters has similar effect as the presence of uninformed voters in Baron (1994). In his model, office-motivated candidates raise campaign contributions by choosing more extreme policies that benefit special interest groups. Contributions are used to influence uninformed voters. As the proportion of uninformed voters increases, the equilibrium policies diverge away from the median informed voter. 2 Glazer et al. (1998) analyze a model where parties cannot commit to certain policy in advance, and change in policy is costly. They show that incumbent government may adopt more extreme policies than it actually prefers for electoral purposes. 11

ical calculations suggest that comparative statics predictions of pure cases with only one criterion carry on to the models that include both criteria. The numerical calculations suggest that if potential political activists and immobile voters are uniformly distributed, political parties converge to symmetrical positions independently of their initial position. Of course, with asymmetric distribution also final party positions may be asymmetric. Numerical calculations suggest that convergence is rapid independently of initial positions, and thus the model predicts that in the long-run, both major parties should have roughly equal probability of winning elections. Models with exogenous party membership are suitable in political systems with clear permanent divisions following socioeconomic, language, or ethnical boundaries. In the United States and in most European countries, exogenous party membership may be a very limiting assumption. In the long run, changes in party membership are a major mechanism in the determination of party platforms. Appendix Proofofproposition1. Party platform from (5) can now be written o (A1) o 5 5 o Next introduce two auxiliary variables. Let and is a monotonic transformation of the proportion of mobile voters. if all voters are mobile, and as the proportion of mobile voters approaches zero. Median member of party is now o Left-hand side of (A1) can now be written: (A2) The term under the square root of (A1) can be written: 5 5 (A3) Next present (A1) by equalizing the square of (A2) to (A3). Simplification results in the form: 5 5 5 5 5 5 Next substitute back f and multiply by : +4Ã5{, 5 5 5 5 5 12

The solution for is 4 5 5 5 5 5 5 5 5 5 It can be proved that only 5 is plausible solution. Denote 5 5 5 5 Now 5 5 5 This is positive, and so the term under the square root is increasing in. Thus, the lower bound for the first root is obtained by letting the term under the square root have its lowest possible value. With, the term under the square root simplifies into 5.The first root simplifies into 4 4 5}. This leads to contradiction as platform of party 5 57}Ã; 4 would be to the right of the platform of party 4. The second root gives the symmetric equilibrium. Proofofproposition2. The derivative of (8) with respect to is 5 5 Next multiply the right-hand side by positive term 5.Thisyields 5 Evaluate this upwards by adding positive term. Next simplify and substitute the definition of to obtain: 5 This is negative with all if. Thus an increase in, that is, an increase in the proportion of mobile voters, moves parties to more extreme positions. Cases where can be ruled out as implausible. Note that with, platforms as far apart as and would result in only the most extreme potential political activists and joining parties and, respectively. Next differentiate (8) with respect to : 5 5 (A4) It can be proved analytically that this holds if all voters are mobile, and numerically, that this holds also in the presence of immobile voters. With complete voter mobility, and (A4) simplifies into 13

5 This is negative with all. The denominator of the second term is always less than and the nominator at least. Numerical analysis to prove the negativity of (A4) was obtained in the following way. was allowed to vary with interval from to and with interval from to. (A4) was negative with all combinations. Some of the combinations with high would violate the condition that median party members are in policy space. Equilibrium with Alienation and Proof of Proposition 4 The left-hand side of (A1) can now be written: (A5) The term under the square root of (A1) can be written 5 5 (A6) (A1) can now be presented by equalizing the square of (A5) to (A6). Next substitute back and multiply by. After simplifying, one arrives in the form: f +4Ã5{, 5 5 5 5 5 5 5 5 5 5 6 This third-order equation requires numerical analysis. Next analyze the case where alienation is the only motivation for staying outside both parties, that is,. With (17), (A1) yields 5 5 There are two roots: 4 5 5 5 5 5 5 5 5 5 The first root can be excluded, as it would lead to. The second root can now be written s 4 ;} d 6 T 5 7 ;} (A7) 5 5 5 5 To find the effect of a binding alienation threshold when alienation is the only reason to stay outside parties, differentiate (A7) with respect to : g{ gd is of the same sign as. The claim was that this is negative. This is equivalent to 14

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