The Review of Economic Studies Ltd.
Electoral Competition and Special Interest Politics Author(s): Gene M. Grossman and Elhanan Helpman Source: The Review of Economic Studies, Vol. 63, No. 2 (Apr., 1996), pp. 265286 Published by: The Review of Economic Studies Ltd. Stable URL: http://www.jstor.org/stable/2297852 Accessed: 05/10/2009 10:50 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=resl. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact
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Reviewof EconomicStudies(1996) 63, 265286 ?) 1996The Reviewof EconomicStudiesLimited
Electoral Special
00346527/96/00120265$02.00
Competition and Interest
Politics
GENE M. GROSSMAN Princeton University
and ELHANAN HELPMAN Tel Aviv University and CIAR First versionreceivedNovember1994;final versionacceptedNovember1995(Eds.) We studythe competitionbetweentwo politicalpartiesfor seatsin a legislature.The parties have fixed positionson some issues, but vary their positionson othersin orderto attractvotes and campaigncontributions.In this context,we examinewhetherspecialinterestgroupsare governedby an electoralmotiveor an influencein theircampaigngiving,and how theircontributions affect the equilibriumplatforms.We show that each party is inducedto behave as if it were maximizinga weightedsum of the aggregatewelfaresof informedvotersand membersof special interestgroups.The partythat is expectedto win a majorityof seats catersmore to the special interests.
1. INTRODUCTION Specialinterestgroupsappearto wield considerableinfluenceover public policy in many representativedemocracies.The trade policies of many industrializedcountries favour vested interestsin the clothing, textile, and heavy industries.Their agriculturalpolicies give various forms of income supportto farmers.Health and safety measuresshow the imprimaturof the local insuranceindustryon the one hand,and of powerfullabourunions on the other. And manufacturershave had much to say about a myriadof environmental and regulatorypolicies. It seems difficultto argue that the political process serves only the interestsof the medianvoter. Interestgroups pursue their quest for political advantageby a numberof different means. They gather informationthat supportstheir positions and make it availableto powerfulpoliticians.They take their argumentsto the public in an effort to win voter sympathy.Sometimesthey undertakedisruptiveactivities,which are intendedto coerce ratherthan persuade.And, of course,they contributeto politicalpartiesand to individual candidates'campaigns. This paperfocuses on interestgroups'use of campaigncontributionsas a vehiclefor influencingpublic policy. Contributionsmay take the form of cash transfersor gifts in kind. In any event, we assume that the contributionscan be used by the candidatesto persuadeand cajole a group of undecidedvoters. Our aim is to characterizethe policies thatemergewhenrivalgroupsvie for the politicians'favourwhilethe politiciansthemselves compete for voter support. The literatureon campaigngiving identifiestwo motives that interestgroups might have when they contribute to politicians or to political parties. Contributorswith an electoral motive intend to promotethe electoralprospectsof preferredcandidates.Those 265
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with an influencemotive aim to influencethe politicians'policy pronouncements.Our model allows interestgroups to entertaineither or both of these reasonsfor giving, but our analysis of the equilibriumemphasizesthe second. We believe that special interests do often try to use their campaigngifts to influencepoliticians'positions and we find support for this view in the empiricalevidence presentedby Kau and Rubin (1982), Fremdreisand Waterman(1985), Tosini and Tower (1987), and others. Our setting is one in which two political parties compete for seats in a legislative body. To attract votes, the parties announce policy platformsand engage in political advertisingand other costly forms of compaigning.The platformsmay includecommitments on two types of policy issues. The firstare issues about which the partyhas strong preferencesor predeterminedpositions. The preferencesmay reflectthe party'sideology, or the positionsmay be inheritedfrom the past if, for example,the partyfeels it must keep earlierpromisesin orderto preserveits reputation.In any event,we take thiscomponentof a party's programmeas fixed. We focus instead on the determinationof what we shall termpliablepolicies.Theseare policiesabout whichthe partieshaveno explicitpreferences and so are willing to tailor theirpositions to furthertheirelectionprospects.' Our interestgroupsare collectionsof individualswho sharea commoninterestin the pliable policies. These organizedgroups can offer contributionsto one or both of the political parties.Their gifts may be grantedunconditionallyor they may be tied to the positions adopted by the recipients.Unconditionalgifts are used to satisfy an electoral motive for giving, while contingentgifts are designedto influencedecisions.We assume that the groupsare able to communicatethe sense of theirconditionaloffers,even if they cannot spell out the details in a legallybindingcontract. If the interestgroupschoose to offercontingentcontributions,they will confrontthe partieswith a fundamentaltradeoff.By settinga platformthat servesthe generalinterest, a party can attract votes from the portion of the electoratethat is wellinformedabout the issues. But by choosing policies that cater to the specialinterestsit may be able to elicit greatercontributionsthat then can be used to influencethe voting of lessinformed or impressionablevoters. We assume that the partiesresolve this tradeoffwith the aim of maximizingtheir representationin the legislature.An equilibriumconsistsof a pair of platformsand a set of contributionschedules,such that no group or partycan betterits lot given the anticipatedactions of the others.The equilibriumplatformsand associated contributionstogetherdeterminethe electionoutcome,whichin turndeterminesthe likelihood that each party'splatformwill be enacted. The remainderof the paper is organizedas follows. In the next section, we discuss the relationshipof our paper to severalothers in the literature.Section 3 describesthe detailsof the model. In Section4, we examinea specialcase in whichthereis only a single, organizedinterestgroup while Section 5 treats the generalcase with competitionamong groups. The last section containsa summaryof our findings. 2. RELATED LITERATURE Thereis, of course,a vast literatureon policy determinationin representativedemocracies. Our goal in this section is to explain the relationshipof our paper to some others that have a similarfocus. We make no claims to comprehensivecoverage. 1. Admittedly,the distinctionbetweenthe pliablepoliciesand othersis not alwaysclearcut. In the longrun,all of a party'spositionsare presumablysubjectto change.But candidatesand partiesare willingto change theirpositionson some issuesmore freelythan others.The set of pliablepolicy issuesmightincludeallocation of "porkbarrel"spending,attitudeson gun control and some environmentalquestions,and positions on a varietyof economicpolicies.
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Our paper has antecedentsin the literatureon probabilisticvoting.2 Enelow and Hinich(1982), for example,developeda "spatial"modelin whichvoters'utilitiescomprise two additivelyseparablecomponents.One component relates to the policy issue under considerationwhile the other reflectsexogenous characteristicsof the candidates.The politiciansare assumedunable to observeindividualtastes with regardto the exogenous characteristics.In consequence,they remainuncertainabout how any individualwill vote, even if they know how he or she will be affectedby the policy in question.3 Lindbeckand Weibull (1987) and Dixit and Londregan(1994) adopted a similar probabilisticvotingapproachto study policies that redistributeincometo narrowgroups of voters.They assumedthat the variousgroupsdifferin theirpredispositionto the parties and identifiedcharacteristicsof a group that make it a good candidateto receivepolitical largesse.Although these authors focused on the determinantsof the political successof specialinterests,thereis an importantdifferencebetweentheirworkand ours. Specifically, they did not allow interestgroupsto competeactivelyfor favourswhereaswe are primarily interestedin how compaigncontributionscan be used as a tool for such competition. We treat campaigncontributionshere in much the same way as in Grossmanand Helpman(1994). Therewe built on Bernheimand Whinston(1986), who describedinfluenceseekingas an exampleof a "menuauction"game. In a menuauction,each of several principals who will be affectedby an action offers a bid to an agent who will take that action. These bids take the form of schedulesthat associatea paymentto the agent with each feasibleoption. Once the agent chooses an action, all of the principalspay the bids stipulatedby their schedules.Bernheimand Whinstondefinedan equilibriumin a menu auction as a set of contributionschedulessuch that each one is a best responseto all of the others, and an action by the agent that maximizesher utility given the schedulesthat confront her. We focused Our 1994paperprovidedan applicationof this view of influenceseeking. on the determinationof importand export taxes and subsidiesin a small,open economy. We took the governmentto be a common agent for a group of special interestgroups, each representingthe owners of some industryspecificfactor. The policy makers,who were alreadyin power, were assumedto set tradepolicy to maximizea weightedsum of total campaign contributionsand aggregate (or average) welfare. In this model, the incumbentgovernmentdid not face any explicit competitionfrom rival candidatesnor did we provideany rigorousjustificationfor its assumedobjective. AustenSmith(1987) and Baron(1994) addressedvery similarissues to the ones that interestus here. Both of these authorsstudiedpolicy determinationin a twopartymodel of electoralcompetition.And both wereinterestedin the effectsof campaigncontributions by specialinterestgroups.AustenSmithassumedthat the partiesuse campaignfunds to alleviate (riskaverse)voters' uncertaintyabout candidates'policy positions. Baron, like us, allowedcampaignspendingto have a directeffecton the voting behaviourof a group of uninformedvoters. A more importantdistinctionbetweentheirpapersand ours concernsthe motivethat groupsare assumedto have for givingto the parties.In both AustenSmith and Baron the lobbies take platformsas given and offer gifts to their favourites with an eye towardaffectingthe probabilitiesof election.45 Here,we do not restrictinterest 2. Weconsiderthis labelto be somethingof a misnomer.In ourmodel,andin manyothersin the literature, It is only that the politiciansdo not know individuals'preferenceson every individualvotes deterministically. some issues,whichcauses them to be uncertainabout how a particularballot will be cast. 3. See also Coughlin(1984, 1986)and Wittman(1983), and Mueller(1989,ch. 11) for a survey. 4. Mageeet al. (1989)makea similarassumptionin the contextof theirmodelsof tradepolicyformation. 5. This is Baron'sassumptionin the last part of his paper,wherehe allowsfor severalcompetinginterest groups and considersthe determinationof "collective"policies. In the first part of his paper, dealing with
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groups to such an electoralmotive, but also affordthem an opportunityto influencethe parties'platforms. 3. THE MODEL We examine a jurisdictionwith two political parties, an exogenous number of special interestgroups, and a fixed continuumof voters. Our descriptionbeginswith the voters. 3.1. The voters
Like Baron (1994), we distinguishthe behaviourof two classes of voters, the informed and the uninformed.Informedvoters are those who know and understandthe parties' positions on both the pliablepolicies and other issues.The welfareof these voters will be affected by the policies that are ultimatelyenacted and perhapsby other (exogenous) attributesof the candidatesand the parties.For example,the voters'welfaremay depend on personalcharacteristicsof the candidates,such as their competenceor charisma,or votersmay derivesome pleasurefrom supportingthe partyto which they have developed an historicalattachment.Informedvoters cast their ballots for whicheverparty offers higher utility, consideringboth their pliable positions and their exogenous programmes and characteristics.In the model developed here, this is a dominant strategyfor these voters. The uninformedvoters, by contrast, do not know or are unable to evaluate the parties'positions on (at least) the pliable issues. These voters may have initial leanings towardone party or the other, but at least some of them can be swayedby the messages they receivein the courseof the campaign.Let a denote the fractionof these uninformed (perhaps"impressionable"is a betterword) voters in the total voting population. Considerthen a typicalinformedvoter with the label i. This individualderivesutility ui(PA) from the vectorpA of pliablepoliciesendorsedby partyA, and utility Ui(pB) from the vectorpB of suchpoliciesendorsedby partyB, with u'( ) continuousand differentiable. She votes for the candidatesfrom party A if and only if ui(pA)  ui(pB)>,', where ,B' measuresher assessmentof the superiority(or inferiority,if negative)of party B's fixed policy positions and other exogenous characteristicsrelative to those of party A. We assume that the parties cannot observe the ex ante proclivitiesof any particularvoter, althoughthey presumethese to be drawnfrom a known distributionF(fB). Moreover,we assumethat the distributionof preferenceson the fixedprogrammesand othercharacteristics of the partiesand candidatesis statisticallyindependentof the effectsof the pliable policies on individuals' utilities. Then both parties will perceive a probability  Ui(pB)] F[Ui(pA) that individuali will vote for the slate of candidatesfrompartyA. With a continuum of informed voters, the law of large numbersimplies that the share of informedballots cast for party A equals ( /n,) fiEI F[Ui(pA)  Ui(pB)]di, whereI denotes the set of informedvoters and n, the total number(or measure)of such individuals. An uninformedvoter, too, may have a predispositiontowardone partyor the other. However,this leaningcan be overcomewith enough campaignrhetoric.In particular,if party A spends more on its campaign than party B, some of those who were initially "particularistic" policies,the contributionsare simplyan exogenousfractionof the net benefitscapturedby the interestgroup.AlthoughBaronrefersto this as a bargainingsolution,he does not specifyany explicitbargaining processand his "solution"fails to accountfor the surplusto the politicalpartyrelativeto the fallbackoption. An advantagethat we see of our model comparedto Baron'sbeyond the one we stressin the textis that it is capableof handlingboth particularisticpolicies (with a singleinterestgroup) and collectivepolicies (with multipleinterestgroups)withinthe same analyticalframework.
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inclinedtowardparty B will vote insteadfor partyA. We denote by H( ) the fractionof the uninformedvoters that votes for partyA, and assumethat it dependson the difference in the parties'total campaignbudgets.6 We assumethat seats in the parliamentare allocatedby proportionalrepresentation. Then the fractionof the legislaturecontrolledby partyA matchesthe fractionof the total votes garneredby this party. Lettings denote this fraction,we have
aJ n,r
F[u(PA)
ui(pB)]di+ aH(CA
CB),
()
iel
where CK is the total campaignspendingundertakenby party K, K=A, B. 3.2. The parties and the government
Each party seeks to maximizeits representationin the legislature(or any monotonically increasingfunctionthereof). The partiesmay see this as theirobjectivefor any of several reasons.For example,politicalpartiesoften rewardtheircore memberswithjobs in and aroundthe government.A party may seek to maximizeits patronageand may recognize a monotonicrelationshipbetweenthe numberof politicaljobs it controlsand the number of its seats in the legislature.Alternatively,a partymay wish to implementits ideological agenda, and may see a positive relationshipbetweenthe prospectsof successfullydoing so and the size of its legislativecontingent.Of course,with two partiesand proportional representation,the objective of maximizingseats is equivalent to that of maximizing (expected)pluralityin the election.This is a commonlyassumedobjectivein the literature on electoralcompetition.7 With this objective,partiesA and B choose theirplatformsof pliablepoliciesin order to maximizes and 1 s, respectively.Theydo so recognizingthat theirpolicyendorsements will affect their popularityamong the informedvoters. At the same time, the platforms are chosen with an eye towardthe organizedinterestgroups,who may vary theirsupport accordingto the positions that are taken. The partiesknow that any contributionsthey collect can be used to financecampaignactivities. After the electionis over, the legislatureconvenesto set policy. We do not model the policysettingprocessin any detail. Rather,we assumethat each partyattemptsto implement its announcedplatformand that a party'sprobabilityof successincreasesmonotonically with the size of its legislativedelegation.In other words, the legislatureadopts the vector of pliable policies pA with probabilityq(s), and the vector pB with probability 1(s),
where () =  and q'(s) > 0. The function q(s) may, for example, increase sharply
just aboves = 1/2, if havinga slightmajorityof the seatsin the parliamentgreatlyenhances a party'sprospectsfor successfullyimplementingits programme. 6. It is perhapsmore commonin the literatureto assumethat the ratio of campaignexpendituresaffects the allocationof votes. See, for example,Baron (1989, 1994), and Snyder(1989). In our view, a specification in termsof absolutedifferencesis morereasonable,becausea largerbudgetallowsa campaignto reacha wider segmentof the population.This view could be formalizedin a model of advertisingsimilarto the one in Grossmanand Shapiro(1984),wherethe fractionof the targetpopulationthat hearsa givenmessageis assumed to vary with the amountthat is spent on the advertisingcampaign.If each messagethat an uninformedvoter hearsmakeshim more likely to vote for the party issuingthe announcement,then the numberof uninformed voterswho cast theirballotsfor partyA will dependon the differencein the sizes of the two budgets. 7. See, for example,Enelowand Hinich(1982),Denzauand Kats (1977)andCoughlinand Nitzan(1981). The differentcampaignobjectivesthat candidatesmight hold are discussedand comparedin Aranson,Hinich and Ordeshook(1974).
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While we believe that it is reasonableto suppose that partiesaim to maximizetheir representationin the legislatureand also that parties in the majoritysometimesfail to implementtheirprogrammes,the Appendixtreatsa more "pure"case. Therewe examine policy determinationwhen the legislatureoperatesaccordingto strict majorityrule and when parties seek to maximizetheir probabilityof winninga majority.To conduct this alternativeanalysis,we must assumethat the numberof voters is largebut finite and that membersof specialinterestgroupsconstitutea negligibleshareof the voting population. With these assumptionsand a furtherone of equalpartypopularity(i.e. the partieswould each capture50%of the vote if they happenedto adopt identicalpositionson the pliable policies and to spend identicalamountson theircampaigns),the equilibriumpolicies are the same as the ones derivedin the main text.8 3.3. The special interests
Special interest groups are collections of voters who share a common interest in the pliable policies. The membersof an interestgroup may differin their views on the fixed programmesand other characteristicsof the candidates,and, in the privacyof the polling booth, they behavejust like any other voters. Nonetheless,these individualsmay have an incentiveto cooperate with one another, if by doing so they can influencethe parties' policy platforms. As Olson (1965) has discussed,the merefact that individualssharea commoninterest in some policy or policies is not enough to ensure that they will engage in collective political action. The temptationalwaysexists for each to free ride on the costly political effortsof the others. But some interestgroupsdo overcomethese freeriderproblemsand manageto coordinatetheir lobbyingactivities.We take the numberand identitiesof the organizedspecialinterestsas given (whilerecognizingthat it would be interestingto know how the policy environmentserves to galvanizecertain interestsand not others), and examinehow these groupsinfluencethe policysettingprocess. Interestgroupsmay have two motivationsfor makingcampaigncontributionsin our model. First, they may hope to influencethe outcome of the election. An interestgroup may gain if it can enhancethe prospectsof the partywhosepositionson the pliablepolicies are more similarto its own. Second,the interestgroupsmay hope to influencethe parties' platforms;that is, to push the candidatesto supportpoliciesthat betterservethe group's interests.Some of the membersof an interestgroup may object to spendingon the first of these objectives,if theirideologicalattitudesdifferfrom those of the partythat is being supported.But all membersof a group will agree on the desirabilityof pushingthe two partiestoward the group'scollectivedesideratumon the pliablepolicy issues. Moreover, as we shall see, the second motive remainsoperativeeven when the individualinterest groups are relativelysmall, so that each has little ability to affectthe election outcome. We denote by Wj(p) the aggregateutility that membersof interestgroupj derive from the vector of pliable policiesp. It is possible that the membersof interestgroupj care directlyabout only one elementof p, say pj, and that the other elementsof p affect these individualsonly indirectly(e.g. as taxpayerswho must pay for the benefitsprovided to other groups),just as they do the generalpublic.Alternatively,the interestgroupmay have a directinterestin severalcomponentsof p, and severaldifferentinterestgroupmay 8. Lindbeckand Weibull (1987) come to a similarconclusionin their study of electoralcompetition withoutinterestgroupsor campaignspending.Ouranalysisof thecasein whichpartiesmaximizetheirprobability of winningis modelledaftertheirs.
GROSSMAN & HELPMAN
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have a stake in the same policy component. If the membersof a group share identical preferencesconcerningthe issues wherepoliticiansare willing to be flexible,then Wj(p) is simply the numberof membersof interestgroupj times the utility componentof the representativeone. In any event, we assume that the members of an interest group cooperate fully in their collective action, and so seek to maximizetheir expectedjoint welfarefrom the pliablepoliciesnet of campaigncontributions.LettingCjK representthe contributionof interestgroupj to party K, we write the objectivefunctionfor this group as (2)
V1= (0(s)W(pA) + [1 ((s)] Wj(pB)BCfC_BC
If an interestgroup hopes to influencea party'spolicy endorsement,it must make sure that the partysees a connectionbetweenits platformand the size of the contribution that will be forthcoming.The group need not announcean explicitquidpro quo; indeed, the publicmightfrownupon politicianswho openlypeddletheirpoliticalinfluence.Rather, the interestgroupneeds only convey an understandingthat its contributionwill vary with the positions that is taken. We would argue that politiciansunderstandthis connection quite well; in the U.S., proponentsof gun control do not, for example,expect to receive donationsfrom the National Rifle Association. We allow the interestgroups considerablefreedom in designingtheir contribution schedules,cf(pK). We assumeonly that the schedulesare continuous,differentiablewhen positive, and everywherenonnegative.The latter means that interestgroups can offer resourcesto the partiesor withhold them, but cannot levy taxes on politicians.A group can, of course, choose to make its contributionindependentof policy; in this way it can bolster the chances of its favourite party without causing it to lose any (additional) informedvotes. A group also might choose to offer its support to only one of the two politicalparties. 3.4. Political equilibrium
We seek a subgameperfectNash equilibriumof a twostage, noncooperative,political game. In the first stage, the various interestgroups independentlyand simultaneously announcetheircontributionschedules,one to each of the two parties.In the secondstage, the parties choose their policy platforms.After the platformsare set, the contributions are paid and the campaignsare waged. Then the election takes place and finally the legislaturemeets to implementone of the party'splatforms.We assumethat all expectations about subsequentevents are accurateand that all promisesare honoured.9 More formally,we propose the following definition: Definition1. An equilibriumconsists of a pair of feasiblepolicy vectors (pA,, pBo) and a set of contributionschedules{q40(pA)q j7fO(pB)} one for each lobbyj, such that (a)
pAo
maximizess givenpBo { C1O( p)} and {j7f?O(pB)}; { CAoPA) ( )} and CBo (pPB) maximizes 1s given ~~~~Ao,
Ro
.
(b) pBo (c) each CjK(.) is continuous and differentiable when positive, with ,
CjK(pK) >
for
all pK; and
9. In our oneshotgame,the interestgroupshave an incentiveto renegeon theircontributionoffersonce the platformsare announced.Similarly,the politicianshave no incentiveto pursuetheir announcedpositions on the pliablepoliciesonce the campaigncontributionshave been paid up. The keepingof promisescould be motivatedin a repeatedgame,whereagentswould be punishedfor failureto live up to theircommitments.
272
REVIEW OF ECONOMIC STUDIES (d) for each lobbyj, there do not exist feasiblecontributionschedulesCj(pA)
and
CB(pB), such that ({s) Wj(pA)
+ [I _(&)]
> p(S) Wj(pAo)
Wj(pB)
+ [1 _ qs)]
_
C/A(,A)
_
cB(pB)
Wj(pBo) _ CAo(pAo)

cBo(pBo)
wherepA maximizesand pB minimizes
1na{
F[ui(PA)
_
Ui(PB)]di+
aH[
A Ck C'o((pA)

+
Z
co
(p B) 
C(kBA
and 1a
s= 1 a IA(' F [u'(ji)  ui(P p)Idi + a H[Zk~ fjCAo(pA)
Cj o(flB)
+ CA (pA)E
CB(fpB)]
Here, conditions (a) and (b) express the Nash equilibriumamong parties in the policy announcementphase, while condition (d) ensuresthat no lobby can beneficiallydeviate duringthe initial stage of the game. Implicitin DefinitionI is the assumptionthat each partycan observethe contribution schedulesofferedto the other. This assumptioncan be justifiedwith the observationthat the "schedules"here are intended as metaphors,rather than as literal descriptionsof explicit contracts. In practice,offers of political support are conveyed as much by the public posture of a lobby as by any privatecommunicationsit may have with the politicians. Accordingly,the quidpro quo for campaignsupport may come to be common knowledgeamong the parties.'0
3.5. Functionalforms
To simplifythe analysis,we adoptparticularfunctionalformsfor the distributionfunction, F( ), and for the effectivenessofcampaignspending function, H( ). We assume that informedvoters' relativepreferencesfor the immutablecharacteristicsand programmeof party B are distributeduniformlyin the range (
'b I 2f f '2f b
'
10. If, instead,we were to allow the contributionschedulesto be communicatedprivatelyto the parties, then each partywould be forced to conditionits policy choices on its beliefsabout the offersthat had been made to its rival. As O'Brienand Shaffer(1992) have arguedin a relatedcontext, such a game has many beliefsof the parties.Still, Nash equilibria,as thereis little to disciplinethe outofequilibrium subgameperfect therewouldbe two reasonsto focus on the equilibriathat satisfyour Definition1. First,evenwith unobservable contributionschedules,theseequilibriaarethe only ones thatcan arisewhenF( ) and H( ) are linearfunctions, as we shallassumein the next subsectionand thereafter.Moreon this point in a moment.Second,the equilibria bilateralrenegotiationbetweena lobby and a describedby Definition1 are immuneto jointwelfareincreasing party, and thus satisfythe conditionsfor a "contractequilibrium"proposedby Cremerand Riordan(1987). See O'Brienand Shaffer(1992) for a discussionof why such equilibriamight be focal in the set of equilibria that can arisewhen contractsbetweena principaland a particularagent are unobservableto otheragents.
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wheref > 0 is a parametermeasuringthe diversityof ex ante viewsabout the parties.Then u'(p)] u
F[ui(pA)
1 ~~A f[ui(p
+b+
2
)u'(p 
B fI
for
foru'(pA)

PB C '2fx,
Ib f
We also take H( ) to be linear and of the form H(CA  CB) =+b+h(CA  CB), where h >0 is a parameterreflectingthe productivityof campaignspending.With this specification, if the two partieshappento endorsethe same pliablepolicies and if they happen to spend the same amounts on their campaigns,then party A will capture a fraction + b of the votes. The parameterb can be interpretedas the ex ante voter bias in favour of party A. We might expect b > 0 if party A is the incumbentparty and b < 0 if party B is the incumbentparty. Such an incumbencyadvantagecould reflectname recognition and perhapsthe feelingthat "the devilyou know is betterthan the devilyou don't". Also, b might differfrom zero because one party'scandidatesare seen as more competentor becauseits ideologicalagendahas greaterpublic appeal.When b = 0, we will say that the parties are equally popular.
One consequenceof linearity(among others) is that the objectivefunctionfor each partybecomesadditivelyseparablein the variablesdescribingits own policy platformand level of campaign spending, and those of its rival. With separability,each party can make its decisionsabout what contributionoffers to accept and what platformto adopt independentlyof its knowledgeor beliefs about the incentivesfacing the other. Accordingly, the equilibriathat arisewhen contributionschedulesare observableto both parties coincidewith those that can arise when the schedulesare communicatedprivately,in the linearcase. 4. EQUILIBRIUM WITH ONE LOBBY We begin the analysiswith the case in which there is only a single, organizedlobby. In this settingwe are able to expose most clearlythe incentivesfacing a lobby and to set the stage for the more complicatedsituation that arises when several groups compete for favours.The singlelobbycase also may be of independentinterest,inasmuchas it sheds light on the determinationof what Baron (1994) refersto as particularistic policies.These are policieswhose benefitscan be deniedto those who do not contributeto the lobbying effortand whosecosts are spreadso thinlyin the populationthat they do not inspiregroups to organizein opposition.Baroncites as examplesthe specialprovisionsin legislationthat favourparticularfirmsor industriesand the interventionsthat legislatorssometimesmake with the bureaucracyon behalf of their supporters. When only a single interest group curries politicians'favours, its problem can be treatedas one of direct control. That is, we can view the lobby as if it could implement any pair of (pliable) policy platformsit desires,providedthat its contributionoffersare sufficientlylarge as to be acceptableto the parties.Each party always has the option of decliningthe lobby's offer, in which case it would choose the platformthat attractedthe greatestnumberof informedvoters.To preventthis fromhappening,the lobby'scontribution must be among those that satisfy a participationconstraint. How largemust the contributionto partyA be in orderto induceit to endorsesome policy PA? Recall the relationshipbetween the parties'platformsand campaignbudgets and the electionoutcome,in the light of our linearityassumptionsfor F( ) and H(.). We have s=b ++ (1  a)f[ W(pA)  W(pB)] + ah(CjACj B), where W(p) (/n,) fic u'(p)di
REVIEW OF ECONOMIC STUDIES
274
is the averagewelfareof informedvoters when the vector of pliable policies is p. If the party were to refuseto be swayedby the lobby's offer, it would supportthe policies that best servedthe averageinformedvoter.This policyvector,whichwe denotebyp*, satisfies V W(p*) = 0.11 So the lobby must guarantee the party at least as many seats as it would
capture by endorsingp*. Evidently,it must offer to party A a contributionof at least [(1  a)f/ah][ W(p*) W(pA)]. Notice that the size of the minimumpayment does not dependon the policy position anticipatedfrom party B. Similarly, the lobby must offer party B a contribution of at least [(1  a)f/ah][ W(p*) W(pB)] in orderto induceit to adopt the platformpB. The lobby's problem,then, is to choosepA andpB to maximize(2), subjectto the constraintsthat CK>(la)f[W(P*) ah
W(pK)]
for K=A, B.
(3)
The constraintsstipulatethe minimumsizes of the campaigncontributionsas functions of the platformsthat the group chooses to induce. 4.1. Contributionswith only an influence motive
Let us suppose, for the moment, that the lobby decides to give the two partiesexactly what is needed to induce them to support the platformspA and pB, but nothing more. contributions,partyA capturesa fraction2 + b of the seats, Withtheseinfluencemotivated whiileparty B capturesthe remainingfraction Ab,no matte whatthepolicy vectors andpB happento be. The lobby'sproblembecomesone of choosing the two platformsto maximizeits expectedutility, given qA = qp(b+) and TB= I  q(b + 2), and contributions that satisfy (3) with equality. We have, then, the following proposition that describes equilibriumpolicies when the lobby eschewsthe electoralmotive for politicalgiving: Proposition 1. If the contributionsfrom a sole lobby satisfy both participation constraints in (3) with equality, the equilibriumpolicy platforms satisfy
p = arg maxp[ where (PA = p(b + 2) and
TB= I
Wj(P) +
ah W(p)1 for K=A, B,
(4)
(b +
Evidently, the influenceseekinglobby induces both parties to behave as if they were maximizingweightedsums of the collectivewelfareof interestgroup membersand the averagewelfareof informedvoters. It may help to think about some specificexamplesin order to understandexactly what this formulameans.Consider,for instance,the classicalproblemof an industrythat generatesa negativeexternality.If the externalityis linkedto the scaleof production,then a perunitoutput tax equal to the marginaldamagebest servesthe interestsof the average voter. But suppose that the industry'slobby links its campaigncontributionsto the size of the industrytax or subsidy.Then the equilibriumplatformswill be ones that maximize weightedsumsof averagewelfare(i.e. consumersurplusplus profitsplus tax revenue)and industryprofits. These platformsmay involve a tax or a subsidy, and will certainlybe sampleof the total populationof voters,in the sensethat 11. If the informedvotersare a representative the distributionof utility functionsamong informedand uninformedvoters is the same, then the policyp* is the one that maximizesa Benthamitesocial welfarefunction.
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moregenerousto the industrythanthe "optimal"Pigouviantax.'2Orconsideran economy that producesa single output from fixed suppliesof capitaland labourand whereutility is linearin consumption.The welfareof the averagevoter is maximizedby a flexiblewage policy that ensuresfull employmentof the L workers.But if a union representingthe workersoffersdonationsto the partiesthat are contingenton theirendorsinga minimum wage policy, then the equilibriumplatformswill contain such proposals as long as the elasticityof labourdemandis not too high.'3 Another illustrationof (4) draws on the politicalscienceliterature.Consider the familiarspatialvoting model, wherea scalarpolicy variablep is to be chosenfrom among points on the real line. Suppose that voter i has bliss point pi and utility from policy p given by Ui= (p pi)2. Let voters'bliss points be uniformlydistributedon [0, 1] and let informedvoterscomprisea representativesampleof the whole.The distributionof voters' ex antepreferencesis, as before,independentof the distributionof benefitsfromthe pliable policy. Finally, let therebe a single,organizedinterestgroup, representingall voters with blisspointsin the range[mn,n]. ThenPropositionI impliesthat,whenthe lobbycontributes only to influencepolicy choices, the equilibriumplatformssatisfy PK=!
[ +oK(n m)(n+m) for K= A, B,  m) J 2L +q(n
where 6 _(1  a)f/ah. Notice that PK 1/2 (the bliss point of the median and average voter) as )Xoo),whilePK (n + m)/2 (the bliss point of the medianand averageinterestgroupmember)as +O.Also, pK> 1/2 when (n+ m)/2 > 1/2 andpK< 1/2 when (n + m)/ 2< 1/2; i.e. the platformsalwayslie betweenthe bliss point of the medianinterestgroup memberand that of the medianvoter. Finally,the largeris pK, the fartheris pK from 1/2 and the closer it is to (n + mn)/2. Returningto the moregeneralinterpretationof the model,we nextestablisha proposition that compares the campaign platforms of the two parties and the contributions receivedby each one, again for situationsin which the lobby pursuesonly an influence motive for giving. Suppose,for concreteness,that party A is the more popularparty; i.e. b > 0. Then we have: Proposition 2. If b > 0 and the contributionsfrom a sole lobby satisfy the par ticipation constraintsin (3) with equality, then Wj(pA)> Jy(pB) W(pA) < W(pB), and CA> CB.
The propositionfollows straightforwardly from (3) and (4).14 Notice first that b>O implies (p(b+ 2) > 1  (p(b+ ). Therefore,it is the more popularparty that appliesgreater 12. Let d be the marginaldamagecausedby a unit of the industry'soutputand let tK be the perunittax advocated by party K. Then in political equilibrium, tK=d
[(TKah)/(I

a)f J(x/x'), where x is industry output
and x' is the slope of the industrysupplycurve. 13. Let F(K, L) be the aggregateproductionfunction.The minimumwage wK supportedby party K maximizesqKwL + ((1  a)f )/ahF(K, L), subjectto the constraintsthat L ? L and FL(K,L) = w. The solution has a minimumwage above the marketclearing wage providedthat E
E
VWj
(pAo)
[ 1q(s)]Z EVWi(p
+ (
a+(I
) V W( Ao)
= 0;
)fVW(pBo)=0.
(13)
(14)
These conditionsimply: Proposition 6. Whenall lobbies satisfy the participation constraints (7) with equality, each party's equilibriumplatform satisfies the necessary conditionsfor maximizing a weighted sum of the aggregate welfare of all interest group members and the average welfare of informed voters.
Conditions(13) and (14) providea partialanswerto the followingquestion:Which interestgroupsare most successfulin influencinggovernmentpolicy?The answer,we find, is that all organizedinterestgroupsare equallysuccessful,in the sense that theirmembers receiveequal weight in the parties'political calculus.The net effect of privatecampaign financingis to push policy in a directionthat is favourableto the averagememberof an interestgroup and away from the policy that would best servethe interestsof the average (informed)voter. Of course, the final platformchoices will not be equally close to the bliss points of all of the lobbies; this dependson how similara lobby'spreferencesare to those of the average voter and how the other interestgroups line up on the issues of concernto it. The conditionsthat characterizethe equilibriumplatformshave anotherinteresting implication.The politicalsystemworksbest, of course,whenall votersare informedabout the issues (a = 0). Then the interestgroups are ineffectualand both parties choose the platformthat maximizesaggregatewelfare.But the same outcome is achievedin a very differentset of circumstances.Supposethat everyvoter is a memberof exactlyone interest group and that the informedvoters constitutea representativesampleof the electorate. Then, no matterhow large the fractionof uninformedvoters nor how susceptiblethese voters may be to campaignrhetoric,the equilibriumpolicies again will be the ones that best serve the voters' (collective)interests. Notice that (13) and (14) do not uniquelydeterminethe equilibriumplatforms,even when W( ) and 4jV(.) are concavefunctions.BesidesPA andpB, the (expected)composition of the legislature(s?) appearsin theseexpressions.The equilibriumseatcountdepends, in turn, on the total amountsof contributionscollectedby the parties.It is true, as in the case of a single lobby, that an individualinterestgroup prefersto concentrateits giving on the party that it expectswill be in a betterposition to implementits platform.And it is also true that the party expected to capturea legislativemajoritycaters more to the special interests.But there is a potential here for selffulfillingprophesiesthat does not exist when a singlelobby plays the contributiongame. The selffulfillingprophesiesreflect a type of coordinationfailureamong the lobbies.20 Suppose, for example, that party A happens to be the more popularparty (b>0), but that each lobby expects that party B will capture the majorityof the seats. These 20. Morton and Myerson(1992) find a similarresultin a onedimensionalspatialvotingmodel, where partiessell "services"to specialinterestgroupsand use the proceedsto fund advertisingthat directlyenhances the welfareof voters.
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expectationsare based on the belief that the other lobbies will give more generouslyto party B than to partyA. Then each lobby will be welljustifiedin concentratingits efforts on influencingB's platformand, in the end, theirexpectationsmay be validated.Whereas an only lobby can alwaysgain by ensuringthat the more popularpartywins the majority of the seats, a lobby that is one among many cannot necessarilydo so. To reversethe fortunes of the two parties in a way that conserves resources,it may need the tacit cooperationof other lobbies. The potential for multiplicityof equilibriacan also be understoodin anotherway. Recall that s=
2+
b + (I

a)f[ W(p,) W(p%,)] + ah[C_4 (pig,)Ci,(p%)]
when lobby
/
makes the minimalcontributionsneededto induce the platformsPAo andpBo. Of course, if all lobbies give minimally,then this condition must hold for each one. The policies A P andp% are the ones that the partieswould choose if they ignoredthe offerfrom lobby p,1 1. Notice that these policies depend on the shapes of the lobbies' contributionschedules And whilethe equilibriumrequirementsplace some restrictions awayfrom the equilibrium. on the global shapes of these schedules(for example, (1  a)f[ W(p_,) W(p_)] + ah[C_ (p_)

must be the same for all 1) the requirementsare not enough to pin down the equilibrium uniquely. Still, some of the Nash equilibriamay be more compellingthan others.For example, if b = 0, the symmetricequilibriumin which the lobbies treat the parties similarlyand the election yields an evenly split legislaturemay be focal. If b >0, the lobbies would have no particularreason to expect the bulk of the contributionsto go to party B, and in some cases they will have good reasons to expect the opposite. One such case arises when all lobbies are offeringpositivecontributionsto both parties,not only in the neighbourhood of the equilibrium,but also around the variouspoints that the partieswould choose if one of the lobby groups were to be ignored.In this situation, the equilibrium with s The alternativeequilibriumcan be constructedas follows. Let each lobby offer to party B in the new equilibriumexactlywhat it offeredto partyA in the old. Let each construct its new offer to party A by subtractinga fixed amountfrom the (positive) offersto party B in the old equilibrium,plus an additionalamountthat increaseswith the distancefrom the initialpBo. Finally,let the fixed reductionsbe chosen so that partyA capturesas many seats in the new equilibriumas party B did in the old, and let the additionalreductions be chosen so that no partywill declinethe offerfrom some lobby in settingits platform.2' The newlyconstructedcontributionschedulesare best responsesto one another,and they induce each party to chose the platformin the new equilibriumthat the other chose in the old. Finally, since each party wins as many seats in the new equilibriumas the other did in the old, the new equilibriumhas exactly the same distributionof policy outcomes as the old. It follows that all interestgroupsgain. 21. That is, let C,K(p) be the initialscheduleofferedby lobbyj to partyK and let C/K(p)be the alternative. We propose Co`(p)= CA(p) for all] and CjA(p)= CjB(p)  z, whereeach Z,() is a functionthat is (pp), everywherenonnegativeand that reachesa uniquemaximumat 0. Let the constantszj be chosenso that z.>O and j, zj= 2b/a h, and the functionsZj() so that , ((I a)f W(p) + ah E (I  a)f W(Mp)+ j C8( p) > maxp
[C(p) Zi(pp?] 

aiz,}
for all 1.This will be possible,providedthat the Cj (p%)in the initialequilibriumare largeenough.In the event, and lobby I gains z1 relativeto the initial party A chooses the platformpA =pB, party B chooses pJ=pA, equilibrium.
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282
More generally,anytimeb >0 and s max r[p pll
1(pB)
CAI (p) _CB
(pll)
_CII]
and a similarconditionfor partyB. We focus on symmetricequilibria,whereinCA(* ) = CR(*), lobbyI chooses the same platformand contributionfor each party,and the participationconstraintsbind. Letp7be the platformdesignatedby lobby1.The firstorderconditionfor maximizingthe lobbies'expected utilitywith respectto the choice of plA implies
(16)
!VW,l(pl)+ (la)fVW(P )+VC,(p7,)0
ah
where we have made use of the fact that 7r(p', p', 0) =2 at the symmetric equilibrium.24 PartyA chooses its equilibriumplatform,pAo to maximizer[pA, pB?, CAo(pA) C"?(p?)]
use of the symmetryconditions,PA,
=p and CAo()=
=pB
C?(
)=Co(
)
Againmaking
this implies
=O. (I  a)fV W(p?)+ ahVCO(p?)
(17)
Consistencyrequiresp7=po for all 1. Thus, (16) and (17) imply IVWI(p0) =VC/O(p),
(18)
whichis another"localtruthfulness"result.Finally,combining(17) and (18) we find 2?
W(p?)
(1af
+(
a)
VW(p0)= 0.
(19)
The platformpo that satisfies(19) is the same as the platformpA, that satisfies(13) and the platformp8' that satisfies(14), when s0=2. We see that, with equal popularity,the platformthat emergesin a symmetric equilibriumwhen the legislatureoperatesby strictmajorityrule and partiesmaximizetheirchancesof winning a majorityis the same as the platformthat emergesin symmetricequilibriumwhen partiesmaximizetheir representationin the legislatureand a minorityplatformhas some chanceof beingimplemented.25 Acknowledgements WethankTim Besley,AvinashDixit,IanJewitt,TorstenPersson,andtwo anonymous refereesfor helpfulcommentsand suggestions,and the National ScienceFoundationand the USIsrael BinationalScienceFoundationfor financialsupport.Grossmanalso thanksthe John S. GuggenheimMemorial Foundation,the SumitomoBank Fund the Daiwa Bank Fund and the Center of InternationalStudies at
23. The approximationfollows from the Liapunovcentral limit theorem,which requiresalso that the variancetermbecomesunboundedas n growslarge.For a discussionof the applicabilityof this theoremin the contextof a probabilisticvoting model, see Lindbeckand Weibull(1987). 24. In deriving(16) we haveusedthe firstorderconditionwithrespectto CAto substituteout the Lagrange multiplieron the participationconstraint.We have also made extensive use of the symmetryconditions, A.RC; 0 Bo=. pi and C, = C/ = C? P1Ao==pi 25. This resultmimicsa similarfindingby Lindbeckand Weibull(1987), who assumedthat all votersare informedvotersand that campaigncontributionsplay no role in the election.
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