stokes 1963 spatial models

7/27/2019 Stokes 1963 Spatial Models

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Spatial Models of Party Competition

Author(s): Donald E. StokesSource: The American Political Science Review, Vol. 57, No. 2 (Jun., 1963), pp. 368-377Published by: American Political Science AssociationStable URL: http://www.jstor.org/stable/1952828 .

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SPATIAL MODELS OF PARTY COMPETITIONDONALD E. STOKESUniversity of Michigan

The use of spatial ideas to interpret partycompetition is a universal phenomenon ofmodern politics. Such ideas are the commoncoin of political journalists and have extraor-dinary influence in the thought of politicalactivists. Especially widespread is the concep-tion of a liberal-conservative dimension onwhich parties maneuver for the support of apublic that is itself distributed from left toright. This conception goes back at least toFrench revolutionary times and has recentlygained new interest for an academic audiencethrough its ingenious formalization by Downsand others.' However, most spatial interpreta-tions of party competition have a very poor fitwith the evidence about how large-scale elec-torates and political leaders actually respondto politics. Indeed, the findings on this pointare clear enough so that spatial ideas aboutparty competition ought to be modified byempirical observation. I will review here evi-dence that the "space" in which Americanparties contend for electoral support is veryunlike a single ideological dimension, and Iwill offer some suggestions toward revision ofthe prevailing spatial model.I. THE HOTELLING-DOWNS MODEL

Because spatial ideas have been woven intopopular and scholarly commentaries on politicswith remarkable frequency, my observationsreach well beyond recent efforts to formalizethe spatial model of party competition. How-ever, the work of Downs gives this conceptionadmirable clarity without removing it too farfrom familiar usage, and I begin with a briefreview of his system. The root idea of Downs'smodel is that the alternatives of governmentaction on which political controversy is focusedcan be located in a one-dimensional space,1 For expositions of Downs's model, see AnthonyDowns, An Economic Theory of Democracy(Harper and Brothers, New York, 1957), pp. 114-141, and "An Economic Theory of Political Ac-tion in a Democracy," Journal of Political Eco-

nomy, Vol. 65 (1957), pp. 135-150. For a similarmodel, developed independently, see DuncanMacRae, Jr., Dimensions of Congressional Voting:a Statistical Study of the House of Representativesin the Eighty-First Congress (University of Cali-fornia Press, Berkeley and Los Angeles, 1958), pp.354-382.

along a left-right scale. At least for illustration,Downs interprets this dimension as the degreeof government intervention in the economy.At the extreme left is complete governmentcontrol, and at the extreme right no govern-ment intervention beyond the most limitedstate operations. Each voter can be located onthe scale according to how much governmentcontrol he wants and each party according tohow much government control it advocates.2As Downs is careful to make clear, this modelextends a line of thought tracing back to thework of Harold Hotelling.3 Thirty years agoHotelling had sought to answer the question ofwhy two competing firms are so often found inadjacent positions near the middle of a spatialmarket (Kresge's and Woolworth's are not atopposite ends of Main Street; they are rightnext door). Assuming (1) that the buying pub-lic is evenly distributed along a linear market(a transcontinental railroad, say), and (2) thatdemand is inelastic (that is, consumers at agiven point of the market will buy a fixedamount of goods from whichever of two pro-ducers is closer and, hence, can offer the lowertransportation costs to consumers located atthat point), Hotelling was able to show thattwo competing firms would converge towardadjacent positions at the middle of the market.If one firm is farther from the middle than itscompetitor, it can increase its share of themarket by moving toward the middle; and soon, until equilibrium is reached. Substitutingvoters for consumers, parties for firms, and the"costs" of ideological distance for transporta-2 Downs's model is a little more complicated

than this. Each voter has not only a most-pre-ferred degree of government intervention (let ussay his "point" on the scale); he has some amountof preference for every other degree of govern-ment intervention (the other points on the scale),the amount decreasing monotonically the fartherthe point is from his optimum. Hence, the prefer-ence of the electorate as a whole for a given degreeof government intervention is the sum of thepreferences of individual voters for that degree ofintervention. Moreover, a party's position on thescale may be thought of as the sum or average ofthe positions it takes on a variety of particularissues.

3Harold Hotelling, "Stability in Competition,"Economic Journal, Vol. 39 (1929), pp. 41-57.

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SPATIAL MODELS OF PARTY COMPETITION 369tion costs, Hotelling felt that his model couldexplain why the Democratic and Republicanparties are so often found close to the centerof a liberal-conservative dimension.Those who have extended Hotelling's ideashave done so by relaxing one or both of theassumptions given above. Arthur Smithies andseveral other economists dispensed with (2),the assumption of inelastic demand.4 Smithiesassumed instead that demand depends on priceand that sales at any given point of the marketwill vary according to how much deliveredprices are raised by transportation costs. Forthis reason two competing firms will be underpressure not only to move closer together toimprove sales in their "competitive region";they will also be under pressure to move fartherapart to improve sales in their respective"hinterlands." When these two opposite forcesare in equilibrium the competing firms couldwell be some distance apart. Continuing theside discussion of politics, Smithies argued thatelectoral "demand" also is elastic, since avoter who feels that both parties are too farfrom his ideological position can simply stayaway from the polls. With this assumptionadded, Smithies felt that the model could ex-plain why the Republicans and Democrats (bythe time of the New Deal era) were some dis-tance apart, ideologically speaking.Downs has retained Smithies's assumptionof elastic demand and has further modified theHotelling model by dispensing with (1), theassumption that the public is evenly distributedover a one-dimensional space. Indeed, inDowns' system, the way the public is dis-tributed along the liberal-conservative scale isa variable of great importance, one that he usesto explain some very notable attributes of(constructed) political systems.5 Under Downs'srevision, the model not only can explain thestrategic choices of existing parties as theyplace themselves along the left-right scale. Itcan also explain the emergence of new partiesand the disappearance of old ones. Downs'sdiscussion can be read equally as a theory ofvoter choice, a theory of party positioning, anda theory of party number.

4Arthur Smithies, "Optimum Location inSpatial Competition," Journal of Political Econ-omy, Vol. 49 (1941), pp. 423-429.

6 Downs makes several other modifications ofHotelling's and Smithies's models in addition totreating the distribution of the public on the scaleas a variable. Especially important is the assump-tion that one party will not "jump over" the posi-tion of another on the liberal-conservative dimen-sion.

Like any good theorist, Downs should beread in the original. However, the inferenceshe makes to the number and positions of com-peting parties from different distributions ofthe public on the left-right scale may be sum-marized as follows. If the distribution has asingle mode, the party system will be inequilibrium when two parties have convergedto positions that are fairly close together. Justhow close depends on how elastic the turnoutis and on how sharp the peak of the distribu-tion is, as well as other factors.6 If the distri-bution has two modes, the system will be inequilibrium when two parties are present, eachhaving assumed a position somewhere near oneof the modes. If the distribution has more thantwo modes,the system will be in equilibrium whena party occupies each of the several modalpositions. In this sense, the presence of morethan two modes of opinion encourages the de-velopment of a multiparty system.Reviewing these ideas, one must first admirethe ingenuity with which Downs has trans-formed Hotelling's brilliant analogy into amodel of party systems. However, the mode]includes some cognitive postulates that needto be drastically qualified in view of what isknown about the parties and electorates ofactual political systems. Of course, it is in thenature of models not to represent the realworld exactly. The more general and powerfula model is, the more severely it will cut awayunnecessary aspects of reality, and any first-class formalization should be forgiven a host ofempirical peccadilloes. However, what is wrongwith the hidden postulates of Downs's modelis more than a petty fault. These postulatesare introduced when the argument shifts fromeconomic competition in a spatial market topolitical competition in an ideological market.In Downs's (and Hotelling's) exposition, thistransition is rather too easily accomplished.The consequences of placing competitors andconsumers in a linear space are developed per-suasively for the economic problem, where themeaning of the space is clear, and transferredtoo easily to the political problem, where themeaning of the space can be far from clear. Theground over which the parties contend is not aspace in the sense that Main Street or a trans-continental railroad is. Treating it as if it wereintroduces assumptions about the unidimen-sionality of the space, the stability of its struc-

6 The assumption that no party can move pastanother on the left-right scale makes the equi-librium positions of two competing parties less welldefined than it is for the competing firms of themodels of Hotelling and Smithies.



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370 THE AMERICAN POLITICAL SCIENCE REVIEWture, the existence of ordered dimensions andthe common frame of reference of parties andelectorate that are only poorly supported byavailable evidence from real political systems.7

II. THE AXIOM OF UNIDIMENSIONALITYThe most evident-and perhaps least funda-mental-criticism to be made of the spatialmodel is that the conception of a single dimen-sion of political conflict can hardly be sus-tained. Such an assumption clearly is false tothe realities of two-party systems, includingthe American, on which intensive studies havebeen made. And there is evidence that it falsi-fies the realities of many multiparty systems,in which the appearance or continued existenceof parties depends less on the electorate's dis-

tribution along a single dimension than on thepresence of several dimensions of politicalconflict.The unreality of a one-dimensional accountof political attitudes in America is attested byseveral kinds of evidence from the electoralstudies of the Survey Research Center at theUniversity of Michigan. The relative independ-ence of various attitude dimensions is a re-peated finding of these studies. For example,over a period of years this research has meas-ured public attitudes toward social and eco-nomic welfare action by government and to-ward American involvement in foreign affairs.The lore of popular journalism would makethese two domains one, with the liberal inter-nationalist position going hand in hand withthe liberal social welfare position. However, theempirical support for this conception is weakindeed. Across a national sample of the elec-torate, there is no relation between attitudestoward social welfare policies and American in-volvement abroad.8 These dimensions of atti-tude are independent in a statistical sense;knowing bow "liberal" a person is on one givesno clue whatever as to how "liberal" he will beon the other.If the voters' own positions on social welfare

7 My remarks here are directed solely to Downs'sspatial model of party competition. An EconomicTheory of Democracy (op. cit.) sets forth a wholecollection of models, elaborated from a few cen-tral variables. All are worth detailed study.Paradoxically, the spatial model described here islikely to have great intuitive appeal for a wideaudience, yet its postulates are almost certainly asradical asthose of any modelin Downs's collection.

8 Angus Campbell, Philip E. Converse,Warren E. Miller, and Donald E. Stokes, TheAmerican Voter (John Wiley and Sons, New York,1960), pp. 197-198.

and foreign involvement prevent our treatingthese two dimensions as one, their reactions tothe domestic and foreign policies of the partiescan also be strongly discrepant. For example,in the presidential election of 1952 the Demo-cratic Party was approved for its domesticeconomic record but strongly disapproved forits record in foreign affairs, particularly theunfinished conflict in Korea. With even-handedjustice the public rewarded the party for pros-perity and punished it for war without reducingthe Democrats' performance to a summary po-sition on some over-arching dimension of po-litical controversy.An intensive search for such a dimension hasmet little success. In the presidential electionsof 1952, 1956, and 1960 the Center's interviewsopened with an extended series of questionsdesigned to elicit the ideas that are actuallyassociated with the parties and their presi-dential candidates. When the answers, amount-ing on the average to a quarter hour of conver-sation, are examined closely for ideologicalcontent, only about a tenth of the electorateby the loosest definition is found to be usingthe liberal-conservative distinction or anyother ideological concept. By a more reasonablecount, the proportion is something like threepercent.9 What is more, when our respondentsare asked directly to describe the parties interms of the liberal-conservative distinction,nearly half confess that the terms are un-familiar. And the bizarre meanings given theterms by many of those who do attempt touse them suggest that we are eliciting artificialanswers that have little to do with the public'severyday perceptions of the parties.The axiom of unidimensionality is difficult toreconcile with the evidence from multipartysystems as well. The support for the parties ofa multiparty system is often more easily ex-plained by the presence of several dimensionsof political conflict than it is by the distributionof the electorate along any single dimension.At least since Marx, the dimension we wouldchoose to account for party support, if allowedonly one, would be socio-economic or class-related. Yet the politics even of western na-tions exhibit many parties that owe theirexistence to religious or racial or ethnic identi-fications or to specialized social and economicinterests (such as the agrarian) that do not fitreadily into the stratification order. For exam-ple, the Zentrum of Weimar Germany andbefore, as the prototype confessional party,drew support from Catholics at all levels of

I Ibid., Chapter 10, "The Formation of IssueConcepts and Partisan Change," pp. 227-234.



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SPATIAL MODELS OF PARTY COMPETITION 371German society. The party could scarcely havesurvived if its strength had depended entirelyon public response to its socio-economicpolicies.'0 My colleague, Philip Converse, andGeorges Dupeux have found that the partypreferences of the mass French public are morehighly associated with attitudes toward re-ligious issues than with attitudes towardsocio-economic issues, despite the immenselygreater attention given the latter by govern-ment and elite circles. If the parties and elec-torate of contemporary France are to belocated in spatial terms, the space must be oneof at least two dimensions.Even support for the occasional third partyof American politics may be understood betterif more than one dimension is considered. TheDixiecrat Party of 1948 is a good case in point.Downs himself describes the Dixiecrats as a"blackmail party" whose intent was to forcethe national Democratic party farther to theright on the general liberal-conservative dimen-sion." But it is at least as plausible to say thattheir rebellion was directed at Truman's civilrights program, as the southern walkout overadoption of a civil rights plank by the nationalDemocratic convention of 1948 would suggest.Undoubtedly for some southerners civil rightswere closely linked with issues of economic andsocial welfare policy. But for others theseissue domains were quite distinct. Americanpolitical beliefs are sufficiently multidimen-sional so that many Dixiecrat votes were castby southern economic liberals.Although the assumption of unidimension-ality is a familiar part of prevailing spatialconceptions of party competition, it might wellbe dispensed with. Hotelling's original argu-ment can easily be generalized to two dimen-sions, as Hotelling himself observed (in mostof the towns we know about, Kresge's andWoolworth's are still right together, eventhough their customers live on a two-dimen-sional surface).12 That the model has not been

10 It is a curious and interesting fact that theagrarian party of modern Norway, like the Cath-olic party of pre-Hitler Germany, has chosen tocall itself the "Center" party, that is, to call itselfby a name that refers to a dimension other thanthe one on which the party's main support isbased. By selecting a title that is neutral in termsof a primary dimension of political conflict, theparty invites potential supporters to ignore thatdimension and rally to the party's special cause.

'1 Downs, op. cit., 1957, p. 128.12 A troublesome problem in applying a more

general model to the real world is that of definingsome kind of distance function over all pairs of

extended may be due in part to the fact thatintroducing more dimensions raises otherquestions about its fit with the real world thatare not likely to be asked about the simple one-dimensional model. In particular, accommo-dating a greater number of dimensions drawsattention to the assumption that the space ofparty competition, whether unidimensionalor multidimensional, has a stable structure.III. THE AXIOM OF FIXED STRUCTURE

The mischief of too facile a shift from theeconomic to the political problem is plainly seenin connection with the assumption of stablestructure. Since the space represented by atranscontinental railroad depends on physicaldistance, its structure is fixed, as the structureof Main Street is. The distribution of con-sumers within these spaces may vary; the spaceitself will not. Hotelling applied his economicmodel to some kinds of spaces whose structurewas not derived from physical distance: forexample, the degree of sweetness of cider. Butthese, too, were spaces of fixed structure.By comparison, the space in which politicalparties compete can be of highly variablestructure. Just as the parties may be perceivedand evaluated on several dimensions, so thedimensions that are salient to the electoratemay change widely over time. The fact of suchchange in American politics is one of the best-supported conclusions to be drawn from theSurvey Research Center's studies of votingbehavior over a decade and a half. For example,between the elections of 1948 and 1952 a far-reaching change took place in the terms inwhich the parties and candidates were judgedby the electorate. Whereas the voter evalua-tions of 1948 were strongly rooted in the eco-nomic and social issues of the New Deal-FairDeal era, the evaluations of 1952 were basedsubstantially on foreign concerns. A dimensionthat had touched the motives of the electoratescarcely at all in the Truman election was ofgreat importance in turning the Democratic

points in the space. The need for such a functionis less acute in the one-dimensional case, becausean approximate ordering of distances betweenpoints can be derived from the strong ordering ofpoints in the space. However, the points of amultidimensional space are no longer stronglyordered, and it may not be possible to comparethe appeal of two or moreparties for voters locatedat a given point by measuring how far from thepoint the parties are. Of course, if the space canbe interpreted in physical terms, as Hotelling'scould, this problem does not arise.



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372 THE AMERICAN POLITICAL SCIENCE REVIEWadministration out of power four years later.If the difference between these two elections isto be interpreted in spatial terms, we wouldhave to say that the intrusion of a new issuedimension had changed the structure of thespace in which the parties competed forelectoral support.However, this way of putting it implies thata dimension either is part of the structure of thespace or it is not, whereas the presence of agiven evaluative dimension is often a matter ofdegree. What is needed is language that wouldexpress the fact that different weights shouldbe given different dimensions at different times.At some moments of political history class orreligious or foreign or regional dimensions are ofgreater cognitive and motivational significanceto the electorate than they are at other times,quite apart from shifts in the positions of thecompeting parties and their consuming public.Drastic electoral changes can result fromchanges in the coordinate system of the spacerather than changes in the distribution ofparties and voters.I think the evidence shows that party man-agers are very sensitive to changes in thegrounds of electoral evaluation. Political for-tunes are made and lost according to theability of party leaders to sense what dimen-sions will be salient to the public as it ap-praises the candidates and party records. Tobe sure, this awareness is not universal, andsome political leaders have imputed to theelectorate a stereotyped cognitive map that isvery close to the Downs model. The discrep-ancy between these imputed cognitions and theelectorate's actual cognitions is a point towhich I will return. But the skills of politicalleaders who must maneuver for public supportin a democracy consist partly in knowing whatissue dimensions are salient to the electorate orcan be made salient by suitable propaganda.The deftness with which Republican leadersturned the changing concerns of the countryto their advantage in 1952 provides an excellentmodern example. Dewey and the other Eisen-hower managers knew that victory lay in ex-ploiting relatively new and transitory politicalattitudes, including the one they could injectinto the campaign by nominating an immenselypopular military figure who was seen in whollynon-ideological terms. The brilliant slogan ofthe "three K's"-Korea, Corruption, Com-munism-with which the Republicans pressedthe 1952 campaign was hardly the work of menwho perceived the cognitions and motives ofthe electorate as tied primarily to the left-rightdistinction. The dominant Republican leader-ship showed a highly pragmatic understanding

of the changing dimensions of political evalu-ation.The case of 1952 leads to a further point ofgreat importance. I have called the new issuesof that year "dimensions" to keep them withinthe terms of this discussion. But one does nothave to take a very searching look at theseissues to feel that some at least are not dimen-sions in any ordinary sense. The issue of cor-ruption, for example, was hardly one on whichthe Democratic Party took a position for the''mess in Washington" and the Republicans aposition against it in appealing to an electoratethat was itself distributed on a dimension ex-tending from full probity in government to fulllaxity and disarray. A consideration of thispoint raises a third difficulty in applying theDowns model to actual party systems.IV. THE AXIOM OF ORDERED DIMENSIONS

For the spatial model to be applied, theparties and voters of a political system mustbe able to place themselves on one or morecommon dimensions. That is, there must be atleast one ordered set of alternatives of govern-ment action that the parties may advocate andthe voters prefer. Degrees of government inter-vention in the economy is such a set, as Downsobserved; so is the extent of American involve-ment in foreign affairs or the extent of federalaction to protect the rights of Negroes. Obvi-ously a good deal depends on how many ele-ments the set has. A spatial language tends tosuggest that the number is indefinitely large,like the number of points in Euclidean one-space or the real line of mathematics. Thenumber of alternatives in a political dimensionis clearly more limited, though it cannot be toolimited if such ideas as modal position and rela-tive distance are to have more than trivialmeaning. However, to make my point asstrong as possible, let me include within thenotion of an ordered set one in which there areonly two alternatives of government actionthat the parties may endorse and the votersprefer.The empirical point that needs to be madeis that many of the issues that agitate ourpolitics do not involve even a shriveled set oftwo alternatives of government action. Thecorruption issue of 1952 did not find theDemocrats taking one position and the Re-publicans another. And neither were somevoters in favor of corruption while others wereagainst it. If we are to speak of a dimension atall, both parties and all voters were located ata single point-the position of virtue in govern-ment. To be sure, enough evidence of mal-feasance had turned up in the Democratic ad-



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SPATIAL MODELS OF PARTY COMPETITION 373ministration so that many voters felt the partyhad strayed from full virtue. But throwing therascals out is very different from choosingbetween two or more parties on the basis oftheir advocacy of alternatives of governmentaction. The machinery of the spatial modelwill not work if the voters are simply reactingto the association of the parties with some goalor state or symbol that is positively or nega-tively valued.To emphasize the difference involved here Iwill call "position-issues" those that involveadvocacy of government actions from a set ofalternatives over which a distribution of voterpreferences is defined. And borrowing a termfrom Kurt Lewin I will call "valence-issues"those that merely involve the linking of theparties with some condition that is positively ornegatively valued by the electorate.'3 If thecondition is past or present ("You never had itso good," "800 million people have gone behindthe Iron Curtain"), the argument turns onwhere the credit or blame ought to be assigned.But if the condition is a future or potential one,the argument turns on which party, givenpossession of the government, is the more likelyto bring it about.It will not do simply to exclude valence-issues from the discussion of party competition.The people's choice too often depends uponthem. At least in American presidential elec-tions of the past generation it is remarkablehow many valence-issues have held the centerof the stage. The great themes of depressionand recovery, which dominated electoral choiceduring the Thirties and Forties, were a gooddeal of this kind. What happened to Hooverand the Republicans was that they got bracketedwith hard times, much as the Democrats later,although less clearly, were to be bracketed withwar. Twenty years after the Hoover disasterthe Republicans were returned to power in anelection that was saturated with the valence-issues of the Korean War and corruption in

13 These terms may recall the distinction be-tween "position issues" and "style issues" madeby Bernard R. Berelson, Paul F. Lazarsfeld, andWilliam N. McPhee, Voting (University ofChicago Press, Chicago, 1954), pp. 184-198. If Iunderstand their point, the difference betweenissues of position and style rests on a material-ideal distinction and hence tends to oppose class-related issues to all others. Their account of styleissues sounds at places like the conception ofvalence-issues here. But many of the style issuesthey cite (e.g., prohibition, civil liberties) wouldbe position-issues under the definitions I havegiven.

Washington. And the question of Americanprestige abroad, to which Kennedy and Nixongave so much attention in the campaign of1960, was a pure specimen of valence-issue.Both parties and all voters, presumably, werefor high prestige. The only issue was whetheror not America had it under the existing Re-publican Administration.The failure to distinguish these types ofissues, whatever they are called, is one reasonwhy journalistic accounts of political trends sooften go astray. Apparently the urge to give anideological, position-issue interpretation ofelection results can be irresistible, despite thereams of copy that have been devoted toMadison Avenue technique and the art ofimage-building. One becomes aware of howoften the impact of valence-issues is mistakenfor ideological movements ("with the electionof Kennedy America has again moved to theleft") simply by reading what the newspapershave continued to say even after careful studiesof American voting behavior began to reporttheir findings.It is of course true that position-issues lurkbehind many valence-issues. The problem ofKorea, which benefited the Republicans sohandsomely in 1952, is a good case. The suc-cessful Republican treatment of this issue wasto link the unfinished Korean conflict with thefact of Democratic presidents during two worldwars to hang the "war party" label on theDemocrats. However, it is not hard to findalternatives of government action that mighthave provided a focus to the debate. For ex-ample, the controversy might have centered onhow aggressive a policy toward the Red Chi-nese forces America should adopt. Should theUnited States carry the war to Manchuria,using all weapons? prosecute the war morevigorously within Korea? negotiate a settle-ment on the basis of existing conditions, essen-tially the course the Eisenhower administra-tion took? or pull back to Japan? The point isthat neither this ordered set of alternatives norany other provided the terms of the debate.Both in Republican propaganda and popularunderstanding the issue was simply a matter ofthe Democrats having gotten the country intoa war from which Eisenhower would extractus-whether by bombing Manchuria or evacu-ating South Korea was not made clear.The question whether a given problem posesa position- or valence-issue is a matter to besettled empirically and not on a priori logicalgrounds. This point is illustrated by the issue ofthe country's economic health. At least sincethe panic of 1837 did Van Buren in, prosperityhas been one of the most influential valence-



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374 THE AMERICAN POLITICAL SCIENCE REVIEWissues of American politics. All parties and thewhole electorate have wanted it. The argumenthas had to do only with which party is morelikely to achieve it, a question on which thepublic changed its mind between McKinley'sfull dinner pail and Franklin Roosevelt's NewDeal. However, to make the point as sharp aspossible, let us imagine that part of the elec-torate wants something less than full prosperity-even that it wants economic distress, for thebracing effect that economic difficulties have onindividual conduct and the moral fiber of so-ciety as a whole. If this unlikely conditioncame to pass and the parties maneuvered forsupport by advocating different degrees ofprosperity or distress, the issue would havebeen transformed from a valence-issue into aposition-issue. That it is not such an issue in ourpolitics is due solely to the fact that there isoverwhelming consensus as to the goal of gov-ernment action.Since the preferences of parties and votersmust be distributed over an ordered set ofpolicy alternatives for the spatial model towork, valence-issues plainly do not fit thespatial scheme. Unless the interaction of votersand parties is focused on position-dimensionsthe model cannot serve as a theory either of themotivation of voters or of the positioning ofparties.'4 This is not to say that the interactionof parties and voters on valence-issues is un-interesting or incapable of being representedby a different model. It is only to say that themodel would be different. When the partiesmaneuver for support on a position-dimension,they choose policies from an ordered set ofalternatives belonging to the same problem orissue. But when the parties maneuver in termsof valence-issues, they choose one or more issuesfrom a set of distinct issue domains. As theRepublicans looked over the prospective issuesfor 1952, their problem was not whether tocome out for or against Communist subversionor prosperity or corruption in Washington. Itwas rather to put together a collection of issues

14Because the public's evaluation of politicalactors is so often and so deeply influenced byvalence-issues the Survey Research Center hasused a model of individual electoral choice (and,by extension, of the national vote decision) thatmeasures only the valence and intensity of theaffect associated with the parties and candidates.The model is described in Donald E. Stokes,Angus Campbell, and Warren E. Miller, "Com-ponents of Electoral Decision," this REVIEW, Vol.52 (June 1958), pp. 367-387, and Campbell, Con-verse, Miller, and Stokes, op. cit., pp. 68-88 and524-531.

of real or potential public concern whose posi-tive and negative valences would aid the Re-publicans and embarrass the Democrats.To be sure, Downs makes allowance forvalence-issues by granting that some voting is"irrational," that is, non-ideological in hisspatial sense. He asserts, in fact, that rationalbehavior by the parties of a two-party systemtends to encourage irrational behavior byvoters. As the parties converge to ideologicallysimilar positions (assuming a unimodal distri-bution of voters) their relative position providesfewer grounds for choice and the voters aredriven to deciding between them on some irra-tional basis. This is an admirable defense-indeed, Downs has come close to constructing atheory that cannot be disproved, since evidenceof voter motivation and party propaganda out-side the bounds of the theory can be cited asevidence that the model applies. For the de-fense to be convincing, however, we must beshown that the ideological dimension on whichthe parties are presumed to be close togetherhas empirical validity.But empirical validity for whom? The spaceof Downs's model is formed out of the percep-tions held by the actors who play roles in thepolitical system. However, the model includesat least two classes of actors-voters and partymanagers-and their perceptions of what thepolitical fighting is all about can diverge mark-edly. Here again, the economic problem has leftits imprint; Kresge's Main Street and thecustomer's Main Street are the same, and thequestion of divergent spaces does not arise. Yetit can easily arise in the political context. It isquite possible that the voters see political con-flict in terms that differ widely from those inwhich the parties see it, and this possibilitydraws attention to a fourth unstated assump-tion of the Downs model.V. THE AXIOM OF COMMON REFERENCE

The versatility of the spatial scheme as aninteractional model is enhanced a good deal byassuming that the public and those who seek itssupport impose a common frame of referenceon the alternatives of government action. Inparticular, it is the assumption of a commonlyperceived space of party competition thatallows the model to serve at once as a theory ofvoter motivation and of party positioning. Butwith the space formed out of perceptions, thereis no logically necessary reason why the spaceof voters and of parties should be identical,and there is good empirical reason to supposethat it often is not. Indeed, in view of the em-phasis on imperfect information elsewhere in hisdiscussion, one might expect Downs to regard



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SPATIAL MODELS OF PARTY COMPETITION 375such an assumption with considerable skepti-cism. The postulate may be faithful to therealities of economic competition, and it servesthe cause of theoretical parsimony, but itsfactual validity in the political context isdoubtful, to say the least.If the model's assumption of common refer-ence is relaxed, its unified theory of voter be-havior and party positioning breaks at least intwo. The behavior of voters depends not onwhere or whether the parties are on an ideo-logical dimension but only on the electorate'sperceptionof these things. It would be possible,although highly improbable in view of what isknown about large-scale publics, for the moti-vation of voters to be governed by a calculus ofideological distance, even though the partieswere not competing for support in these termsat all. And it would be possible, and a gooddeal more probable, for the parties to seekelectoral support by positioning themselves onan ideological dimension, even though thepublic evaluated their stands in wholly non-ideological terms. Admittedly, it is extreme tothink of the pieces into which the spatial modeldivides (without the assumption of commonreference) as two completely intrapsychic theo-ries, since the voters' perceptions of partiesdepend to some degree on what the parties areactually doing and vice versa. But it is equallyextreme to assume away the possibility ofdivergence between the space that is real tovoters and the space that is real to partyleaders.Relaxing the assumption of common refer-ence necessarily opens Pandora's box. If we arewilling to assume that Kresge's and the cus-tomer's Main Street are not the same, there isno reason why Woolworth's Main Street can-not be different, too. We may, in fact, have asmany perceived spaces as there are perceivingactors. Certainly the way public policy alterna-tives are perceived varies widely across theelectorate. A few voters, as we have seen, im-pose a clear ideological structure on politicalconflict. But the vast majority rely on assortednon-ideological ways of structuring the politicalworld. And an appreciable stratum of voterscan scarcely be said to have any cognitivestructure at all as it tries to make sense out ofthat distant and confusing world.Likewise, different political leaders mayimpose different frames of reference on thealternatives of government policy. And theymay attribute very different cognitive struc-tures to the public. In the intraparty strugglepreceding the 1952 Republican convention, thelate Senator Taft and his lieutenants offered adiagnosis of the Republican situation that was

remarkably faithful to the one-dimensionalideological model. According to Taft, the coun-try had been moving strongly to the right onthe liberal-conservative dimension since theheyday of the New Deal, but millions of poten-tial Republican voters had been kept from thepolls by the party's liberal, "me-too" candi-dates (because demand is elastic, Willkie andDewey were said to have lost more votes in theparty's hinterland than they gained in itscompetitive region). Hence, victory lay innominating an unmistakably conservative can-didate. The Taft diagnosis and prescriptionhad an appealing simplicity, but the conven-tion was dominated by men whose view ofpopular thought was very different and far morerealistic. Their struggle to control the nomina-tion was fought at least in part on the issue ofhow the public looks at party competition.The truth is that we do not yet have verycareful evidence about what frames of refer-ence party leaders use in their perceptions ofthe alternatives of government policy and littleenough evidence about the cognitive structuresthe voters use. Various scaling studies of legis-latures suggest that at least the political spaceof legislators has a fairly definite structure, al-though it is typically multidimensional.' In avariety of multiparty systems the simple factorof seating legislators from left to right helpsgive political conflict a dimensional character-and has done so as far back as the NationalConvention of revolutionary France."6 It islikely that political leaders impute more struc-ture to the perceptions formed by the publicthan actually exists; in some cases party ac-tivists see the electorate in thoroughly Downs-ian terms, as Senator Taft did. But the ques-tion of what cognitive structures are meaning-

16 See, among others, Duncan MacRae, Jr.,"The Role of the State Legislator in Massachu-setts," American Sociological Review, Vol. 19(1954), pp. 185-194; Duncan MacRae, Jr., andHugh D. Price, "Scale Positions and 'Power' inthe Senate," Behavioral Science, Vol. 4 (1959), pp.212-218; and George M. Belknap, "A Method forAnalyzing Legislative Behavior," Midwest Journalof Political Science, Vol. 2 (November 1958), pp.377-402.

16 In view of the ambiguity of party ideologiesand the multidimensional grounds of party con-flict, the necessity of agreeing upon a unidimen-sional seating order can itself lead to conflict in alegislative chamber that follows a left-rightscheme. An interesting example of this is the at-tempt of the Finnish People's Party to move itsseats to the left of the Agrarian Party in Finland'sEduskunta after the 1951 election.



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376 THE AMERICAN POLITICAL SCIENCE REVIEWful to political leaders remains an immenselyimportant matter for future inquiry.

VI. TOWARD REFORMULATIONThe conclusion I would draw from all this isnot that the spatial model should be rejectedroot-and-branch but rather that we shouldtreat as explicit variables the cognitive phe-nomena that the prevailing model removes fromthe discussion by assumption. Bringing thesevariables into the model would lessen its ele-gance and parsimony in some respects butwould vastly increase the scientific interest ofthe model as a theory of party systems. With-out these variables the model is likely to re-main a kind of instructive insight that seemsplausible in some contexts, implausible inothers, and only poorly suited to guide em-pirical observation of real political events.One implication of treating these cognitivefactors as variables is to acknowledge that theycan assume a configuration of values in thereal world that approximates the assumptionsof the classical spatial model. Political conflictcan be focused on a single, stable issue domainwhich presents an ordered-dimension that isperceived in common terms by leaders andfollowers. Let us call this the case of strongideological focus. On the other hand, politicalcontroversy can be diffused over a number ofchanging issue concerns which rarely presentposition-dimensions and which are perceived indifferent ways by different political actors. Letus call this the case of weak ideological focus, acase that is well illustrated by the contempo-rary American scene.Treating these cognitive phenomena as vari-ables would lead naturally to a comparison ofpolitical systems in these terms. Certainlythere are very significant differences in thevalues these variables assume in different partysystems, just as there are very importantdifferences in their values for the same systemover time. Although the historical evidence istantalizingly ambiguous, I think it reasonableto conclude that the strength of ideologicalfocus in the United States was greater duringthe Roosevelt New Deal than it is today. Then,more than now, the intervention of governmentin the domestic economy and related socialproblems provided a position-dimension thatcould organize the competition of parties andthe motivation of electors.However, the moment of American politicalhistory when political conflict was most in-tensely focused on a single ordered-dimensionwas undoubtedly the period just prior to theCivil War. As the prewar crisis deepened, politi-

cal discussion became more and more absorbedin the overriding issue of slavery and its at-tendant controversies. The fact that the struggleover slavery had overtones of economic interestand constitutional theory and regional loyaltydoes not undermine the point; it is exactly thegathering of several facets of conflict into asingle dimension that characterized the politicsof the day. The focusing of controversy on thisdimension became at last so strong that it pro-vided a basis for the dissolution of long-stand-ing party loyalties in much of the electorate,something that has not happened again to anequal degree in a hundred years. This historicalcase is the more interesting since the all-con-suming dimension of conflict had so little to dowith the class-related dimensions that weusually associate with the spatial model.If a single position-dimension was of trans-cendant importance in the convulsions leadingto civil war, the spatial model ought to predictthe appearance of the new party of the prewarera. The period of the Republican Party's earlysuccess exhibited the strong ideological focusthat would make the model applicable. Thenthe period ought also to exhibit the conditionsfrom which we would predict the birth of a newparty. There is persuasive evidence that it did.As the dimension of slavery became more andmore salient, almost certainly there was ananti-slavery shift of opinion in the older statesof the North, just as there was a shift to a moreaggressively pro-slavery opinion in the South.And what is equally important, the Northernelectorate was rapidly extended in the fifteenyears prior to 1860 by the granting of state-hood to five new states-Wisconsin, Iowa,Minnesota, California, and Oregon-all anti-slavery. These changes in the North presentedthe Republican Party with the chance to ex-ploit a new "mode" of anti-slavery opinion towhich the Democrats and Whigs, in seeking tokeep the allegiance of old friends, were muchless able to respond. Yet if the slavery dimen-sion had been only one of several influencingthe electorate, the new party would hardlyhave succeeded. Only with the cognitive pre-conditions of the spatial model satisfied couldthe distribution of voters on the slavery ques-tion bring a revolutionary change in the struc-ture of the party system.Elaborating the model to take account ofthese cognitive variables is more than a matterof seeing that Downs's assumptions are metbefore plugging the model in. In particular,extending the model to the case of two or morestable, ordered dimensions will lead to resultsthat do not have any analogues in the one-dimensional case. For example, the degree of



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SPATIAL MODELS OF PARTY COMPETITION 377orthogonality of several dimensions clearly hasimplications for electoral behavior, party posi-tioning, and party number. And in the multi-dimensional case a good deal would rest onwhether the electoral support of the parties isdefined in terms of several dimensions at oncethat is, on whether the parties' support is basedon joint distributions or marginal distributions.At the very least the formation of coalitionswill differ according to whether the parties'electoral strength is differentiated on commonor distinct dimensions. The politics of Israel,for instance, will be quite different accordingto whether the parties are referred to all majordimensions of conflict-Zionism, secularism,socialism, attitude toward the West, and soforth-or tend to attract their support on thebasis of one or a very few dimensions only.The reaction to political models is likely todepend partly on taste for some time to come.So few formalizations have added to our knowl-edge of politics that their potential value canbe a matter for honest debate. The Hotelling-Downs model makes a good case for model-building in political research. Certainly no onewho compares the inferences this apparatuspermits with the inferences that can be drawnfrom loose popular ideas of spatial competitionwill fail to gain new respect for a model of thissort. However, the usefulness of models de-

pends absolutely on the interchange betweentheory-building and empirical observation.This interchange is essential to show the limitsof a model's application and guide its futuredevelopment. No theory is unconditionallytrue. Learning what the conditions are is anindispensable step toward giving the theory amore significant domain of application.If anything, the exchange between theory-building and empirical observation is moreimportant in social than in natural science,since the social scientist so rarely has it in hispower to make the conditions of his theorycome true, as the natural or physical scientistoften can. One reason the physicist is un-troubled by the fact that his law of gravity doesnot describe the behavior of many fallingbodies (snowflakes, for example) is that he isable to control the disturbing factors wheneverthe need arises. But the social or political theo-rist cannot manipulate the conditions of partysystems whose dynamics he would predict orexplain. No engineering is available to producethe conditions of strong ideological focus sothat the prevailing model of spatial competi-tion will apply. If it is to be empirically success-ful the theory itself must be extended to takeaccount of the varying cognitive elementsfound in the competition of parties in the realworld.

stokes 1963 spatial models

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