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Public Choice46: 45-60 (1985).
a 1985MartinusNijhoff Publishers,Dordrecht.Printedin the Netherlands.
The politics of flatland*
MATHEW D. McCUBBINS
THOMAS SCHWARTZ
Department of Government, University of Texas, Austin, TX 78712
Abstract
A versionof the median-votertheoremholds for two-dimensionalspatialmodels in which
votersregardthe two dimensionsas economicgoods or goodlikeactivitiesand in whichthe
set of feasibleoutcomesis constrainedby budgetor technology.Althoughmathematically
trivial,this facthaswidespreadanalyticaluses.Afterarguingthatourtwo-dimensional
model,
with its stabilityproperty,fits a numberof importantand generalpolicyareas, we use our
theoretical
issues.
analysisto addresssomeprominent
In the one-dimensionalspatialmodel of voting, voters'ideal points are arrayedalong a singleissue dimension,and any medianof these ideal points
mustbe stableundermajorityrule:no point is preferredto it by a majority.
This simplebut powerfulresult, which we owe to Hotelling(1929), Black
(1948, 1958),and Downs (1957: 115), contrastswith extant findingsabout
stability in multidimensionalvoting models. Not only need there be no
stablepoint in an issue spaceof two or more dimensions,but a numberof
instabilitytheoremsshow that there almost certainlywill be none, given
some plausible-lookingassumptions.
Thesetheoremscome in two varieties,spatialand exchange-based.In his
seminalcontributionto spatial voting theory, Plott (1967) showed that a
kind of perfect symmetryof voters' ideal points is sufficient for the existenceof a stable point. Enelow and Hinich (1983) have shown a weaker
but still quite severe condition to be necessary as well as sufficient.
McKelvey(1976), Schofield(1978), and Cohen (1979)have provedthat almosteverypossibleprofileof voterpreferencesyieldsa majority-preference
cycle that exhausts the issue space. The exchange-basedinstability
theorems,discoveredby Kadane(1973),Oppenheimer(1972),andBernholz
(1973, 1974),with correlationsand generalizationsby Schwartz(1976)and
variationsby Miller(1976)and Enelow and Koehler(1975), show that the
* We thank Gary Cox, Melvin Hinich, Peter Ordeshook,Gordon Tullock, and Harrison
Wagnerfor helpfulsuggestions.
46
outcomeof majorityvoting mustbe unstableif it requiresany vote trading
or similarexchange - any packagingof positions from different issues.
Schwartz(1981)hasgeneralizedthis set of theorems,droppingtheirvarious
restrictiveassumptionsabout individual preferencesand the collectivechoice rule while allowingthe set of feasible alternativesto be any subset
whateverof the cross-productof issues.
The lessonoften drawnfrom such resultsis that the tidy stabilityfeature
of one-dimensionalvoting models not only fails to hold generally for
models with two or more issue dimensions,but collapsesutterlyfor such
models: when there exist even two issue dimensions,the conditions for
stability are so severe that instabilityis a virtual certainty. Thus Riker
(1980):'Disequilibrium,or the potentialthat the statusquo be upset, is the
characteristicfeatureof politics.' (See also Fiorinaand Shepsle, 1982).
Such sweepingconclusions overstate the truth. The spatial instability
resultsrely on two empiricallyrestrictiveassumptions.Whenthese are replaced by an alternativepair, no less reasonableon their face, while the
numberof issue dimensionsis assumedto be two, the instabilityresultsno
longer follow, and a version of the median-votertheoremholds. This is
becauseourassumptionsenableus, in a sense,to reducethe two-dimensional case to the one-dimensionalcase.
Althoughutterlytrivial,this resulthas gone unremarkedin the literature,
perhaps because its analyticalpotential has not been appreciated.After
presentingthe model, its stabilityproperty,and some generalizations,we
show how the modelfits commonconceptionsof a greatdeal of real-world
politicalactivity:manypolicyquestionsare describedand debatedin terms
of our two-dimensionalmodel. We then use our analysis to address a
numberof issuesraisedin the literatureon majorityvoting, answeringquestions and extendingprevious results. In particular,we extend Shepsle's
(1979) resultregardingthe stabilityof decentralizedlegislatures.
1. Assumptions
The spatialinstabilitytheoremsall rest on two assumptions:
NO CONSTRAINT The feasibleset - the set of alternativesfrom which
a choice is to be made by majorityrule - is the whole positiveorthantof
the issue space:it is not constrainedby budget, technology,constitutional
principles,or anythingelse.
SATIATION Every voter has a point of satiation - an ideal point - in
the issue space.
47
A
A
0
B
(a)
0
B
(b)
Figure1.
No Constraint is also assumed by all the exchange-basedinstability
theoremsexcept that of Schwartz(1981); Satiation is irrelevantto those
results.
Althoughit is worthwhileto explorethe consequencesof No Constraint
and Satiation, neither enjoys any general validity. The No Constraint
assumptionignoresthe distinction,commonlyandcarefullymadein socialchoicetheory,betweenthe set of all conceivablealternativesand the feasible
set of the moment(Arrow, 1963:61; Plott, 1976;Schwartz,1984;Ch. 10).
Economic theory deals entirely with choices from sets constrainedby
budgetsor technology.Formaloptimizationproblemstypicallyrequireoptimizationsubject to constraints.Clubs, committees,parliaments,democraticpolities,andothervotingbodiesoften facepredetermined
budgetceilis
a
reasonable
ings, agendas, or ballot lists. In some contexts Satiation
assumption.In othersit is not. It is unreasonable,in particular,wheneach
dimensionhas the formalcharacteristicsof an economicgood: otherthings
being equal, more of it is preferredto less.
To deriveour median-voterresult, we assume that a finite numberof
n, are to choose among alternatives represented
....,
by points in two-dimensionalEuclidianspace. Contraryto No Constraint,
voters, Messrs. 1, 2,
we assumethat the feasibleset is constrainedby a (weakly)concave function, representedby the curveAB in Figure1. It is naturalto interpretAB
frontier.The feasibleset is the
as a budgetline or a production-possibility
closed set ABO.
Contraryto Satiation,we assumethat each voterhas indifferencecurves
withoutany satiationpoint, as in Figure2a ratherthan 2b. This meansthe
two issue dimensionsare goodlike: voters always favor an increasein the
level of activityin eitherdimensionwhen the other dimensionis held constant,and they maketradeoffsbetweenthe two dimensions,so that a voter
48
(a)
(b)
Figure2.
is willingto tradesome amountof activityin eitherdimensionfor any given
incrementof activityin the otherdimension.In short,eachvoterhas a utility function on two-space that is strictly increasingand strictly quasiconcave.
It has been suggestedto us that even a consumerof two economicgoods
has a satiationpoint, the point at which one of his indifferencecurvesis
tangentto his budgetline. What our assumptionrulesout, however,is not
such an inducedsatiationpoint, whichriseswith the subject'sbudget, but
rathera pure satiationpoint, whichremainsfixed even as budgetrises. At
an inducedsatiationpoint, the subjectis as happyas his budgetpermits.At
a pure satiationpoint, the subjectis as happy as his tastes permit.
In the two-dimensionalspatialvotingexamplesof Tullock(1967:Ch. 2),
votershave satiationpoints of a sort - optimalpoints, Tullockcalls them
- even though the two dimensionsrepresenteconomic goods (food and
fireworksat a club'sFourthof Julyparty).Thisis becausevotersaresimultaneously choosing a budget and its allocation: a voter's satiation point
representshis ideal budget(how much he thinks the club shouldspend for
the party)as well as his ideal allocationof that budget(betweenfood and
fireworks).We insteadassumethat the budgethas alreadybeen chosen, so
that higherlevels of spendingare infeasibleand any of the budgetthat is
not spent is simplywasted. In rc3 and 5, however,we examinewhat happens when voters must choose the budget as well as its allocation, both
separatelyand simultaneously.
2. The theorem
For each voter, thereexists a uniquepoint at whichone of his indifference
curvesis tangentto AB; call it his tangencypoint. A mediantangencypoint
is a tangencypoint suchthat no majorityof votershavetangencypointson
49
A
M
x
0
B
Figure3.
eitherside of it. Theremustexist eitherone or two mediantangencypoints
(as theremustexist eitherone or two mediansin any finite, weaklyordered
set).
One point beats anotherif a majorityof voters preferthe formerto the
latter. A stable point is a memberof the feasibleset that is not beaten by
any point in the feasible set.
Hereis our versionof the median-votertheorem:Giventhe assumptions
of our model (two dimensions,no satiationpoints, standardconstraint),if
Mis a mediantangencypoint or a point on AB betweentwo mediantangency points then M is stable.
Proof. Drawa line fromM to the origin,and let x be any point in the closed
set MBO. It is clear from Figure3 that any voter whose tangencypoint is
at M or to the left of M prefersM to x unlessx = M. But at least half the
votershave suchtangencypoints sinceno majorityof votershavetangency
points to the right of M. So x cannot beat M. Likewise,no point in the
closed set MAO beats M. Hence, M is stable.
Wherethe classicalmedian-votertheoremrefersto ideal points along a
singleissuedimension,ours refersto tangencypointsalong a budgetline or
production-possibilityfrontier.The only other differenceis that our feasible set containspoints belowAB as well as on AB. This means, in effect,
that our assumptionsensure stability by enabling us to reduce the two-
50
dimensionalto the one-dimensionalcase, or somethingclose to it. We cannot use the same ploy to prove a stabilityresult for threeor more dimensions, sincethe feasibilityconstraintwouldthenbe a hyperplaneor a convex
cone ratherthan a line or curve.
We can relaxthe assumptionthat the feasibleset is the closed set ABO.
To provethe existenceof a stablepoint, all we neededwerethe assumptions
(1) that the feasibleset is a subsetof ABO, and (2) that the feasibleset containssomemediantangencypointor somepointon AB betweentwo median
tangencypoints. Note that (2) is weakerthan the assumptionthat AB is a
subset of the feasible set. This relaxationallows a great degree of nonconvexitywhilemakingit easierto add constitutionaland otherconstraints
to the budgetaryand technologicalones alreadymentioned.
The assumptionthatvotersdo not havesatiationpointsalso can be weakened, in two ways:First, nothingin our proof precludesas manyvotersas
you pleasefrom havingsatiationpoints on or aboveAB. (Voterscan have
satiationpointsas long as the constraintis bindingto them, and theirsatiation pointsare not feasible.)A votermightfeel that no resourcesshouldbe
spent beyond a certainlevel, but the given budget might not exceed that
level. Second, we can allow as manyvotersas you pleaseto have satiation
points whereveryou please, providedthe feasible set consists just of AB
itself and AB is linear.' This proviso means, in effect, that the voters are
constrained,by constitutionalor other requirements,to allocateall of the
given resources.
3. Applications
A greatdeal of U.S. politicaldecisionmakingcan plausiblybe interpreted
as satisfyingeitherthe one-dimensionalmodelof Hotellinget al. or else our
two-dimensionalmodel. Here we surveyseven types of policy decision to
whichour model seemsapplicable- often becausepublicdebateor scholarlyanalysisalreadyis couchedin termsof two goodlikeissue dimensions.
We do not deny that some of these policy areascan be conceivedin other
terms, nor do we try to provethat policy choicesin these areasare best explained by our model. Rather, we argue that it is plausible and even
customary to characterizeeach of these policy areas in terms of two
goodlike issue dimensionsand that doing so yields some interestingand
credibleconsequences.Our purpose, in short, is hypotheticalratherthan
demonstrative - to recommend a tool for analyzing a large variety of policy
decisions under majority rule, not to elaborate and confirm any specific
analysis.
i) Explicit allocational decisions. Many voting decisions explicitly concern the allocation of a predetermined budget between two good-like activi-
51
ties - of whichvotersalwaysprefermoreto less, otherthingsbeingequal.
In decidingthe level of fundingfor the Office of Toxic Substances(OTS),
the HouseAppropriationsSubcommitteewithjurisdictionover EPA (Subcommitteeon HUD and IndependentAgencies)makesexplicittradeoffsbetweentwo broadcategoriesof OTS activity,enforcementand rulemaking.
Congressionalactivityon the 'Defensebudgettendsto concentrateon procurementand researchand developmentitems,' leavingunexaminedsuch
other items as personneland operations(Ripleyand Franklin,1976: 146).
In eachof thesecases,budgetis predetermined
by proceduresdetailedin the
is preBudgetand ImpoundmentAct of 1974.Budgetarypredetermination
valentin Americanpolitics:manystateconstitutionshave balanced-budget
clausesrequiringan independentexecutiveofficer to set budgetceilings.
ii) Separatechoice of budgetand allocation. Sometimesa committeeor
othercollectivityis not simplygiven a budgetto allocatebut has to choose
both a budget and its allocation betweentwo activities.When these two
choicesaremadesimultaneously,the outcomeneednot be stable.Suppose,
however,that budgetand allocationare decidedseparately:Messrs. 1, 2,
.., n firstchoosea budgetline,AB, thenchoosethe mediantangencypoint
on AB. Becausethe choiceof a budgetlineensuresthe choiceof the median
tangencypoint on that line, the budget choice is, in effect, a choice from
the locus, L, of median tangencypoints on all possible budget lines, as
shown in Figure4. It is reasonableand customaryto assumethat such a
choice is one-dimensional,or single peaked, so that the median-voter
theoremof Hotelling, Black, and Downs appliesto it: the median, M, of
voters' ideal points on L beats everyother point on L.2 Once the budget
representedby AB is chosen(becauseit containsM), our own theoremapplies:M beats everyother point in ABO. If budgetlevel is voted on again,
M will not be overturnedbecauseit beatseveryotherpoint on L. If allocation is voted on again,M will not be overturnedbecauseit beatseveryother
point in ABO.
iii) Regulatory issues. Economic regulation is often described as a
redistributionof market surplus from consumersto producers(Stigler,
1971; Posner, 1971, 1974; Peltzman, 1976). Such regulationoften establishes price and entry restrictions,creatingmonopolisticor oligopolistic
rentsfor producers.In choosinga regulatoryscheme,membersof a regulatory commissionor legislatureare choosingthe distributionof welfarebetweenthesetwo groups,whoseinterestsmaybe representedby ourtwo issue
dimensions.
If economic regulation is indeed two-dimensional, we would expect
regulatory outcomes to be fairly stable. As it happens, of the twenty-one
economic regulatory acts passed between 1900 and 1940, twenty remain
largely unchanged. Policy has changed little over the last five decades at the
Federal Maritime Commission (Mansfield, 1980) or at the Texas Railroad
52
A
Locus L of median tangency
points on all possible
budget lines
Median of voters' ideal
points on L
Somepossible budget
lines with their median
tangency points
0
B
Figure4.
Commission(Prindle, 1981). Wherechange has occurred,notably in the
regulationof civil aviation, there had been a changein the preferencesof
the two groups (and therewiththeir representatives)whose interestsare
representedby the two dimensions(see Weingast,1978).Withnew entrants
outcomeshiftedtowarddefavoringderegulation,the median-equilibrium
regulation.
For environmentalregulation,too, the policyproblemis two-dimensional. Pollutors wish to minimizethe costs of environmentalregulationto
themselves,but all else beingequal,wouldpreferless pollutionto more. Environmentalists(and others who bear the externalenvironmentalcosts of
productionand consumption)wish to minimizethe level of pollution, but
all else equal,wouldpreferto do so at the leastcost. Thus,both groupshave
naturalsatiationpoints at zero cost with zero pollution. The currentantipollution technologyguarantees,however,that these satiationpoints will
not be within the set of feasible alternatives,representedby the crosshatchedarea in Figure5.
Health and safety regulationalso fits our model. In the congressional
debateoverthe Toxic SubstancesControlAct, for example,the dimensions
of controversywere, naturallyenough,humanhealthand technologicalinnovation(McCubbinsandPage, 1983).Tradeoffsbetweenthesetwo dimensions areevidentthroughoutthe act and are spelledout explicitlyin the preamble.3 Similarly,the major tradeoff consideredin the debate over the
53
Regulation
of
Cost
Technological
Constraint
0
Quantity of Pollutants
Figure 5.
FederalFood, Drug, and CosmeticsAct was betweenhuman health and
costs to industry,particularlyto patent-medicinemanufacturers(Jackson,
1970).In effect, Ripleyand Franklin(1976)describethe debateover stripmininglegislationin termsof two dimensions:congressmenmadetradeoffs
between the quality of the environmentand the price of energy (pp.
99-103). Anderson,Brady,andBullock(1978)suggestthatthe debateover
energypolicyfits this two-dimensionalframework(pp. 51-58, 98-100). As
our model predicts,environmental,safety, and healthregulationshave remainedstablein form and substanceoverthe last five decades(McCubbins,
1982:Ch. 10).
iv) Haves vs. have-nots.Often policy decisionsconcernthe allocationof
socialproductbetweenprosperousand nonprosperousclassesof citizens between haves and have-nots. Medicarewas explicitly redistributivebetweentwo classes(Marmor,1973),and the debatefocusedon the interests
of those classes(see also Ripleyand Franklin,1976;Friedman,1969;and
Anderson,Brady,and Bullock, 1978).Mortgagesubsidyprograms,old-age
assistance,and Aid to Familieswith DependentChildrenare similarlytwodimensional(see Ripley and Franklin, 1976). Rural electrificationredistributeswealth from urbanto ruralareasthroughpublic-worksprograms
and constructionloans. Protectivetariffs transfersurplusfrom domestic
consumersand foreignproducersto domesticproducers.In each case the
54
big question is two-dimensional: how much of the pie does each of the two
contending sides get? The constraint, the size of the pie, is derived from the
production-possibility set. And in each case the program is well entrenched,
exhibiting remarkable stability (Wilson, 1980).
v) Guns vs. butter. National political controversies often concern the
allocation of resources between national security and domestic improvements - guns and butter. Although voters differ in their marginal rates of
substitution, just about everyone would like to do as much as possible, all
else constant, in each of the two categories. For the most part, then, voters
do not have satiation points - or, at least, none that fall below reasonable
budget ceilings - but do have different points of tangency with the budget
line. As our analysis predicts, the allocation of resources for national security is relatively stable, hovering about 6% of the GNP since the Second
World War.
vi) Macro-economic policy. Sometimes fiscal policy is debated in terms
of tradeoffs between full employment and price stability, two goodlike issue
dimensions (Anderson, Brady, and Bullock, 1978: 182-88). To be sure, the
issue is not always so simple: such additional dimensions as public-sector
size sometimes come into play.
vii) Private vs. public. Often ideological differences between political
candidates (and parties) concern the allocation of social product between
private and public consumption (or the private and public sectors): conservatives differ from 'liberals' in favoring more private and less public consumption. In this interpretation, AB represents the technology available to
political parties, given constitutional limits on their activities. If the vertical
axis represents public spending and the horizontal axis private spending
then most conservatives will have tangency points to the right of those of
most liberals. Given the constancy over time of public opinion regarding the
relative size of the public and private sectors (Page and Shapiro, 1982), our
model explains why public spending has remained fairly stable as a proportional share of GNP.
Even if each of these seven types of policy question can be conceived in
terms of two goodlike issue dimensions, a combination of two or more of
them cannot. We hypothesize, however, that there is a tendency in political
debate and congressional voting not to combine these questions. Politicians
might debate and decide the allocation of the federal budget between guns
and butter and separately debate and decide the allocation of the butter
budget between haves and have-nots, but they do not usually debate or
decide, as a single question, the allocation of the federal budget among
guns, butter for the rich, and butter (or oleomargarine) for the poor.
55
4. Implications
Besidesshowingthat at least one importanttwo-dimensionalvoting model
guaranteesstability,our little theoremcasts light on four issues that have
been raisedin the literature:
i) Stability of two-partypolities. The peculiar stability sometimes attributedto certain(moreor less) two-partypolities, such as GreatBritain,
might be explainedon the basis of our model as follows: Each partyhas a
permanentprimary constituency - a fairly well-definedclass whose interestsit triesto promote.The two dimensionsrepresentthe interestsof the
two constituencies.AB representssocialproductor welfaresurplus- whatever it is that the governmentcan allocate. Apart from cost, every voter
regardsthe interestof each primaryconstituencyas worth serving.Thus,
votershaveno satiationpoints. Swingvoters,who belongto neitherprimary
constituency,profit to some extent from policiesthat favor eitherprimary
constituency,althoughthey prefera mixedpolicyto the moreextremeallocationsfavoredby the primaryconstituencies.Eachpartytriesto win favor
with sufficientlymanyswingvotersto securea majorityof votes. (Herewe
follow Downs, 1957:144, in simplifyingrealvotingschemes:puremajority
rulediffers, for example,fromrepresentationby single-memberconstituencies.) Ourtheoremsuggeststhat the winningparty'splatformwill be nearer
thanthat of the losingpartyto the mediantangencypoint of the electorate.
ii) No vote tradingon two-dimensionalallocationalissues. By virtueof
the theoremof Schwartz(1981), the outcomeof majorityvoting - or, for
that matter,any collective-choiceprocess - mustbe unstableif it requires
vote trading.Becausethis is truehoweverthe feasibleset be constrainedand
whatevervoter preferencesmay be, nothing in the theoremconflicts with
our assumptions(standardconstraintand nonsatiation).Thus, since our
assumptionsimply stability, they furtherimply that the final voting outcome cannotrequirevote trading:whenvotersdecideby majorityrulehow
to allocatea given budgetbetweentwo activities,they have no incentiveto
trade votes.
This consequencewill be less surprisingif looked at as follows: Thinkof
AB as a budget line. Owing to our nonsatiationassumption,every voter
wants to spendthe entirebudget. But the game of choosingamongpoints
on the budgetline is constantsum, hencestrictlycompetitive.Consequently, mutualgains from trade are impossible.
iii) Stabilityof redistributivechoicesin a democracy.A classiccase of instability under majority rule is that of three people deciding by majority rule
how to divide a dollar (or other infinitely divisible good) among themselves.
Ward (1960) generalized this example, arguing that purely redistributive
choices always are unstable in a democracy. This assumes a multidimensional model in which each dimension represents the interest of a single
56
voteror, at most, a groupcomprisinga minorityof voters(FrohlichandOppenheimer,1978:126).Often, however,redistributivequestionsare cast in
termsof only two dimensions,representingthe interestsof havesand havenots. In suchcases,strictlyredistributivechoicesare, if anything,peculiarly
stable.The U.S. socialsecuritysystem,for example,has provedremarkably
stable. Although the median outcome shifts with changes in the demographicsof the Americanelectorate,the systemhasendured(andexpanded)
for the last half century.
iv) Stabilityin decentralizedlegislatures.Shepsle(1979)has constructed
a model of decentralizedlegislaturesin which (1) every legislator has
separablepreferences,(2) decisionsare made by autonomoussubcommittees with nonoverlappingand selfselectedmemberships,(3) each subcommitteechooses along a singleissue dimension,representingits jurisdiction,
and (4) thereis no collusionbetweensubcommittees.In this model, the vector consisting,for eachdimension,of the medianidealpoint of the subcommittee responsiblefor that dimensionis stable in the following sense: no
grouphas the powerand incentiveto overturnit. Shepsle'sresultis important because Congressseems to approximatethe model. Even assuming,
however,that subcommitteejurisdictionsare quitenarrow,assumption(3)
is ratherstrong.But our theoremshows that (3) can be relaxedas follows:
each subcommitteeeitherchooses along a singledimensionor else chooses
from a two-dimensionalspace for which there is a predeterminedbudget
constraintand no satiationpoints or no feasiblepoints below the budget.
The secondpartof this relaxedassumptionseemsespeciallyrealisticfor Appropriationssubcommittees,whose choices are constrained(ideally, at
least) by a concurrentbudgetresolution.
5. Conclusion: Why so much stability?
So askedGordonTullock(1981)in his famouschallengeto a PublicChoice
communityenthralledby variousinstabilitytheoremswiththeirintimations
of universalpoliticalchaos:
If we look at the realworld ... we observenot only is thereno endlesscycling,but acts are
passedwith reasonabledispatchand then remainunchangedfor very long periodsof time.
Thus,theoryand realityseemto be not only out of contact,but actuallyin sharpconflict.(p.
189)
A partial answer to Tullock's question is that so much of American politics
fits our two-dimensional model with its stability property. This, however,
is only the beginning of a long story. Here are a few topics demanding further investigation:
57
L
A
M'
M
0
x
B
Figure6.
i) Besidesthe broad policy areaswe have surveyed,thereare likelyto be
othersthat fit our model. In additionto identifyingthese, it wouldbe interestingto identifypolicyareasthat cannotbe madeto fit our model - limits
on the model's domain of application.
ii) Some policyquestionsare conventionallyframedin termsof our twodimensionalmodel when they could as easily be framedin termsof three
or more issue dimensions - witness redistributivequestions, which we
usually discuss in terms of the interestsof haves vs. have-nots, older vs.
youngergenerations,urbanvs. ruralpopulations,and the like. Whyis this?
One possibleexplanationmightbe basedon the stabilityof our two-dimensional model:perhapsthe practiceof framingso manypolicy questionsin
terms of two goodlike issue dimensions is a convention that somehow
evolvedbecauseof its stabilizingeffect.4 Part of what has to be explained,
of course,is whyit is (if it is) that societytendsto selectstabilizingpractices.
iii) When the constraintAB is a budget line, stability depends on the
assumption- true in many cases - that the budgetis chosen priorto or
separatelyfrom its allocationbetweenthe two dimensions.Canthe tendency to separatebudgetaryfrom allocativedecisionsbe given a generalexplanation?Can it be explained,in part, by the stabilityit helps ensure?
iv) Factoranalysisof pollingdata fromU.S. presidentialelectionsshows
the U.S. electorateto have preferencesrepresentedin two issuedimensions
(Weisbergand Rusk, 1970;Ruskand Weisberg,1972;Enelowand Hinich,
1984).To applyourmodel,we canassumethatAB representssocialproduct
or prevailingpolitical technology. But can the two issue dimensionsbe
58
regardedas goodlike, so that votershave no satiationpoints?The problem
is that althoughone of the dimensionsseems to be 'social' and the other
'economic,' it is not clear how more preciselyto describethem.
v) Supposebudgetand allocationare decidedsimultaneously(as a single
package)ratherthan separately.It is still true, of course, that the M of
Figure4 - the medianpoint on the locus L of mediantangencypoints on
all possiblebudgetlines - beatseveryother point on L and everypoint in
ABO. Once M is reached,then, it will not be overturnedin favor of any
otherpoint on L or any other point in ABO. But it mightbe overturnedin
favor of a point x that lies above AB but off L, as in Figure6. Becausex
would be beatenby the mediantangencypoint M' on the potentialbudget
line that intersectsx, whileM' wouldin turnbe beatenby M, a cyclewould
result:M would not be stable. Still it has a partialstabilityproperty:it is
downwardstablethough not upwardstable. This meansthat if instability
causes a budget revision, the result must be a budgetaryincrease, not a
decrease.Can this finding be used eitherto demonstrateor to explainexcessivelyhigh budgets?Does M have any further(partial)stabilityproperties? Can any normativejustificationbe given for the choice of M over the
likes of x?
NOTES
1. Nonlinearitymakesit possiblefor one voter to have two tangencypoints.
2. Althoughreasonable,this assumptionis not necessary.Supposea particularvoter has a
satiationpointwhenconsideringbudgetlevelandallocationtogether.Thenone of his indifferencecontoursmightbe tangentto L at more than one point.
3. On TOSCA,see Libraryof Congress,ThelegislativeHistoryof the ToxicSubstancesControl Act, Washington,D.C.: U.S. GovernmentPrintingOffice, 1976.
4. On relatedstabilizingnormsor practices,see Mayhew(1974)and Weingast(1979).
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