Weingast B.R., Wittman D. The Oxford Handbook of Political Economy

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92 political income redistribution

average transfer, the third candidate would incur negative votes only from the 25 per

cent of voters who received oﬀers above one-half from both of the other candidates,

whereas the other candidates would evenly divide the remaining negative votes, each

getting 37.5 per cent. Of course, equal oﬀers is not an equilibrium, even with three

candidates, but the oﬀer distribution that does emerge in the symmetric equilibrium

includes a maximum oﬀer of only

times the average, a minimum oﬀerof0and

a standard deviation of only 0.45, about half the value for the equilibrium oﬀers

under simple majority rule. With more than two contenders under negative approval

voting candidates are more concerned about not making enemies than they are with

cultivating loyal friends—a candidate who is the next to last choice of every voter

receives no negative votes!

Myerson shows that among the array of electoral systems he considers, simple

plurality rule, with its intense rewards for cultivating a plurality of supporters, and

its mild penalties for making enemies, leads to particularly unequal allocations of

campaign promises.

4 Redistribution Targeted to

Heterogeneous Groups

.............................................................................

Wenowturntomodelsinwhichvotershaveallegiancestopoliticiansorpolitical

parties that cannot be fully unmade during the course of a single election cycle.

Several of these models

share a common structure. So to simplify the exposition,

I will present their common ideas in the context of the Dixit and Londregan (1996)

model, showing which parts of the structure need to be modiﬁed to lead to each of

the other models.

Voters in these models care about consumption, and they have attachments to

parties. The parties make balanced budget promises about the amount of redistri-

bution they will oﬀer. While the parties are not acquainted with the voters and their

preferences on an individual level, they can treat diﬀerent groups of voters diﬀerently,

and they observe the distribution of party attachments for each group. These groups

reﬂect the accuracy of politicians’ information about the voters. Poorly informed

politicians may only be able to apply a fairly coarse partition of the electorate: men

and women, blue-collar and white-collar workers, renters and retirees, and so forth.

More astute politicians (and those better supplied with accurate information) may

be able to make much ﬁner distinctions, for example treating beer-drinking Catholic

steel workers’ union members in Pittsburgh diﬀerently from teetotaling Protestant

¹³ In the symmetric equilibrium the probability density function f (x) for each candidate’s oﬀers will

be f (x)=

√

9−6x

for x on the interval [0,

), and zero otherwise.

¹⁴ ThesearedevelopedinCoughlin1986; Lindbeck and Weibull 1987; Dixit and Londregan 1995, 1996,

1998, 2000.

john londregan 93

steel workers’ union members from Youngstown. However ﬁne the information parti-

tion available to the parties, they recognize that the groups retain some heterogeneity:

even among the beer-drinking Catholic steel workers’ union members of Pittsburgh

one will ﬁnd a few Republicans. Of course, the distribution of preferences will diﬀer

across groups.

Each party must promise to treat all members of a given group in the same way, but

they can treat diﬀerent groups of voters diﬀerently.

The parties try to maximize their

vote shares.

The key feature to this family of models is that voters make a trade-oﬀ

between their partisan attachment and the attractiveness of the transfers that are on

oﬀer.

To formalize this, index groups by g ∈{1,...,G}. Suppose the value to a member

of group g of privately consuming c

is U

). There are two parties, labeled L

and R. Suppose that party L oﬀers every individual in group g an after-tax-and-

transfer consumption level of c

,whilepartyR oﬀers c

. A member of group g

with a partisan attachment to party R measured by X (with higher values of X

indicating greater levels of partisan attachment) will vote for party L if the diﬀerence

between the utility of consuming party L’s oﬀered income transfer U

), and the

utility of consuming party R’s oﬀered income transfer U

) exceeds her partisan

attachment to party R:

) −U

) > X (5)

while she will give her vote to party R if the inequality is reversed.

Here, to keep things simple, everyone in the group has the same pre-transfer

earnings power, and the same post-transfer consumption. However, each group

member has her own degree of attachment, X,topartyR.DeﬁneX

, c

)as

the attachment to party R that leaves a group g voter indiﬀerent between voting for

L and voting for R. Of course, this depends on c

and c

.Holdingtheoﬀer from

party R constant, an increase in c

will increase X

, while a more generous oﬀer

from party R, corresponding to a larger value for c

will lead to a reduction in X

If we let the function 

(X)telluswhatfractionofgroupg have an attachment

to party R of X or less, while N

is the number of individuals in group g ,thenparty

L will receive N



) votes from members of group g ,whilepartyR receives the

other N

[1 −

)] votes.

IfweaddupthevotesN



, c

)), from each

group, we have the total vote for party L:

({c

, c

}

g=1



g=1



, c

)) (6)

¹⁵ At this point it is useful to note that there is a strong similarity between models in which

politicians are uncertain about the type of an individual, as in Coughlin, and models in which they

confront a heterogeneous group of individuals who must all be treated equally, as in the Cox and

McCubbins, and Dixit and Londregan models. In ex ante terms, making an oﬀer to N individuals each

of whom has a 40% chance of accepting it is very similar to making the same oﬀer to a group, 40% of

whom will accept it.

¹⁶ Though Lindbeck and Weibull 1987 and Dixit and Londregan 1998 consider variants of the model

in which the parties seek instead to maximize their probability of election.

¹⁷ All voters are assumed to vote for their most preferred party rather than abstain.

94 political income redistribution

Since everyone votes, the objective for a vote-maximizing party L is to make V

aslargeaspossible,whilepartyR maximizes its vote by making V

as small as it

can.

While every party would like to audition for the role of Santa Claus, oﬀering high

consumption levels to all voters, they face the grim reality of a budget constraint. The

transfers made to all groups must sum up to the total resource endowment of the

government, B. In several models, this is zero, so that every transfer to one group

of voters entails a transfer from other voters. If we let T

denote the net per capita

transfer to group g oﬀered by party p, then the cost of the party p promise to group

g is simply N

, the per capita transfer times the number of members in the group;

notice that this number could be negative if group g is taxed to ﬁnance transfers to

other groups. The budget constraint requires that when we add up the costs of the

party p platform across groups, the total cost does not exceed B:



g=1

≤ B where p ∈{L , R} (7)

In a vote-maximizing equilibrium, party L chooses the consumption levels it oﬀers

to voters, {c

}

g=1

, in order to maximize its total vote (6) subject to satisfying the

budget constraint (7), taking the oﬀers of party R; {c

}

g=1

as given, while party R

chooses its consumption oﬀers; {c

}

g=1

to minimize the party L vote (6) subject to

the budget constraint (7) on its own transfer oﬀers, and taking the oﬀers of party L;

}

g=1

,asgiven.

This framework subsumes several important variants

as special cases. One of

these is Coughlin (1986), who assumes a particular functional form for the distribu-

tion of preferences that leaves the median member of every group indiﬀerent between

the parties but allows some groups to be more responsive to redistributive oﬀers

than are others. This is a stylized setting with no deadweight losses due to taxes and

transfers, and full symmetry between the parties. Under these circumstances he ﬁnds

that the parties will make identical oﬀers to each group, with the most responsive

groups gleaning the highest transfers.

Lindbeck and Weibull (1987) substantially generalize Coughlin’s formulation to en-

compass a much wider and more interesting set of circumstances. In particular, they

generalize the utility function, and the model for politicians’ uncertainty about voter’s

leanings, allowing for the possibility that groups exhibit electoral biases. However,

they continue to assume that the parties are the same in terms of their abilities to

transfer resources.

Lindbeck and Weibull generalize Coughlin’s prediction that both

parties will make identical transfer oﬀers to every group.

Lindbeck and Weibull go on to consider the impact of voter apathy (so that indif-

ferent voters do not bother to cast ballots), which shifts the balance in favor of groups

¹⁸ For example the models of Coughlin 1986 and Lindbeck and Weibull 1987, and Dixit and

Londregan 1995.

¹⁹ In one formulation of their model they do experiment with deadweight losses from taxation,

which they refer to as “administrative costs,” but these are taken to be quadratic, and to be the same no

matter which party is levying the tax.

john londregan 95

of voters with relatively many members at the point of indiﬀerence between voting

or not voting, as opposed to favoring groups with relatively many voters indiﬀerent

between the two parties. Lindbeck and Weibull also consider the possibility that

parties seek to maximize the probability of winning, as opposed to trying to maximize

their plurality. In this case parties’ attention is shifted toward voters who tend to be

partisans of the more popular party.

One of the most striking behavioral implications of the Lindbeck and Weibull

model is their claim that, absent voter apathy, redistributive politics will tend to

favor “swing voters” with relatively moderate preferences. To obtain this implication,

Lindbeck and Weibull make a set of assumptions almost as strong as Coughlin’s, and

their result hinges on assumptions about diﬀerences in the marginal responsiveness

of diﬀerent groups to oﬀers of income redistribution. If relatively moderate voters are

assumed to be relatively responsive to transfers, then they will fare relatively well.

In a closely related model

Dixit and Londregan (1996)pointoutthattheactual

size of groups is largely irrelevant to the transfer they receive. What matters is the

relative payoﬀ in votes per dollar that a party receives when it makes a transfer

to the group. This helps to explain why relatively small groups, such as US alfalfa

farmers, can receive large per capita subsidies at the expense of large groups, for

which the subsidies impose small per capita costs. This is what we would expect if

the beneﬁciaries, for example the alfalfa farmers, included relatively many “swing

voters” prepared to change their votes on the basis of the transfers they receive, while

groups paying the taxes to ﬁnance the transfers contain a relatively small proportion

of swing voters. This provides a potential explanation for small groups beneﬁting at

the expense of large ones that relies neither on imperfect information nor on the costs

of collective action.

Note that Lindbeck and Weibull are both from Sweden, where subsequent empiri-

cal analysis of local transfer schemes supports the hypothesis that communities with

relatively many swing voters receive relatively favorable treatment in redistributive

politics (Johansson 2003). In contrast, Ansolabehere and Snyder (2003) ﬁnd that in

state-levelpoliticsintheUSA,itisthecountiesthatarethemoststalwartsupporters

of the party in power that receive the most favorable treatment in redistributive

politics. So it is perhaps not surprising that Cox and McCubbins (1986), two students

of US politics, construct a model in which core supporters of each political party are

more responsive to oﬀers of redistributive beneﬁts.

Unlike Coughlin and Lindbeck and Weibull, Cox and McCubbins identify core

supporters as more reliably responsive to oﬀers of redistributive beneﬁts.

Dixit and

Londregan (1996) show that one can obtain very similar results to those of Cox and

McCubbins within the framework presented here if one assumes that the parties

diﬀer in their eﬃciency at making transfers. If core supporters are easier to reach

²⁰ In this version of the model party L seeks to maximize its vote share, given by (6) subject to the

budget constraint in equation (7), with no “leaky bucket” problems, while party R seeks to minimize the

party L vote subject to its own budget constraint.

²¹ The Cox and McCubbins model takes equation (6) as primitive, rather than deriving it from an

individual-level model of voter behavior.

96 political income redistribution

with transfers this will increase the “payoﬀ” in votes per dollar of making transfers

to them. Of course, this has to be weighed against core groups’ loyalties, which may

make it unnecessary to oﬀer them bribes. In the context of urban machine politics

in the nineteenth-century USA the assumption that the parties’ eﬃciency at making

transfers diﬀered across groups and parties seems to ﬁt well, and it is perhaps not

surprising that the urban political machines of that era tended to cultivate groups

of core supporters. In the context of twenty-ﬁrst-century politics in Scandinavia

with a large government bureaucracy that is relatively insulated from direct par-

tisancontrolwemightexpectthepartiestobeaboutequallyeﬃcient at making

transfers, leading to the focus of tactical redistribution on swing voters observed

by Johansson (2003).

With the exception of the Cox and McCubbins model, which takes the voting

probability functions as given rather than explicitly tracing them back to voters’

preferences, all of the models considered thus far in this section share the feature that

voters have attachments to parties that are additively separable from consumption.

Yet one of the most important objects of political conﬂict in the contemporary world

is the redistribution of income itself. The assumption that political preferences and

preferences over private consumption are separable is untenable when the parties’

main ideological programs are focused on the distribution of incomes.

Dixit and Londregan (1998) address this concern by constructing a model that en-

compasses both “tactical redistribution” aimed at appealing to voters by oﬀering them

higher levels of private consumption, and “programmatic” redistribution, in which

the parties’ ideological programs prescribe diﬀerent levels of income inequality and

ineﬃciency. In this model, the overall shape of the income distribution has aspects of

a public good, but it is a public good about which voters harbor disagreements.

In Dixit and Londregan (1998) the budget constraint is augmented to encompass

the deadweight losses of taxation by making these a quadratic function of the dif-

ference between initial allocations and actual consumption; thus redistribution is

accompanied by inevitable ineﬃciencies.

Rather than simply seeking to maximize votes, the parties in Dixit and Londregan

(1998) care about winning and they care about policy. Policy preferences in this model

are weighted averages of two archetypes: an extreme leftist social welfare function that

cares only about inequality, and an extreme rightist social welfare function that cares

only about avoiding the ineﬃciencies imposed by taxation.

Taking these one at a time, the archetypal leftist social welfare function seeks to

minimize the variation of incomes. That is to say, it seeks to make the distance of

each person’s consumption from average small, with large deviations from the aver-

age being treated as disproportionately more serious. Dixit and Londregan capture

this idea using the sample variance of incomes, e.g. the average squared distance of

incomes from the sample mean consumption level of

c. Given that consumption for

each member of group g is c

,andthatgroupg has N

members, the average squared

deviationisgivenby−S

({c

}

g=1

)where:

({c

}

g=1

)=−

g=1

−

(8)

john londregan 97

Notice that the archetypal social welfare function for the left, S

({c

}

g=1

), which is

largest when the variance of consumption levels is smallest, depends on the consump-

tion level of each group.

Now let’s turn to the archetypal social welfare function for the right. This welfare

function cares only about minimizing the ineﬃciencies implied by taxation and

transfers. These are modeled as increasing with the square of the gap between an

individual’s actual consumption level, c, and her endowment, y, yielding a loss of

−(y −c)

. As all members of the same group g have the same endowment, y

,and

the same consumption level, c

, the contribution of the N

members of group g to

the deadweight losses is N

− y

)

. When we add up these deadweight losses for

all the groups we have the archetypal rightist social welfare function S

({c

, y

}

g=1

({c

, y

}

g=1

)=−

g=1

− y

)

(9)

Political parties (and individuals) in the Dixit and Londregan (1998)modelcare

about both ineﬃciencies and inequality, but those on the right place more weight on

ineﬃciencies, while their counterparts on the left place greater weight on inequality.

Voters also diﬀer in the relative weights they place on both sets of considerations. A

type ˜ voter in group g will side with the party whose promised redistributive scheme

oﬀers the highest value for:

+(1− ˜)S

({c

}

g=1

)+˜S

({c

, y

}

g=1

) (10)

Notice that in this framework

there is no longer a primitive preference for one party

or the other. Instead voters care about the transfer they receive, the level of taxes, and

the amount of inequality implied by each party’s proposed policies. However, voters

with higher values of ˜ will, all else equal, be more sympathetic to the goals of party

R, while lower values for ˜ predispose voters towards party L. There is a similarity

between ˜, the relative weight placed on the rightist welfare function, and X,the

partisan attachment to party R that was central to several of the models discussed

previously.

The parties choose redistributive schemes subject to the budget constraint in order

to maximize a payoﬀ that depends on the value to them of being elected, and on

their preferences over the promised policy platform, which itself balances the goals

of eﬃciency and equality. All else equal, the party on the left will give more weight

to equality while the party on the right will place more emphasis on eﬃciency when

committing to taxes and transfers. More “power-hungry” parties will be less willing

to sacriﬁce votes in order to adopt ideologically pure platforms, and so they will more

aggressively favor blocks of swing voters.

²² As in several of the other models considered in this chapter, groups diﬀer in their willingness to

sacriﬁce their most preferred distribution of income for greater private consumption beneﬁts. Higher

values for · correspond to groups that are less concerned about the overall distribution of resources, as

compared with the level of their own personal consumption.

98 political income redistribution

In the equilibrium that emerges from this framework each party oﬀers a linear

tax rate Ù on income,

with the party placing relatively more weight on equality

setting a higher tax rate, and then, depending on parties’ degree of power hunger,

the resulting revenues are divided between redistribution from the well oﬀ to the

poor and lump-sum payments to groups of swing voters. Qualitatively, the tendency

for tactical redistribution to favor “swing voters” survives even when the focus of

programmatic diﬀerences between the parties is the very distribution of income itself.

5 Imperfect Information and

Redistribution

.............................................................................

Another approach to modeling redistribution is to assume that voters are not equally

well informed. Notably, Olson (1965) looked at asymmetries among voters. He con-

tended that small, well-organized groups with high per capita stakes would tend to be

better informed (and otherwise more eﬀective in the political struggle for resources)

than their larger, poorly organized counterparts with low per capita stakes. Part of this

heuristic argument is formalized by Lohmann (1998), who shows that in the context

of a model with quadratic preferences, politicians will rationally tilt policy in favor

of better-informed blocks of voters, be they large or small. This is because the better-

informed voters are more responsive to oﬀers of transfers (and threats of taxes) than

are their less well-informed fellow citizens. Add a story about why small groups with

high per capita stakes are better informed and this leads to Olsen’s prediction. Coate

and Morris (1995) also model redistribution using a framework in which information

asymmetries have an important eﬀect on redistributive outcomes.

Acompletelydiﬀerent approach to imperfect information is provided by Piketty

(1995). His interest is in the persistence of individuals’ political orientations as their

economic interests change. He oﬀers an interesting potential explanation for this:

in the context of a model akin to that of Meltzer and Richard (1981), individuals’

preferences for redistribution are sensitive to their beliefs about the incentive eﬀects

of taxation. In Piketty’s model, inﬁnitely lived dynasties of individuals form beliefs

about the relative importance of eﬀort and luck (parameterized by a parameter that

measures the impact of eﬀort) on economic outcomes. The greater the importance

of eﬀort, the higher the deadweight losses from taxation, and the lower an individ-

ual’s preferred tax rate—even when individuals care about the level of inequality.

Piketty notes that under plausible assumptions, dynasties with a greater belief in the

importance of eﬀort will tend to be wealthier, while those that believe in luck will

²³ While the linear functional form depends on the details of the utility function, it is perhaps

surprising that this redistributive model which allows parties to select G distinct tax rates results in a

linear tax rate on income (albeit one that is supplemented by lump-sum taxes and transfers), thus

obtaining endogenously as a result of the model the sort of tax rate which parties are exogenously

constrained to use in many of the models discussed in Section 2.

john londregan 99

tend to be poorer, though as long as there is at least some luck involved in economic

outcomes there will be a mixture of dynasties among both the well oﬀ and the impov-

erished.

Moreover, dynasties will adapt, partially, to new information, so that the

newlypoorshifttheirviewsleftward,butwillremaintotherightoftheirchronically

poor neighbors in the income distribution, and likewise, the nouveaux riches will

be to the right of their parents, but to the left of “old money” dynasties that have

remained well oﬀ for generations. The qualitative predictions of the Piketty model

are consistent with some stylized facts from polling data comparing economically

mobile individuals with people whose incomes have remained stable, and with some

cross-national evidence. By recognizing the importance of imperfect information on

the part of voters about the structure of the economic system Piketty has opened up

a very promising, and as yet under-exploited, avenue for future research.

6 Conclusion

.............................................................................

I do not pretend that the preceding pages constitute anything like an exhaustive

review of the literature on the political redistribution of income. Instead, they are

intended to introduce some of the salient issues, and to inspire or provoke scholars to

contribute to our advancing knowledge about this central topic.

As the reader has seen, the literature on political income redistribution has taken

several directions, depending on the particular interests of researchers. One strand of

the literature imposes restrictions on the set of tax schedules that can be imposed.

Keeping the redistributive component of the model simple facilitates the incorpora-

tion of other considerations into tractable models, an approach that has been taken

with respect to locational models, in which citizens can simultaneously vote with

their hands (by casting ballots in local elections) and with their feet (by relocating

to districts with policies they prefer).

This approach has also been applied to the

analysis of non-majoritarian electoral systems.

Another segment of the literature has examined the the fundamental instability of

pure redistributive politics, in which almost any allocation is subject to “poaching”

by political entrepreneurs, and by those who are badly treated by the status quo allo-

cation. Building on these models, scholars have integrated redistributive politics with

other, not necessarily orthogonal, considerations of party loyalty and programmatic

ideological policies on the part of candidates and parties. Another direction taken in

response to the “chaos” of pure redistributive politics has been to seek stability in the

form of institutions, such as those that promote universal coalitions in legislatures.

²⁴ To keep his model simple Piketty resorts to some technical slight of hand to prevent his agents

from experimenting to learn more about the importance of eﬀort. Work by Rothschild 1974; McLennan

1984; Easley and Kiefer 1988;andAghionetal.1991 indicates that even when such experimentation takes

place there are circumstances in which even inﬁnitely lived agents will not choose to learn fully the

characteristics of their economic environment.

²⁵ See the chapter in this volume by David Wildasin for a discussion of this family of models.

100 political income redistribution

Yet another family of models focused on political income redistribution has looked

at the importance of asymmetric information in shaping the distributive policies of

governments. While the literature has almost universally adapted the hypothesis that

agents know the structure of the model, relaxing this assumption to allow asymmetric

information about the structure of the economy, opens an exciting frontier for further

research.

Along all fronts, the literature discussed here has been cumulative, with scholars

building on existing results developed by others. This has facilitated rapid progress

over the past thirty years, and holds out the promise of much more to come during

thenextthirty.

References

Aghion,P.,Bolton,P.,Harris,C.,andJulien,P.1991. Optimal learning by experimentation.

Review of Economic Studies, 58: 621–54.

Ansolabehere,S.,andSnyder,J.M.2003. Party control of state government and the distri-

bution of public expenditures. MIT Dept. of Economics Working Paper No. 03–38.

Aumann,R.J.,andKurz,M.1977a. Power and taxes. Econometrica, 45: 1137–61.

1977b. Power and taxes in a multi-commodity economy. Israel Journal of Mathematics, 27:

185–234.

Austen-Smith,D.2000. Redistributing income under proportional representation. Journal of

Political Economy, 108: 1235–69.

Baron,D.,andFerejohn,J.1989. Bargaining in legislatures. American Political Science Review,

83: 1181–206.

Bertrand,J.1883. Théorie mathématique de la richesse sociale. Journal de savats, 67: 499–508.

Buchanan,J.,andTullock,G.1962. The Calculus of Consent: Logical Foundations for Consti-

tutional Democracy. Ann Arbor: University of Michigan Press.

Coaste,S.,andMorris,S.1995. On the form of transfers to special interests. Journal of

Political Economy, 103: 1210–35.

Coughlin,P.1986. Elections and income redistribution. Public Choice, 50: 27–91.

Cox,G.D.,andMcCubbins,M.D.

1986. Electoral politics as a redistributive game. Journal of

Politics, 48: 370–89.

de Palma,A.,Ginsburgh,V.,Papageorgiou,Y.,andThisse,J.-F.1985.Theprincipleof

minimum diﬀerentiation holds under suﬃcient heterogeneity. Econometrica, 53: 767–82.

Dixit,A.,andLondregan,J.B.1995. Redistributive politics and economic eﬃciency.

American Journal of Political Science, 89: 856–66.

1996. The determinants of success of special interests in redistributive politics.

Journal of Politics, 58: 1132–55.

1998. Ideology, tactics, and eﬃciency in redistributive politics. Quarterly Journal of

Economics, 113: 497–529.

2000. Political power and the credibility of government debt. Journal of Economic

Theory, 94: 80–105.

Easley,D.,andKiefer,N.1988. Controlling a stochasitic process with unknown parameters.

Econometrica, 56: 1045–64.

Grossman,G.,andHelpman,E.1994. Protection for sale. American Political Science Review,

84: 833–50.

john londregan 101

Hotelling,H.1929. Stability in competition. Economic Journal, 39: 41–57.

Johansson,E.2003. Intergovernmental grants as a tactical instrument: empirical evidence

from Swedish municipalities. Journal of Public Economics, 87: 883–915.

Kuznets,S.1955.Economicgrowthandincomeinequality.American Economic Review,

45: 1–28.

Lindbeck,A.,andWeibull,J.1987. Balanced budget redistribution as the outcome of political

competition. Public Choice, 52: 273–97.

Lohmann,S.1998. An information rationale for the power of special interests. American

Political Science Review, 92: 809–27.

McKelvey,R.1976. Intransitivities in multidimensional voting models and some implications

for agenda control. Journal of Economic Theory, 12: 472–82.

McLennan,A.1984. Price dispersion and incomplete learning in the long run. Journal of

Economic Dynamics and Control, 7: 331–47

Marx,K.1867. Das Kapital und seine international Wirkung.Hamburg:O.Meissner.

Meltzer,A.H.,andRichard,S.F.1981. A rational theory of the size of government. Journal

of Political Economy, 89: 914–27.

Meyerson,R.D.1993. Incentives to cultivate favored minorities under alternative electoral

systems. American Political Science Review, 87: 856–69.

Olson,M.1965. The Logic of Collective Action. Cambridge, Mass.: Harvard University Press.

1993. Dictatorship, democracy, and development. American Political Science Review,

96: 567–76.

Persson,T.,Roland,G.,andTabellini,G.2000. Comparative politics and public ﬁnance.

Journal of Political Economy, 108: 1121–61.

Piketty,T.1995. Social mobility and redistributive politics. Quarterly Journal of Economics,

110: 551–84.

Roemer,J.1999. The democratic political economy of progressive income taxation. Economet-

rica, 67: 1–19.

Rothschild,M.1974. A two-armed bandit theory of market pricing. Journal of Economic

Theory, 9: 185–202.

Snyder,J.M.,andKramer,G.H.1988. Fairness, self-interest, and the politics of the progres-

sive income tax. Journal of Public Economics, 36: 197–230.

Sraffa,P.1926. The laws of returns under competitive conditions. Econometric Journal,

36: 535–50.

Weingast,B.R.1979

. A rational choice perspective on congressional norms. American Journal

of Political Science, 23: 245–62.