Weingast B.R., Wittman D. The Oxford Handbook of Political Economy
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892 anarchy
know more about the winners of such gambles, because they are the ones who are
more prominent in the historical record, that record is also strewn with a lot more
less successful individuals as well as states who have been on the losing side of these
gambles. Asymmetry of information, of course, is present in one form or another and
could account for cases in which a tribute was not agreed and instead a battle had to
take place, but overall the inability to commit along with a long shadow of the future
is, I think, a very underrated source of conflict and its persistence.
4 Other Topics in Brief and
Future Prospects
.............................................................................
Because of space limitations we will now briefly refer to some important topics that
have been examined thus far, as well as discuss possible fruitful directions that such
research could take.
4.1 Alliance Formation
States have rarely viewed all other states the same way. They are usually allied with
some and not with others. What are the determinants of alliance formation? Is there a
tendency for bipolarity (i.e. have two grand alliances) or not? The approach reviewed
in this chapter could be promising in trying to answer such questions, and there have
been some initial attempts in such a direction.
In studying the problem, there are two critical modeling issues that need to be
confronted. First, once an alliance has formed, how do members of the alliance
divide the total pie? In particular, does relative arming determine at all members’
shares and how are these shares determined otherwise? Thus, Bloch, Sanchez-Pages,
and Sonbeyran (2002) suppose members of the alliance do not use arms at all in
determining shares whereas Skaperdas (1996) analyzes the case in which shares are
determined through arming. Second, there is no unique concept of equilibrium of
different alliance structures (comparable, say, to Nash equilibrium) and, when there
is, there can be more than one alliance structure that would be predicted (Ray and
Vo hr a 1999). Perhaps, as can be expected given these issues, there are no universal
predictions about how alliances form or about bipolarity. Bloch, Sanchez-Pages, and
Sonbeyran (2002), with restrictions on the possible stability of alliances that favor
the formation of large coalitions, predict the grand alliance; Skaperdas (1996)who
analyzes the case of three countries finds a critical role for the technology of conflict
in determining whether any alliances form; and Garfinkel (2004), who employees a
solution concept that is not as advantageous to large coalitions, finds a number of
different plausible outcomes other than the grand alliance.
6
⁶ Sandler and Hartley 2001 survey the literature on burden-sharing in already established alliances.
stergios skaperdas 893
The multiplicity of possible outcomes suggests a critical role for history and path
dependence, something that has not been incorporated into current models, pri-
marily because the problem of alliance formation is computationally rather complex
already in static settings. Clever ways of introducing dynamics could thus yield new
insights into this important problem.
4.2 Trade Openness and Insecurity
From a classical liberal perspective—which by default is the perspective of neoclas-
sical economics as well—international trade alleviates the problems with anarchy
and is enough of a carrot to bring together potential adversaries. From a realist
perspective, though, trade openness with adversaries can be anathema, especially
when the “relative” gains from trade go to the adversary. Conventional models of
international trade assume all resources and trade itself are perfectly enforceable
without leaving any room for arming and conflict, whereas our benchmark model
allows for arming and conflict but not for trade. In order to examine the validity of
the claims made by classical liberals and realists, however, we need to allow for both
trade and conflict. One possibility is to analyze a model with complementarities in
production or consumption like the one that was briefly specified in Section 2.Findlay
and Amin (2000) and Skaperdas and Syropoulos (2001) have analyzed such models.
They find conditions under which free trade can be better than autarky as well as the
other way around.
The key in making such comparisons is whether security costs (defense expendi-
tures and other costs of conflict) under autarky can be lower than the same costs
under trade. If they are and they are greater than the gains from the trade, then
autarky can be better than trade. Security costs could be higher under trade if a
disputed territory or resource (like oil or diamonds) has much higher value inter-
nationally than it would have domestically and thus induces higher security costs
on the part of the adversaries. When, however, the disputed resource has less value
internationally that it would have under autarky, security costs are lower under trade
and free trade is unambiguously superior to autarky.
4.3 Restraints and Governance
As we have discussed extensively in Section 2, anarchy does not imply warfare or
economically crippling cold wars and high levels of arming. Norms, international
law, institutions, and organizations can limit the resources that are devoted to arming.
An alternative to the anarchy of the international system is a more hierarchical, even
imperial, form of governance. Without being able to get into any detail here, certainly
that has been one major way that lower-levels of anarchy have evolved into states. In
this context there has been a debate about the effects of hierarchical governance. Find-
lay (1990) and Grossman and Noh (1994) first examined settings in which the state is
894 anarchy
“proprietary;” that is, it is owned by someone who taxes and provides services so
as to maximize profits. McGuire and Olson (1996) argued that such an arrangement
can be nearly efficient but Moselle and Polak (2001) have found several problems
with that argument. Furthermore, Konrad and Skaperdas (1999) have argued that
monopolistic governance invites competition, and competition between different
proprietors would eliminate all efficiencies and lead to a higher level of organized
anarchy (see also Greif, Bates, and Singh 2000, for another comparative treatment of
the emergence of governance through violence). That is, breaking down anarchy by
creating a hierarchical order does not look theoretically promising in addition to the
objections one might have on empirical grounds.
4.4 Future Prospects
One main weakness of the approach reviewed in this chapter is the conception of
states not only as unitary actors but also as not responding to concerns that are not
material in nature. That might have been true up to about two centuries ago, when
the state was indeed largely owned by king or emperor and fighting to defend it was
his private affair. Beginning with Napoleon, who managed to motivate Frenchmen to
fight for their own country, and the emergence of nationalism which is an integral ele-
ment of the modern state, the world appears to have become more complex. Notions
like “ideology,” “legitimacy,” or “sovereignty” do not have a place in the approach
reviewed in this chapter, or at least they do not have one yet beyond those of norms
for rules of division, but they do appear important in practice. As far as I can tell,
and as an outsider to the relevant debates I cannot be completely sure, these are also
concerns directed against the realist school. It would be advisable at least to attempt
thinking about how such notions could modify any insights that might come out of
the approach reviewed here.
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part xiii
..............................................................
METHODOLOGICAL
ISSUES
..............................................................
chapter 50
..............................................................
ECONOMIC
METHODS IN
POSITIVE
POLITICAL
THEORY
..............................................................
david austen-smith
1 Introduction
.............................................................................
Economics and political science share a common ancestry in “political economy”
and both are concerned with the decisions of people facing constraints, at the individ-
ual level and in the aggregate. But while rational choice theory in some form or other
has been a cornerstone of economic reasoning for over a century, with the mathemat-
ical development of this theory beginning in the middle of the nineteenth century, its
introduction to political science is relatively recent and far from generally accepted
within the discipline.
1
Three books proved seminal with respect to the application
¹ A suggestion (first made to me in conversation many years ago by Barry Weingast) as to why the
two disciplines differ so markedly with respect to the use of mathematical modeling is that political
science has no analogous concept to that of the margin in economics. And the importance of the margin
in this respect lies less with its substantive content than with the amenability of its logic to elementary
diagrammatic representation. Economic theorizing evolved into its contemporary mathematical form
through a diagrammatic development of the logic of the margin, whereas positive political theory,
almost of necessity, bypassed any such graphical development and jumped directly to applied game
theory.
900 economic methods in political theory
of economic methods in political science, the first of which is Kenneth Arrow’s Social
Choice and Individual Values (1951, 1963).
2
Although mathematical models of voting can be found at least as far back as
the thirteenth century (McLean 1990) and despite Paul Samuelson’s claim, in the
foreword to the second edition of the book, that the subject of Arrow’s contribution
was “mathematical politics,” an appreciation within political science (as opposed to
economics) of the significance of both Arrow’s possibility theorem itself or, more im-
portantly for this chapter, the axiomatic method with which it is established was slow
in coming. An exception was William Riker, who quickly understood the depth of
Arrow’s insight and the significance of an axiomatic theory of preference aggregation,
both for normative democratic theory and for the positive analysis of agenda-setting
and voting.
The remaining two of the three seminal books are Anthony Downs’s An Economic
Theory of Democracy (1957) and William Riker’s The Theory of Political Coalitions
(1962). These books were distinguished for political science by their use of rational
choice theory and distinguished for rational choice theory by their explicit concern
with politics.
Downs’s 1957 volume covers a wide set of issues but is perhaps most noted for
his development of the spatial model of electoral competition and for the decision-
theoretic argument suggesting rational individuals are unlikely to vote. The spatial
model builds on an economic model of retail location due to Hotelling (1929)and
Smithies (1941). Approximately a decade after the publication of Downs’s book, Davis
and Hinich (1966, 1967) and Davis, Hinich, and Ordeshook (1970) described the
multidimensional version of the (political) spatial model, the mathematics of which
has given rise to a remarkable series of results, exposing the deep structure of a variety
of preference aggregation rules, most notably, simple plurality rule (e.g. Plott 1967;
McKelvey 1979;Schofield1983; McKelvey and Schofield 1987; Saari 1997). Similarly,
Downs’s decision-theoretic approach to turnout elicited a variety of innovations as
authors sought variations on the theme to provide a better account of participation
in large elections (e.g. Riker and Ordeshook 1968;FerejohnandFiorina1975). But
although treating voters as taking decisions independent of any consideration of oth-
ers’ behaviour (as the Downsian decision-theoretic approach surely does) yields some
insight, the character of most if not all political behavior is intrinsically strategic, for
which the appropriate model is game theoretic.
3
Riker understood the importance not only of Arrow’s theorem and a mathematical
theory of preference aggregation, he also recognized that game theory, the quintessen-
tial theory of strategic interaction between rational agents, was the natural tool with
which to analyze political behaviour. In his 1962 book, Riker exploited a cooperative
game-theoretic model, due to von Neumann and Morgenstern (1944), to develop an
² Duncan Black’s The Theory of Committees and Elections (1958) has some claim to be included as a
fourth such book. However, although Black considers similar issues to those taxing Arrow, his concern
was more limited than that of Arrow and his particular contribution to political science was generally
recognized only after the importance of Arrow’s work had begun to be appreciated.
³ Palfrey and Rosenthal 1983 and Ledyard 1984 provide the earliest fully strategic models of turnout.
david austen-smith 901
understanding of coalition structure and provide the first thoroughgoing effort to
apply game theory to understand politics. Cooperative game theory is distinguished
essentially by the presumption that if gains from cooperation or collusion were
available to a group of agents, then those gains would surely be realized. As such,
it is closely tied to the Arrovian approach to preference aggregation and much of
the early work stimulated by Riker’s contribution reflected concerns similar to those
addressed in the possibility theorem. An important concept here is that of the core of
a cooperative game.
Loosely speaking, if an alternative x is in the core, then any coalition of individuals
who agree on a distinct alternative y that they all strictly prefer, cannot be in a position
to replace x with y. For example, the majority rule core contains only alternatives that
cannot be defeated under majority voting. Similarly, if we imagine that a group uses
a supramajority rule requiring at least 2/3 of the group to approve any change, then
x is in the core if there is no alternative y such that at least 2/3 of the group strictly
prefer y to x. So if a group involves nine individuals, five of whom strictly prefer x to
y and the remaining four strictly prefer y to x, then the majority rule core (when the
choice is between x and y)isx alone whereas both x and y are in the 2/3 rule core.
The concept of the core is intuitively appealing as a predictor of what might hap-
pen. Given the actions available to individuals under the rules governing any social
interaction, and assuming that coalitions can freely form and coordinate on mutually
advantageous courses of action, the core describes those outcomes that cannot be
overturned: even if a coalition does not like a particular core outcome, the very fact
that the outcome is in the core means that the coalition is powerless to overturn it.
On the other hand, when the core is empty (that is, fails to contain any alternatives)
then its use as a solution concept for a cooperative game-theoretic model is suspect.
For example, suppose a group of three persons has to use majority rule to decide
how to share a dollar and suppose every individual cares exclusively about their own
share. Then every possible outcome (that is, division of the dollar) can be upset by
amajoritycoalition.Toseethis,supposeafairdivisionof$(1/3) to each individual
is proposed; then individuals (say, A and B) can propose and vote to share the dollar
evenly between themselves and give nothing to individual C; but then A and C can
propose and vote to give $(2/3)toAand$(1/3) to C. Because A and C care only about
their own shares, this proposal upsets the proposal favoring A and B. But by the same
token, a division that shares the dollar equally between C and B, giving nothing to
A, upsets the outcome that gives B nothing; and so on. In this example, the core
offers no guidance about what to expect as a final outcome. Furthermore, it does not
follow that the core being empty implies instability or continued change. Rather, core
emptiness means only that every possible outcome can in principle be overturned; as
such, the model offers no prediction at all. It is an unfortunate fact, therefore, that,
save in constrained environments, the core of any cooperative game-theoretic model
of political behavior is typically empty, attenuating the predictive or explanatory
content of the model.
Discovering the extent to which the core failed to exist was disappointing and in-
duced at least some pessimism about the general value of formal economic reasoning