. 10
( 11)


The heart of the constitution is the complex pattern of belief and ac-
tions, all of which are individually rational with respect to empirical real-
ity, and tenable, according to the ideological attitudes of the members of

Preferences and Beliefs

the community. It is de¬ned by certain barriers, or boundaries, to belief,
cognition, and behavior. What I have termed the chaos hypothesis (my in-
terpretation of Keynes™ key insight), was a device by Keynes to overcome
a belief barrier that prevented his understanding of the Depression. The
discussion in Chapter 7 was meant to show that Keynes™ insight made
accessible a number of different possible “constitutional hearts.” One of
these eventually came into focus in the period after World War II, and
the evolution of the Atlantic Constitution can generally be regarded as
continuous since that time.
The fundamental problem of political economy, as I see it, is to ob-
tain a general understanding of how a core belief, or more properly the
heart of the constitution, transmutes itself through a cascade to a new
con¬guration. The various analyses of quandaries that have been under-
taken recently have provided a number of interesting examples of such
cascades. The work by Margolis (1987) on the evolution of research pro-
grams, as well as insight into the interaction of shared mental models,
ideologies, and institutions are obviously important (Denzau and North,
As I have suggested by the discussion of Einstein™s work, a belief com-
ponent of the heart may be considered to be an essential aspect of a
paradigm (Kuhn, 1962). The collapse of such a component has some of
the features of a scienti¬c revolution. To escape or resolve a scienti¬c
or constitutional quandary may involve overcoming a conceptual barrier
(such as the equilibrium thesis that beset Keynes or the notion of absolute
space and time that Einstein rejected). Even when the barrier is overcome,
it may prove dif¬cult to construct a new core belief, because of the resis-
tance, or “risk-aversion,” of the participants, or because of the profound
disagreements between the members of the society.

8.6 modelling beliefs
The human brain is, without a doubt, the most complex physical object
known to us. It contains about 30 billion (30 — 109 ) neurons and a million
billion (1015 ) connections, or synapses. The number of “neural” states of
the brain is to all intents and purposes in¬nite. More to the point, the struc-
ture of synapse ¬ring is neither independent (in the sense that synapses
¬re without pattern) nor correlated (in that all ¬re together). Instead, the
brain is characterized by shifting, currently mysterious, patterns of local
correlations (Edelman and Tononi, 2000).

Architects of Political Change

It is surprising, therefore, that economic theory has used an extremely
simple model of the mind (namely, preferences and their supposed “ra-
tionality” properties of transitivity, etc.) to derive hypotheses concerning
human interaction. It is even more remarkable that the theory has any pre-
dictive power at all. As we have observed above, economic theory asserts
the existence of concatenations of behavior known as equilibria, at least
for the limited sphere of commodity markets. An underlying assumption
of economic theory is that each individual is “an autonomous end in him-
self” and to this extent, “somewhat mysterious and inaccessible to one
another.” Another way of expressing this assumption is that the acts of
individuals are independent, and therefore uncorrelated.
In contrast, one interpretation of the key idea put forward by Keynes
in his General Theory is that individual acts in certain kinds of asset
markets need not be independent, but may, in fact, be highly correlated.
For example, a “speculator” will value assets not by any intrinsic value
that they may have, but in terms of the choices of other speculators. Such
correlations may induce market chaos.
Game theory, as it is currently understood, has, in a sense, accepted
the possibility of correlated individual choices. Savage™s work on the ax-
iomatic structure of preference can be seen as the basis for this theory
(Savage, 1954). In this framework, fundamental preferences are indeed
“mysterious and inaccessible,” but secondary preferences, those that gov-
ern individual acts, are mediated by the beliefs of the agent. These beliefs
can be interpreted as probability assessments over the possible states of the
world, over beliefs held by other agents and so forth. Clearly, the “belief
space” thus generated may be of extreme complexity (see e.g., Gribben,
Moreover, choice by the individual depends on the individual™s risk
posture, and this is characterized by fundamental preferences, not by sec-
ondary preferences. It is hardly surprising that secondary preferences over
risky choices may appear to violate the usual axiomatic properties im-
puted to preference (Kahneman and Tversky, 1979).
A “Nash equilibrium” can be thought of as a collection or vector of acts
by the individuals in the game, with the property that no one individual
has a motivation and capability to switch to a different act. However, since
secondary preferences are determined by beliefs, it obviously follows that
each equilibrium (in acts) is characterized by a set of beliefs, one for each
agent. These “equilibrium beliefs” reside, of course, in the belief space and
may be as complex as one could imagine. It is for this reason that game

Preferences and Beliefs

theory is beset by an abundance of Nash equilibria. This problem for game
theory is thus very different from the principal problem of nonexistence
of equilibria in social choice theory.
A second problem for game theory arises out of this multiplicity of
equilibria: Some equilibria are “unstable,”since they are sustained by be-
liefs that, while rational in some sense, are only barely credible. To ¬lter
these out by a re¬nement exercise, and to construct a plausible mode of
transition from one equilibrium to another, has occupied many theorists
in recent years.
Perhaps an illustration to do with the story of the emperor™s New
Clothes would be useful. The emperor was persuaded by a gifted con-
¬dence trickster that his new clothes, while invisible to the emperor, were
nonetheless superlative, and visible to everyone else. That the emperor
should believe this story does, of course, require a stretch of the imagina-
tion. During the parade through the town, nearly every individual must
have disbelieved the evidence of their own eyes. Nonetheless, because
all the other townspeople were cheering the emperor and his new clothes,
each individual gave greater credence to the particular inference that there
was nothing amiss (except for that individual™s hallucination). This is a
Nash equilibrium in the acts of the townspeople. Of course, the “belief
equilibrium” underlying this joint act was broken when a single child
laughed out loud on seeing the naked emperor. The childish act led im-
mediately to a credible inference that the emperor was indeed naked, and
thus to another joint equilibrium act, the expression of derision by the
townspeople. The point is that the original belief equilibrium was bro-
ken by the act of a child which, under normal circumstances, would not
warrant attention. Both equilibria were associated with highly correlated
acts. Almost everyone applauded in the ¬rst equilibrium, and everyone
(except the Emperor) laughed in the second. The transformation from one
equilibrium to another has been called an informational cascade, and it
is true that information was provided by a child™s laugh. However, what
was crucial was the effect of this information (and its credibility) on the
beliefs of the townspeople. For this reason, throughout this book I have
used the term belief cascade for the correlated changes in beliefs associ-
ated with a move from one Nash equilibrium to another (Bikhchandani,
Hirschleifer and Welsh, 1992). I am certainly not in a position to pro-
vide a general model of belief cascades, but I believe that the stochastic
model of elections can be used to indicate how such a model may be

Architects of Political Change

8.7 modelling elections
Game theoretic accounts of social “acts,” such as voting, have been hard-
pressed, in the past, to give a plausible, individual-focused account of
why individuals vote, or act altruistically, or engage in battle. In contrast,
sociological accounts assume, as a matter of course (in the terminology
used here), that individual acts are highly correlated through correlated
beliefs called culture or norms. For example, a generally accepted “so-
ciological” mode of analysis of elections is that voters “identify” with
a particular party. The implicit idea underlying party identi¬cation (PI)
is that voters with similar histories will make similar judgments early in
their lifetime that one party is preferred. (Campbell et al., 1960; Butler
and Stokes, 1969). Clearly PI implies that voter choice satis¬es a particular
“correlation structure” which is stable over time, and de¬ned by societal
cleavages. (This framework also suggests that all the electoral action re-
sides in the choices of “independents,” who perhaps base their decisions
on small, indeterminate, or chaotic features of each election.)
Such a framework is very different from the “rational choice” model
derived from Downs (1957), where each individual is assumed to interpret
the policy implications of the parties, de novo, and to make a choice
based on the individual™s idiosyncratic preferences. In such a model, the
correlation in acts of the voters must be low.
It would seem, however, that neither the pure PI model nor the pure
rational choice model gives a satisfactory account of elections. On the
one hand, PI in Britain and the United States appears to be on the decline
(Clarke and Stewart, 1998). On the other hand, there is some evidence
that the pure rational choice model needs to be modi¬ed to take account
of correlations in voter perceptions and choices. For example, so-called
probabilistic spatial voting models typically assume that the probability
that a voter chooses a party, or candidate, is a monotonically decreas-
ing function of “distance” from the party or candidate. The implicit er-
rors in the model are generally assumed to be independent (Enelow and
Hinich, 1984). This implies voter choice is (pairwise) statistically inde-
pendent. More recent empirical work suggests that, in fact, voter choice
is (pairwise) statistically correlated (Quinn, Martin, and Whitford, 1999).
This work has also attempted to combine “rational choice” and “soci-
ological” accounts of elections, by utilizing the notion of Nash (1950,
1951) equilibrium and, in the terminology used here, allowing for the
possibility of correlations in voter beliefs and choices. Once the idea of
correlations in voter choice is considered, then it is possible to imagine

Preferences and Beliefs

episodes where the correlation structure within the electorate dramati-
cally changes. Such transformations would naturally be associated with
“critical” elections, wherein voters™ perceptions of the parties, and the
resulting electoral choices, change suddenly. Burnham (1970), for exam-
ple, posits that the elections of 1800, 1828, 1860, 1896, and 1932 were
Mayhew (2000, 2002) has recently argued that there is no clear evi-
dence that such elections were indeed critical, in the sense of being turning
points in U.S. political history. In fact, what is missing in the earlier polit-
ical historical accounts is a theory that would give some mode of analysis
by which to de¬ne what is meant by “critical.”
In this book I have developed the idea of a constitutional quandary,
associated with profound uncertainty over the proper institutional rules
of the society. As the uncertainty deepens, coalitional or political chaos
intensi¬es. Behavioral correlations, such as party identi¬cation, collapse.
Very often, a new belief or interpretation of the world, is put forward,
and the society bifurcates into those who accept the belief and those who
deny it. Depending on the institutional rules, one of these two groups
may have the will and power to bring about a new social state, and pos-
sibly a new interpretation of the constitution. By analogy with social
choice theory, I have called the resulting constitution a core outcome,
and the belief that underpins it, a core belief. I have also emphasized
that constitutional transformations are brought about by the resolution
of a quandary intrinsic to the society. Although electoral preferences may
be described within a policy space of relatively low dimension, the way
these preferences are aggregated at crucial junctures depends on how
uncertainty and risk are interpreted by social “architects” of the even-
tual decision. At these junctures, contingency may play a role in how the
quandary is understood. Because the consequences of the decision can be
only dimly perceived, the architect must undertake two related tasks. The
¬rst, which I have characterized by the term expected utility calculus, is
to lay out as clearly as possible the various eventualities and the associ-
ated probabilities. The second is to acknowledge the risk associated with
the decision, and to offer an argument for what seems to be the correct
choice. The acceptance of this choice by the electorate not only legit-
imizes the eventual decision, but adds weight to the belief that it is indeed
Although the construction of a formal model of such a belief game is
not possible at present, the following section offers a tentative ¬rst attempt
based on an adaptation of the stochastic model of voting.

Architects of Political Change

8.8 a formal model of elections
Throughout this book I have used the idea of collective decision mak-
ing under risk. The notion has been to formulate the costs of the vari-
ous options facing a society, together with the subjective probabilities of
the eventualities. However, estimates of costs and subjective probabilities
will differ across the members of the society. I propose now to adapt the
standard apparatus of the spatial model of voting so that it can incor-
porate both preferences and beliefs. As suggested in the above discus-
sion, beliefs are essentially subjective probability assessments. Recent
formal models of voting have also made use of the Condorcetian idea
that voters may form judgments about the validity of various political
propositions. Unlike Condorcet™s conception that these propositions are
“universally true,” the kind of propositions that I consider here have the
form, “The South does indeed intend to extend slavery to the Paci¬c,” and
“The North is indeed based on capitalist expansion that is inimitable to the
South.” Evidence can be given as regarding propositions and, depending
on the interests of voters, the beliefs so generated will affect the choices of
The “stochastic” variant (Hinich, 1977) of the spatial model allows
voters to be uncertain in their choice, and it is this model that I shall
The primitives12 of the model are:

(i) some “policy” space X which characterizes both voter interests, and
possible eventualities.
(ii) the population or “electorate,” N, of size n, is described by a set {xi }
of “ideal points,” one for each “voter,” i = 1, . . . , n. An individual™s
ideal point describes the location of the voter in the space X, and
represents that voter™s interests.
(iii) the set of options, S, of size s, is a set {z j }, each one being a point in
X. In the situation of an election, each element of S is a declaration
of intended or proposed policy. There is one for each candidate, j.
(iv) in the simplest model, the “latent utility,” ui j , of voter i for candidate
j has the form

ui j (xi , z j ) = »i j ’ Ai j (xi , z j ) + θ T ·i . (8.1)

Here I repeat the de¬nitions given in section 1.2 of Chapter 1.

Preferences and Beliefs

Here θ T ·i models the effect of the sociodemographic characteristics ·i
of voter i in making a political choice. That is, θ j is a k-vector specify-
ing how the various sociodemographic variables appear to in¬‚uence the
choice for party j. The term Ai j (xi , z j ) is a way of representing the in-
terests of voter i. In particular, Ai j (xi , z j ) will be some function of the
distance between xi , the preferred position of voter i and z j , the declared
policy of candidate j, according to some appropriate metric. In Chapter
6, for example, the metric is assumed to be “ellipsoidal,” assigning dif-
ferent valences to different axes for different individuals. In the standard
electoral model, however, it is assumed that Ai j (xi , z j ) = β xi ’ z j 2 is
the Euclidean quadratic loss (with β > 0) associated with the difference
between the two positions.
The model is stochastic because of the implicit assumption that
»i j = » j + µ j , for j = 1, . . . , s. Here {µ j } is a set of possibly correlated
disturbances and » j is the “valence” of candidate j. This valence is a way
of modeling the nonpolicy judgment by voter i of the quality of candi-
date j.
The probability that voter i chooses candidate j is

ρi j = Pr[ui j (xi , z j ) > ui j (xi , zk) for all k = j]. (8.2)

Hinich (1977) assumed each candidate, j, adopted a declaration, z j ,
chosen so as to maximize the expected vote share of the candidate. The
vote share is given by the average

ρi j . (8.3)
n i=1

He argued that the resulting “Nash equilibrium” would be one in which
both candidates adopted the same position, at the mean of the voter dis-
tribution. However, there is one proviso. If the “valences” are ranked
»s > »s’1 > . . . > »1 , then it is necessary for this convergence result that
a “convergence coef¬cient”

c(», β) = 2β[1 ’ 2ρ1 ]v2 (8.4)

be bounded above by the dimension of the space. In this expression, ρ1 is
the probability that each voter picks the lowest valence candidate when
all candidates adopt the same position at the mean, while v2 is a measure
of the electoral variance. In the case the disturbances are independent and

Architects of Political Change

generated by a logistic distribution, then

ρ1 = 1 + exp [»k ’ »1 ] . (8.5)

A similar expression can be obtained under assumptions that the errors
are multivariate normal and correlated.
Obviously, if candidate s has much higher valence than candidate 1,
or if the variation, v2 , in electoral beliefs is signi¬cant, then this necessary
condition will fail. The consequence is that low-valence candidates will
not locate near the electoral mean.
Empirical analyses of elections in Britain, the United States, as well as
of polities using proportional electoral methods such as Israel and Italy
demonstrate that the empirical values obtained for the parameters imply
that the necessary condition fails (Scho¬eld, Miller and Martin, 2003;
Scho¬eld and Sened, 2005a,b, 2006).
The conclusions of this valence model suggest why convergence to an
electoral center is a nongeneric phenomenon. Indeed, it is only likely to
occur when the election involves such a high degree of uncertainty (or
electoral variance) that policy differences are irrelevant.
This valence model can be interpreted in terms of Madison™s theo-
rem in Federalist X. We may view » j as the average electoral judg-
ment that candidate j is a “¬t choice” for the position of the Chief
Magistrate. In the model outlined above, the particular weighting that
i gives to j is a stochastic variable, »i j = » j + µ j , where µ j has some
explicit stochastic distribution, either Gaussian or so-called “Type I ex-
treme value” (see Scho¬eld and Sened, 2006, for a full de¬nition of the
model). The logic underlying this model is that it may be, in principle,
impossible to gauge precisely what weight an individual, i, gives to the
arguments for the option offered by candidate j. It is clearly possible in
this model for a voter to actually vote for candidate j over k even though,
in terms of explicit policies, candidate k has declared an intended op-
tion that more closely matches i™s interests. The fact that candidates do
not converge to an electoral mean provides a reason why the candidate
positions represented in Figures 6.2 through 6.5 in Chapter 6 are not
The model can be extended in the obvious way, because there is no
compelling reason to assume that the stochastic component is random in
the manner just speci¬ed. It is more plausible that the judgment made by
i of candidate j is a function of j™s stated option. Indeed, the judgment

Preferences and Beliefs

»i j by i of j could be a function »i j (xi , z j ) of both the preferred point, xi ,
of the voter, and the declared option z j . In this case, the stochastic error,
µ j , associated with voter i could also depend on the preferred point, xi , of
the voter. Moreover, judgments about different candidates could move in
different directions in different subsets of the population. Such a model
has been proposed by Miller and Scho¬eld (2003) and was presented in
Chapter 6 in order to account for the effect of activists on candidate sup-
port. The key idea in this model is that judgments are more like infections
and are subject to contagion. In other words, an increase in the posi-
tive judgment for one of the candidates by some subset of the electorate
may trigger further changes in such electoral judgments”positive among
some members of the electorate, and negative among others. Although the
model has not been fully developed, it does seem to suggest that party po-
sitions slowly evolve over time as new activist coalitions come into being.
Figures 6.3 and 6.4, in Chapter 6 for example, give hypothetical illus-
trations of the transformation of party positions from 1860 to 1896 and
from 1896 to 1932 in the United States. Implicitly, I argue that these trans-
formations at times of “critical” elections (Key, 1955) are brought about
by the electoral belief cascades. It seems obvious that the belief cascades in
the northern and southern electorates moved in opposite directions from
1858 to 1860. That is, the judgments »i j (xi , z j ) for j = Lincoln or Breck-
inridge became large depending on whether i belonged to the North or
South. An electoral game of this kind would induce extreme divergence.
This could account for the lack of success of a moderate candidate like
While this model involving electoral judgments has some af¬nities to
Condorcet™s Jury theorem and Madison™s version of it in Federalist X, the
theorem itself cannot be used directly to argue that the selected candidate
is necessarily superior. Because the probabilities ρa j , ρbj (that voters a, b
choose j) depend on xa and xb, they will not be independent. We can
interpret this to mean that the stochastic disturbances display complex
correlations. Only if the electoral variation, v2 , is very small, will con-
vergence occur. If one candidate has a clearly dominant valence then this
candidate will win the election, with high probability.
To interpret this observation, suppose that β approaches zero so that,
in the limit, the interests of the voters become irrelevant. Suppose further
that there is information available to some subset M of the electorate
which is consistent with the judgment

»s > »s’1 > . . . > »1 . (8.6)

Architects of Political Change

Then it will be the case that, for every voter i in M, the probabilities will
be ranked
ρis > ρis’1 > . . . > ρi1 (8.7)
for these voters. From the multinomial theorem it follows that the majority
rule preference within the set M will choose s with greater probability than
s ’ 1, s ’ 2, . . . , 3, 2, 1. If M is itself a majority under the electoral rule,
then candidate s will win. (A proof of a version of the Jury theorem is given
in the appendix to this chapter. It is important to note that the theorem
depends on the assumption of independence of voter choice.) This is an
analogue of Condorcet™s Jury theorem, in the case that both interests and
judgments are involved.
If there is some linkage between information available to the electorate
and the individual judgments made by voters, then the stochastic spatial
model just presented can be interpreted as a generalization of the Jury
theorem (see also Scho¬eld, 1972a, for an early attempt at formulating
Madison™s argument in terms of a version of the Jury theorem where
different groups in the society have differing notions of a ¬t choice).
In the case where electoral interests are relatively weak, because β is
small we can infer that the second aspect of the Jury theorem will also
hold. In the limit, as the population size, n, becomes large, the probability
of a ¬t choice approaches 1. Because the model can incorporate interests,
which were of concern to Madison in writing Federalist X, we may also
view the model as a method of studying the interaction of interests and
judgments in a polity.
Even when interests are involved, so β is signi¬cant in magnitude, we
can still draw some conclusions about the equilibrium behavior of can-
didates as they respond to electorate incentives. Since we can infer that
the relevant necessary condition for the “mean voter theorem” will fail,
it follows that candidates will adopt very different positions. If the indi-
vidual judgments are correlated in some fashion, then this phenomenon
will be more pronounced.
If there is a single dimension involved, as suggested by Figure 2.4
for the Jefferson election of 1800, then it is plausible that there exists
only a unique vector of equilibrium positions for the candidates. In-
deed, the ¬gure is meant to suggest that this was the case from 1800
until at least 1852, and this is why I suggested that the two-party sys-
tem was in balance in this period. If there are two dimensions, as I have
suggested is a plausible assumption for the election of 1860, then the
equilibrium will depend on the valence characteristics of the candidates.

Preferences and Beliefs

Figure 2.5 positions the four presidential candidates for 1860 within a
two-dimensional policy space, characterized by a land/capital axis and a
labor/slavery axis. In a pure stochastic model for such a situation there
would be multiple possible equilibria. The activist version of the model
proposed by Scho¬eld (2005a) suggests that if these activist valence func-
tions are suf¬ciently concave in the candidates™ positions, then there will
indeed be a unique equilibrium (that is, a set of positions, one for each
It is implicit in this model, that contention, rather than compromise, is
the fundamental characteristic of politics. It should also be obvious that
each candidate should do everything in his (or her) power to enhance his
(or her) valence.
If my argument about the importance of judgments is correct, then the
kind of deterministic instability implicit in the Arrovian or chaos theo-
rems will not occur in the election of the Chief Magistrate. Instead, such
elections will be affected by changes in average societal judgments, and
by the possible correlation and sectional distribution of these judgments.
This may be what Beard (1913) had in mind.
I have conjectured here that the U.S. political system tends to sustain
risk-taking policy options by successful presidential candidates and by
in¬‚uential policy makers or architects of change, such as Franklin, Madi-
son, Jefferson, Lincoln, or Johnson. I also conjecture that risk taking by
candidates is enhanced by the effects of activist interest groups. This bal-
ance between presidential risk taking and congressional risk aversion was
seemingly intended by the Founders.
Clearly, the social world of beliefs is much more complex than the
world of preferences. As I have suggested, the space of beliefs, regarded
as a mathematical object, is extremely complex. The historical illustra-
tions of this book suggest that dramatic transformations can occur as
core beliefs in the society are transformed. It is this feature of social trans-
formation that the notion of the heart tries to capture.

8.9 appendix: condorcet™s jury theorem
The Jury theorem formally only refers to a situation where there are just
two alternatives {1, 0}, and alternative 1 is the “true” option. Further,
for every individual, i, it is the case that ρi1 > ρi0 . We can assume that
ρi1 + ρi0 = 1, so obviously ρi1 > 1 . To simplify the proof, we can assume
that ρi1 is the same for every individual, thus ρi1 = ± > 1 for all i. We use
χi (= 0 or 1) to refer to the choice of individual i, and let χ = i=1 χi be

Architects of Political Change

the number of individuals who select the true option 1. We use Pr for the
probability operator, and E for the expectation operator. In the case that
the electoral size, n, is odd, then a majority, m, is de¬ned to be m = n+1 .
In the case n is even, the majority is m = 2 + 1. The probability that a
majority chooses the true option is then
±ma j = Pr[χ ≥ m].

The theorem assumes that voter choice is pairwise independent, so that
Pr(χ = j) is simply given by the binomial expression n ± j (1 ’ ±)n’ j .
A version of the theorem can be proved in the case that the probabilities
{ρi1 = ±i } differ but satisfy the requirement that 1 i=1 ±i > 1 . Versions
n 2
of the theorem are valid when voter choices are not pairwise independent
(Ladha and Miller, 1996).
The Jury Theorem.13 If 1 > ± > 1 , then ±ma j ≥ ±, and ±ma j ’’ 1 as
n n
n ’’ ∞.
Proof. Consider the case with n odd. Now
nj n
± (1 ’ ±)n’ j = ± j (1 ’ ±)n’ j .
Pr(χ = j) =
n’ j
we see that ± n’ j (1 ’ ±) j > ± j (1 ’ ±)n’ j . Thus,
Since ± > 2

m’1 m’1
j Pr(χ = n ’ j) > j Pr(χ = j)
j=0 j=0

’ k) Pr(χ = k) > = k).
k=0 k Pr(χ
k=m(n (8.8)

n n
= k) > = k) + = k).
n k=0 k Pr(χ k=mk Pr(χ
k=m Pr(χ

n±ma j = n = k)
k=m Pr(χ

E(χ) = = k) = n±.
k=0 k Pr(χ

Thus, ±ma j > ± when n is odd.

This proof is adapted from Ladha (1996).

Preferences and Beliefs

The case with n being even follows in similar fashion, taking m =
n n
+ 1, and using an equiprobable tie-breaking rule when k = 2 . This gives

±ma j = = k) + Pr χ =
k=m Pr(χ .
2 2
For both n being even or odd, as n ’’ ∞, the fraction of voters choos-
ing option 1 approaches 1 E(χ) = ± > 1 . Thus, in the limit, more than
n 2
half the voters choose the true option. Hence the probability ±ma j ’’ 1
as n ’’ ∞.
Laplace also wrote on the topic of the probability of an error in the
judgment of a tribunal. He was concerned with the degree to which ju-
rors would make just decisions in a situation of asymmetric costs, where
¬nding an innocent party guilty was to be more feared than letting the
guilty party go free. As he commented on the appropriate rule for a jury of
twelve, “I think that in order to give a suf¬cient guarantee to innocence,
one ought to demand at least a plurality of nine votes in twelve” (Laplace
1951 [1814]: 139).

Political Change

The essential point to grasp is that in dealing with capitalism we are dealing with
an evolutionary process. . . . Capitalism, then, is by nature a form or method of
economic change and not only never is but never can be stationary. And this
evolutionary character of the capitalist process is not merely due to the fact that
economic life goes on in a social and natural environment which changes. . . . The
fundamental impulse that sets and keeps the capitalist engine in motion comes
from the new consumers™ goods, the new methods of production or transportation,
the new markets, the new forms of industrial organization that capitalist enterprise
creates. . . . [T]he . . . process of industrial mutation . . . incessantly revolutionizes
the economic structure from within, incessantly destroying the old one, incessantly
creating a new one. This process of Creative Destruction is the essential fact about
capitalism. It is what capitalism consists in and what every capitalist concern has
got to live in. . . .
It must be seen in its role in the perennial gale of creative destruction.
(Schumpeter, 1942: 82“4)

We can agree with Schumpeter that the future will be one of technolog-
ical change and what is now called “globalization.” We need not accept
all of Schumpeter™s arguments about capitalism, but we can extend his
metaphor of the dynamical system of the “weather” to make some gen-
eral points about the process of change in the global political economy.
Weather is a dynamical system involving the oceans and the air on the
surface of the earth. Even though the local laws of motion, the “physics”
of the weather are well understood, its global behavior defeats computa-
tion except in the very short run. As Lorenz (1993) has noted, this system
may contain local chaotic subsystems”hurricanes and the like”but also
major discontinuities, like the onset of an ice age. The theory of dynamic
systems, originating in the work of Poincar´ (1993 [1892“9]) and more re-
cently of Smale (1966), would suggest that such a complex dynamic system

Political Change

is unlikely to be structurally stable.1 We are now sensitive to the fact that
relatively small changes, induced by our own actions, can potentially in-
duce dramatic change in the qualitative aspects of the system of weather.
If we now think of the social world as a dynamical system, driven by
changes in the beliefs of its members, then we can use this metaphor of
the global weather system to draw out some tentative parallels.
First, it will never be in equilibrium. There may be temporary domains
of relative stability, or equilibrium, but these will in time be transformed.
Second, the interactions that can occur, and the “causes” of the trans-
formations, may take place over extended temporal and spatial domains,
and involve very subtle and unsuspected linkages.
Third, just as the weather system is “forced,” by periodicities generated
by the sun and the moon, and possibly by our own actions, so is the
social system “forced” by technological change. Different subdomains,
or political economies, may well be forced in different directions by the
effects of technology. While the weather system is generally predictable, it
does contain small-scale, chaotic events, like hurricanes, and on occasion
very large-scale changes. We might expect the social system to exhibit
the same pattern of unpredictability occurring at different levels (Stiglitz,
2002; Mandelbrot and Hudson, 2004).
While the local laws of motion of the weather system were found by
studying much simpler, isolated physical systems (Gribbin, 2004), we only
have very local models of subsets of the social system by which to make
guesses about its true laws of motion. These local social models were
discussed in Chapter 8 and include “the general equilibrium model of
economics” as well as versions of Condorcetian “belief aggregation,”
“social choice theory,”“game theory,” and the models of scienti¬c inno-
vation discussed by Popper, Kuhn, and Feyerabend. Obviously enough, all
of these are very incomplete theories, that can, at best, only give us some
insight into local aspects of the social dynamic. Developing these models
requires both extensions of the deductive theories of dynamic processes
and of inductive techniques for perceiving patterns in the world.
It was Condorcet™s belief that
the moral and political sciences are capable of the same certainty as those that
comprise the system of the physical sciences, and even as those branches of physical
science which like astronomy, seem to approach mathematical certainty.2

Further comments on these observations are given in Scho¬eld (2003d).

Quoted in Gillespie (1972: 2). See also Gillespie (1980, 2005).

Architects of Political Change

In fact, it was Condorcet™s contemporary, Pierre-Simon Laplace, who
contributed most to this enlightenment research program by his develop-
ment of celestial mechanics, but also by his efforts to formulate a theory
of induction applicable to social analysis.3 Two centuries after Condorcet
and Laplace, we have a somewhat better understanding that dynamic sys-
tems, whether physical or social, need not exhibit the certainty imputed
by Condorcet. My own inclination is that it is important to continue the
research program that I have associated with Condorcet and Laplace by
embracing both deductive and inductive aspects of learning and of the
mind. Recent developments in stochastic models of behavior of complex
systems (Mumford, 2002) suggest that such a program is not impossi-
ble. However, we should be cautious and resist the inclination to jump
too readily to grand conclusions about the nature of change in the global
In this book, I have used a version of the electoral model, and have
tried to combine aspects of both preference and belief aggregation. The
formal model, while fairly simple, is essentially based on Bayesian and
stochastic techniques (Scho¬eld and Sened, 2006). It can, in principle, be
extended to incorporate more subtle aspects of belief, and what I have
called valence. As I have emphasized, valence is an aspect of judgment,
and can be subject to rapid change”a kind of infection, in any democratic
society. The historical occasions I have considered suggest that these belief
transformations may take the form of a change in a key constituent or
core belief induced by the obvious need to deal with a quandary facing
the society. I have also used the example of Keynes™ ideas to suggest that
the way to resolving such a quandary may be by overcoming a theoretical
barrier associated with a core belief that has proved to be false. Chapters
5 and 6 used the examples of events in 1860 and 1964 to infer that the
belief changes that were brought about were coherent or rational in some
sense. At the same time, of course, these belief changes led, respectively,
to the Civil War and to the unrest associated with the Vietnam War. In
more developed versions of the electoral model, it would be necessary to
focus on the rationalizability of the belief changes.
There are instances, of course where belief changes can be rationalized.
The collapse of the Soviet Union in the early 1990s appears to have been
due to a general realization that the “imperial” system of the USSR was ill

See Trait´ de m´ canique c´ leste (Laplace, 1798“1825) and his theories of induction
e e e

in Th´ orie analytique des probabilit´ s (1812) and in Essai philosophique sur les
e e
probabilit´ s (1814).

Political Change

designed to solve the quandaries resulting from increasing technological
competition with the West. However, this example certainly does not
imply the end of history”the universal acceptance of the superiority of
capitalist democracy. As Keynes foresaw, the chaos resulting from very
rapid political-economic change can induce risk-averse electorates to opt
for autocracy. This may be happening now in Russia and in other countries
which, for whatever reason, ¬nd themselves overwhelmed by the effects
of globalization.
It is obvious that some countries will founder in a world where ef¬cient
institutions are crucial for prosperity. Indeed, there will be countries that
¬nd it impossible to construct or maintain institutions that give them
hope for survival. Poverty and disorder will engender beliefs that have
their bases in nationalism and religion. Because these beliefs owe their
origin to social processes that are essentially chaotic, the effect will be to
create very dif¬cult and unpleasant quandaries for other societies.
In those countries that do not adapt, poverty and disorder will con-
tinue to conspire to bring autocrats to power. In many countries in Africa,
for example, this will induce further economic collapse. One way to help
such countries build sustainable and ef¬cient institutions would be for the
developed countries to open themselves to a greater degree of agricultural
trade with the less-developed world. How this may be done in the face of
protectionist pressure is just one of the quandaries associated with glob-
alization. A deeper quandary is how best to assist the struggling polities
in constructing ef¬cient institutions and learning to deal with economic
Throughout this book, I have emphasized that one necessity of a demo-
cratic polity is that its leader be willing and able to take risk in the face
of a fundamental quandary. However, I have also argued that risk taking
should be balanced by the concerns of the sceptical, and by the calculation
of reasonable guesses about the probabilities of possible outcomes. Obvi-
ously, if the outcomes are truly uncertain, then there can be no guarantee
that correct choices are made.
How Al-Qaeda came about, and the origin of the beliefs that sustain it,
are quite mysterious (Gray, 2003). But it does seem that while the social
and moral beliefs of the members of Al-Qaeda are unintelligible to us,
this has not prevented them from adapting the technology of this age,
producing consequences that are completely out of proportion to their
The extreme heterogeneity of beliefs that may have been triggered by
the coalition invasion of Iraq and the capture of Saddam Hussein seem

Architects of Political Change

to be incompatible with any peaceful move to democratic institutions in
that country. Although attempts are being made to create a constitutional
design that will bring about some degree of political balance, this may
take many years, or even be impossible. But the choices that have been
made during the last few years by U.S. decision makers appear, at least in
retrospect, to have ignored the real possibility that the attempt to impose
order in Iraq would lead to political chaos and trigger further changes in
belief throughout the Middle East. The U.S. Presidential election of 2004
turned on a core belief in the electorate that linked Al-Qaeda to Saddam
Hussein. On this basis it was believed that the military strategy was a
risky but appropriate response to a fundamental quandary. This belief
may turn out to be a chimera.


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