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. 9
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somewhat clumsily, call “National Mercantilism” and “National Keyne-
sianism.”
A fourth non-Keynesian possibility for the future focused on “Hege-
monic Internationalism.” It was obvious to any observer of world events
in 1944 that the interwar era was different from the “golden age” of
1816 to 1910. Although ¬nancial crises had occurred with some regular-
ity,46 the gold system of the nineteenth century had generally seemed to
function well. Indeed this fact probably endowed the Marshallian equi-
librium thesis with credibility. The one obvious difference between the
golden age and 1918 to 1939 was the dominance of Great Britain in
the earlier period, and the lack of such a dominant, hegemonic power
in the latter (Ferguson, 2001, 2002, 2003). An empirically credible hy-
pothesis, as of 1944, was that the United States could act as hegemonic
leader.

See the discussion in Harrod (1971).
45

Kindelberger (1973) mentions nine (in 1816, 1825, 1836, 1847, 1857, 1866, 1873,
46

1890, and 1907).

232
Keynes and the Atlantic Constitution

A brief digression on the nature of a hegemon is appropriate. The
prophets of chaos, who had interpreted the events of the 1970s in terms
of an nPD, tended to focus on the cooperative bene¬ts of trade. From
this point of view, the earlier British hegemony in the nineteenth century
was coupled with free trade policy, even though it was a costly exercise,
in some respects.
Nye (1991) has reviewed the recent literature from economic history
on Britain™s role in the nineteenth century and argued, “To the extent that
Britain maximized, it was out of the imperatives of narrowly individual
economic well-being and without any considerations for . . . shaping the
international system” (209).
Here he directs his comments to the theorists who seem to suggest that
the hegemon guides the international system to cooperation by accepting
costs resulting from increasingly open trade. My view of the nPD differs
from these theorists. I assume that the hegemonic power has a reasonably
clear understanding of the game, and realizes that by “cooperating” either
in trade, or money, it will realize both short- and medium-term bene¬ts.
The medium-term bene¬ts result from the inducements that the hegemon
can offer to potential allies. These side-payments are intended to offset
the sel¬sh bene¬ts of beggar-thy-neighbor strategies and are paid for out
of the hegemon™s own gains. A danger for the hegemon is that its potential
allies will demand too much. In such a situation, it is not inconceivable
that the hegemon can resort to punishment of some kind. By ensuring
cooperation from its allies and thus facilitating their economic growth,
international trade increases, and all bene¬t. The long-term problem for
the hegemon is the probable decline of its relative power. Whether it is
rational in the long-run for the hegemon to pursue this “cooperative”
strategy depends both on its beliefs and on its discount rate.
As we know, a version of hegemonic internationalism was, in fact,
adopted after World War II, and functioned fairly successfully until about
1965. In the next section I examine why this solution was chosen, and how
it meshed with a set of core beliefs that came into being in the immediate
post“1944 period in the United States.

7.8 architects of change, 1944“1948
Core, possibly from old French, cors, body or Italian, cuore; French, coeur, and
Latin, cor, the heart.

The story of the post-war decision has been told many times. I depend
in large degree on the account by Block (1977) for the period from 1944

233
Architects of Political Change

to 1948, starting with the disagreement between Secretary of the Treasury,
Henry Mongenthau, and Secretary of State, Cordell Hunt, over how to
structure the international economy.47
Morgenthau™s assistant, Henry Dexter White, had, by 1942, already
drafted a proposal for an international bank, with capital stock of
10 billion dollars, and a stabilization fund with 5 billion dollars. (In cur-
rent terms, these amounts are approximately 200 billion and 100 billion
dollars, respectively.) The ¬rst institution would become the International
Bank for Reconstruction and Development (IBRD) and the latter the In-
ternational Monetary Fund (IMF).
In the negotiations between the United States and Britain, Keynes es-
sentially kept two options open: International Keynesianism as opposed
to a form of national mercantilism, involving the maintenance of the sys-
tem of imperial preference in the sterling area. For the former, he proposed
a total of 26 billion dollars, or 520 billion dollars in current terms, for the
clearing union, with quotas of the order of 5 billion dollars for Britain,
3 billion dollars for Germany, and 2 billion dollars for France. Members
would be entitled to draw a quarter of their quota per year for ¬ve years.
The Articles of Agreement were drawn up in July 1944 at Bretton Woods.
The non-interventionist aspect of the Agreement induced many members
of Congress to oppose approval of the fund because of the likelihood that
countries could escape monetary discipline. Nonetheless, the Bank started
operations in June 1946, with an authorized capital stock of 10 billion
dollars.
Before the Bank even started, Franklin D. Roosevelt died (April 1945).
President Truman immediately replaced Morgenthau with Fred Vinson.
White™s in¬‚uence, and the acceptability of the Treasury™s “Keynesian Inter-
nationalism,” both faded. The State Department wanted to force Britain
to open up the sterling bloc to U.S. interests, and, in particular, to oblige
sterling to become, once again, fully convertible.
The problem with this aim was the 14 billion dollars of sterling balances
held by the member states within the British Empire. The termination of
lend/lease and the ¬‚ow of U.S. capital to Britain obliged the new Labour
government (as of June 1945) to deal with a serious balance of payments
problem. Keynes, as principal negotiator for Britain, requested 6 billion
dollars, but the United States scaled this down to 3.75 billion dollars,
and required commitments that the British would open the sterling area.

My discussion of the founding of the World Bank and of the Marshall Plan is drawn,
47

with permission, from unpublished work by Imke Kohler (1998).

234
Keynes and the Atlantic Constitution

Legislation would probably have failed in the House of Parliament in
December 1945, had not Keynes spoken up for the plan in the Lords. The
loan agreement almost failed in the U.S. House of Representatives as well,
but passed partly because of the recognition of Britain as an ally against
possible Soviet threats in Europe. The French also requested a 4 billion
dollar trade credit, which was reduced to 650 million dollars.
At the founding meeting of the IMF in Savannah, Georgia, in March
1946, Keynes had expected that White would be appointed managing di-
rector and the fund located in New York. The Americans vetoed White,
arguing that both the IMF and the Bank should be guided by people con-
sidered to be cautious by the ¬nancial community. Eugene Meyer was
appointed the ¬rst President of the Bank, and Camille Gutt, a former Bel-
gian Finance Minister, was chosen as the Fund™s ¬rst Managing Director.
U.S. voting power in the Bank was particularly pronounced. The United
States with a subscription of 41.4 percent had 37 percent of the voting
weight, while the second strongest was Britain with about 17 percent of
the subscription and 15.3 percent of the voting weight.48 The Bank™s pres-
ident, Meyer, resigned in December 1946 and a Wall Street lawyer, John
McCloy, took over somewhat later in March 1947.
On July 15, 1947, Britain started to move toward convertibility. Some
of the U.S. loan had already been used by this time; conversion of sterling
to dollars immediately drained the remaining dollars from the British
account. The experiment ¬nished on August 21, 1947.
Keynes had died a few weeks after the Savannah meeting in 1946.The
third volume of Skidelsky™s biography (Skidelsky, 2000) suggests that by
1945 Keynes realized that some form of International Keynesianism could
not be brought into existence. On the other hand, it seems that he did be-
lieve that protection of British interests, within a framework of National
Keynesianism, was viable. The high costs of the British experiment with
convertibility would have suggested, however, that international cooper-
ation would have to depend on U.S. capital ¬‚ows.
The immediate problem facing the European nations was, of course,
the terrible destruction of the war. The UNRRA (U.N. Relief and Rehabil-
itation Administration, set up in November 1943, prior to the founding
of the United Nations) had channeled 2.6 billion dollars of U.S. funds,
principally to Europe. This institution closed, however, in March 1947.
Partly as a result of this aid ¬‚ow, the U.S. export surplus for 1946 was of

The voting weight was computed as follows: Each country had 250 votes (out of
48

86,000) plus an additional one for each 100,000 dollars invested in the Bank.

235
Architects of Political Change

the order of 38 billion dollars. This surplus would obviously decline un-
less some form of capital ¬‚ow could be organized.49 Incidents in 1946 in
Europe reinforced the views of prominent U.S. policy makers that it would
be irrational to provide money to an institution such as the UNRRA.50 On
the other hand, there was much enthusiasm for the recently established
United Nations and support for the principle that aid should be chan-
neled through a multilateral agency. Indeed, George Kennan (who moved
to the State Department to set up the Policy Planning Staff, in May 1947)
has made this point in his memoirs (1976: 338). An offer of aid by the
United States, to be channeled through the Economic and Social Council
of the United States, was considered in June 1947 by the Foreign Minis-
ters of Britain, France, and the USSR. Russia™s Foreign Minister, Molotov,
rejected the plan. This implied that aid ¬‚ow would be directed at West-
ern Europe, (possibly through the OEEC, the Organization of European
Economic Cooperation).
The Bank was an obvious, potential channel for the aid ¬‚ow. This
would obviously be more attractive to members of Congress than the
UNRRA. However, McCloy, the Bank™s president, had declared in early
1947 that if “European recovery required massive new loans, then the
American taxpayer [will] have to ¬nance a bilateral program” (Bird, 1992:
292).
In 1947, the Bank did provide a number of loans and credits: 250
million dollars to France in May, 195 million dollars to the Netherlands,
in August, and 52 million dollars to Denmark and Luxembourg. An offer
in the region of 3.1 billion dollars to the Bank by the United States was
turned down by McCloy. In addressing the Bank™s Board of Governors,
he observed that accepting the loan would have gone against the Bank™s


Between the second quarter of 1946 and the fourth, overall U.S. aid dropped from
49

6.5 billion dollars to 4.2 billion dollars. During the same period, the U.S. export
surplus in goods and services dropped from 9.9 billion dollars to 7.7 billion dollars.
By the third quarter of 1947, when aid had increased to 7.8 billion dollars, the
surplus had increased to 10.3 billion dollars. It could be fairly easily deduced that
there was almost a linear relationship between aid and surplus. Thus, the initial ¬‚ow
of aid that seemed to be required under a strategy of hegemonic internationalism
can be deemed to be rational for the United States in terms of immediate trade
consequences.
According to Secretary of State James Byrnes, Czech delegates had applauded a
50

denunciation of the United States by a Soviet of¬cial just after the United States had
approved a 50 million dollar credit. In his view, there was no point in an institution
that the United States funded and yet held only one vote in seventeen. See Byrnes
(1947: 143).

236
Keynes and the Atlantic Constitution

international standing, and essentially turned it into a U.S. organization
(Kapur, Lewis, and Webb, 1977: 292).
Concerns about the stability of Greece and Turkey in early 1947 con-
tributed to the formulation of the so-called Truman doctrine of March
1947. As President Truman said, “It must be the policy of the United
States to support free peoples who are resisting attempted subjugation by
armed minorities or by outside pressures.”51
In conjunction with the Truman proposals, directed against the Soviet
Union, it was seen as important to provide substantial aid for reconstruc-
tion to Western Europe, as a buttress against communism.52 However,
McCloy, in a speech in New York in April 1947, said that the Bank “can™t
and won™t grant loans in order to accomplish political objectives.”
The Bank became a specialized agency of the U.N. on November 15,
1947,53 and in January 1948, McCloy again declared that the Bank could
not be used as a vehicle for massive aid ¬‚ow, through the ERP (the Euro-
pean Recovery Program) of the Marshall Plan:

[We] would give consideration to [any loan tied to the ERP]. We might, however,
not have enough money to meet all of the good hard loans that may be needed,
because of my dependence on the market. . . . I want to keep emphasizing the fact
that we have 46 nations with which to deal, not 16.54

The process of approving the ERP speeded up after Czechoslovakia was
taken over by the Soviet Union in February 1948. After Marshall™s speech
in 1947, the Europeans had put in a proposal for 40 billion dollars in aid,
which had been reduced to 20 billion dollars (about 360 billion dollars
current). The plan was approved on April 3, 1948, and commenced on
July 1, 1948. The actual overall aid ¬‚ow to Europe was, in fact, of the
order of 13 billion dollars.
Of the ERP capital ¬‚ow, from then until 1952, 80 percent was in the
form of grants, and the interest rate on loans was about 2.5 percent. In
contrast, the Bank depended almost entirely on the market for its capital.

President Harry Truman, address delivered before a joint session of Congress, Eight-
51

ieth Congress, March 12, 1947.
The outlines of the proposed ¬‚ow of aid to Western Europe were given in a speech by
52

Secretary of State George Marshall at Harvard on June 5, 1947. The whole program
became known as the Marshall Plan. For the formulation of this plan by the U.S.
architects of change, see Jones (1955).
However, the Bank insisted that it was required “to function as an independent
53

organization.” See Mason and Asher (1973).
John McCloy, hearings before the Committee on Foreign Relations (concerning the
54

European Recovery Program), Eightieth Congress, January 16, 1948.

237
Architects of Political Change

Although the “authorized” capital stock was 10 billion dollars, 80 percent
of this was “on call.” Of the other 20 percent (2 billion dollars), 1.8 billion
dollars was paid in the respective currency of the member country, and 200
million dollars paid in dollars or gold. Since only dollars were convertible,
the loanable assets were about 740 billion dollars. In July 1947, the Bank,
under McCloy, had issued bonds in the U.S. stock market of 100 million
dollars (at an interest rate of 2.25 percent over ten years) and 150 million
dollars (3 percent over twenty-¬ve years). These brought total loanable
assets to just under 1 billion dollars. Any loans that the Bank could make
during the operation of the ERP would clearly be less attractive than
Marshall aid or loans. In fact, the Bank loaned only 28 million dollars
from 1948“1949 (to Belgium and the Netherlands) although it had earlier
made a major loan to France of 250 million dollars.
Although McCloy had supported the ERP during the Congressional
Hearings in 1948, he believed by 1949 that the United States should
cede the loan component of the Marshall Plan to the Bank. His letter
to Truman, making such a case, received no reply from the president.55
By 1949, McCloy™s attempt to preserve something of Keynesian Interna-
tionalism had clearly failed. Hegemonic Internationalism, as represented
initially by the Marshall Plan, was ¬rmly in place, and was to persist in a
strong form through the 1950s. Although the early phase of the strategy
required a substantial aid ¬‚ow to Europe, the signi¬cant bene¬t to the
United States, in the form of a large export surplus, is consistent with the
analysis of hegemonic behavior in the international economy. A further
key element in U.S. strategy was to push for convertibility of currencies.
To facilitate this, trade cooperation within the little Europe of the EEC
was emphasized. To attempt to stabilize currencies, a dollar“gold stan-
dard was adopted, involving devices such as the “snake in the tunnel”
(Solomon, 1977: 276).56
The strategy of hegemonic internationalism was, in a sense, based
on two economic beliefs. First, assuming that convertibility could be at-
tained, then a dollar“gold standard would support economic equilibrium.
Second, this equilibrium could be maintained even when member coun-
tries utilized internal macroeconomic neo-Keynesian strategies to attain

Bird (1992: 299). See also McCloy (1949). In fact, Truman™s proposal shortly af-
55

terwards, to initiate a U.S. loan program for non-European countries, suggests that
McCloy™s argument was completely rejected.
The “snake” was the 2.5 percent bound within which the European currencies
56

were allowed to ¬‚uctuate, while the “tunnel” was the 5 percent bound restricting
¬‚uctuations against the dollar.

238
Keynes and the Atlantic Constitution

full employment. As has been well documented, it became increasingly
dif¬cult in the 1960s to maintain this international equilibrium, and by
1971 it was obvious to everyone that the attempt had failed. Keynes™ intu-
itions about the propensity to engage in “beggar-thy-neighbor” strategies
were eventually seen to be justi¬ed.
For the next ten years, fairly erratic attempts were made to ¬nd a new
core belief, a theoretical foundation for the stabilization of the interna-
tional system. As we have seen, such a foundation was eventually put in
place in the early 1980s.
It was not inevitable, however, that “hegemonic internationalism”
would be the strategy adopted from 1944 to 1948. It is clear from Mc-
Cloy™s argument, both to the Bank™s Board and to Truman, that he believed
that the Bank could have played a much more important role in restruc-
turing the world economy after 1948. Indeed, McCloy obviously felt that
it was important that the Bank remain a multilateral institution, rather
than an instrument of U.S. policy. A dif¬culty for McCloy, of course, was
that the resources on which the Bank could draw never exceeded 1 billion
dollars, while Marshall aid was of the order of 13 billion dollars. The
U.S. policy makers were not inclined to let the ERP resources go to a
“multilateral” agency, such as the Bank. However, it is inconceivable that
the larger resources of an enhanced IBRD could ever have been used di-
rectly against U.S. interests in the way these policy makers feared. There is
also no reason to suppose that channeling the aid ¬‚ow through the Bank
would have slowed down the process toward a liberal economic order.
Given McCloy™s respectability and familiarity with Wall Street, it is
clear that the Bank, under his leadership, could have been the instrument
by which private capital was channeled to Europe. Combing both private
capital and U.S. aid, under the aegis of the Bank, could have led to a very
different international regime. In any case, McCloy did not play a role in
the future development of hegemonic internationalism.57
It is, of course, impossible to do full justice to the political complexi-
ties of the period 1944 to 1948 in a few pages. But one general point is
worth making. I have emphasized the two related economic equilibrium
hypotheses that underpinned the Bretton Woods system. However, the
Marshall aid ¬‚ow, which was so crucial to the stabilization of the Euro-
pean economies, was acceptable to U.S. policy makers precisely because of


McCloy resigned from the presidency of the Bank in 1949 to become high commis-
57

sioner for Germany (until 1952). He came back from private life (in ¬nance) in 1961
to be Kennedy™s advisor.

239
Architects of Political Change

a political belief in the necessity for “containment” of the Soviet Union.
While the Truman doctrine to this effect was ¬rst proposed in March
1947, it would appear from George Kennan™s memoirs (1976) that his
own paper of 1947, “The Sources of Soviet Conduct,” had a signi¬cant
impact on the U.S. interpretation of Soviet intentions (354“67). As I un-
derstand Kennan™s observations, made in 1967, he regretted that the belief
cascade that occurred in 1947 among U.S. policy makers did not allow
for the nuanced responses to Soviet actions recommended in his article.
Obviously enough, the strategy of hegemonic internationalism was one
solution consistent with both the economic core beliefs, and the contain-
ment belief. It is unclear whether a strategy of some kind of Keynesian
internationalism would have been possible in the presence of a strongly
held belief in “containment.” In any case, given the present absence of any
obvious threat from an aggressive nuclear power, a vigorous multilateral
strategy based on some of Keynes™ insights could be relevant in framing
a solution to the current international quandary.


7.9 concluding remarks
In the current situation, it is entirely possible that very large volumes
of capital will be required in the near future to stabilize the “emerging
markets” of the world. One can only guess at the necessary volumes, but
a ¬rst estimate would be the scale of the initial proposal for Marshall aid
¬‚ow (about 20 billion dollars in 1948 terms, or about 320 billion dollars
currently). Such an amount is easily within the scope of private ¬nancial
markets. It is evident today that private capital is abundant, but in need
of a relatively risk-free haven. The currency turmoil in Southeast Asia
and Russia in the late 1990s dramatically increased global ¬nancial risk.
As a consequence, capital ¬‚owed into the U.S. bond, money, and stock
markets in the period December 1998 to May 2000. Although the U.S.
stock market fell from May 2000 to the re-election of George Bush in
November, 2004, because of uncertainty about events in the Middle East,
it has risen during 2005. However, the vast, and rapidly growing Federal
Budget De¬cit and U.S. trade de¬cit have begun to seem unsustainable at
the time of writing (December, 2005).
It seems obvious that a bond market, based on the IBRD, could be
established, with a risk-premium of the order of a few percent over and
above the U.S. bond rate, in order to stabilize the capital out¬‚ows from
the “emerging” economies. Risky ¬nancial institutions, in Russia, for ex-
ample, are currently unable to attract capital even at very high interest

240
Keynes and the Atlantic Constitution

rates, because potential investors are afraid of potential economic and
political chaos there. Thus, there is a pronounced mismatch between the
beliefs of holders of capital, even those called enterprise by Keynes, and
the needs of developing markets. A recon¬guration of the Articles of the
World Bank would help resolve this disequilibrium. This is not, of course,
to suggest that speculative ¬‚ows would be completely damped, though the
effects could be mitigated.
One of the triggers for the current disequilibrium is the scale of losses
in Japanese ¬nancial and property markets. This is at least of the order
of a trillion dollars. Unfortunately, the Japanese polity is “sclerotic” (for
reasons that are obvious from the viewpoint of public choice theory).
To free up the Japanese market appears impossible because of the debts
and obligations that link corporate and banking entities to the polity. It
is probable that these markets will eventually crash completely, bringing
down the Japanese political system with them. Such a prospect reminds
us of the 1930s. It would be more prudent, perhaps, to bring increasing
pressure to bear on the Japanese polity to free itself from these obligations
to the corporate world.
A possible solution to the quandary that appears before us could in-
volve a combination of the Keynesian Internationalism based on a Clear-
ing Union, as in the original Bretton Woods scheme, together with the
discipline of the market.58 On the one hand, this resolution might avoid
the specter, feared by Keynes, of a global speculative crash. On the other
hand, it would be different from the distorted form of the Bretton Woods

See Block (1996) for suggestions on how the international economic system might
58

be “weakly regulated” in this fashion. Note that the dif¬culty on regulation depends
on scale, correlation, and the degree of acceptable volatility. Because the dangers
at present lie in emerging economies and Japan, it would be prudent to set up an
institution of whistle-blowers to provide advance warning of economic or political
shocks in such countries. None of the international economic institutions provide
such information at present. Moreover, Sobel (1999) suggests that the market it-
self does not interpret such information ef¬ciently. With greater resources than at
present, the clearing union would be able to mitigate the effect of capital ¬‚ight,
when it did occur, more successfully. Because much of the problem of capital ¬‚ight
is due to short-term investment, this could also be mitigated through the use of long-
term investment under the aegis of the International Bank for Reconstruction and
Development. The purpose of such local strategies would, obviously, be to reduce
the degree of contagion, or correlation of economic instability, among a large num-
ber of economies. Block estimates that the daily trading volume on international
exchange markets is about 1.2 trillion dollars and that 90 percent of this is specu-
lative. Clearly, no reserve fund of plausible size could hope to regulate such a ¬‚ow.
The mechanisms suggested above are intended as devices to decrease the possibility
that speculative cascades might occur.

241
Architects of Political Change

system, namely Hegemonic Internationalism, that Keynes obviously be-
lieved would be inadequate to the task of maintaining mutual cooperation
in the long run, both within the Atlantic Alliance, and between the devel-
oped and less developed economies.
At a more abstract level, the rejection of the strong equilibrium the-
sis could result in the overthrow of the hegemony of economic theory,
and open the way to a more “disordered” family of social, political, and
economic subdisciplines that could, paradoxically enough, give a better
understanding of, and basis for, the Atlantic Constitution.




242
8
Preferences and Beliefs




8.1 introduction —
The great theorems of social mathematics discovered during the twentieth
century can be separated into those that emphasize equilibrium and those
that hint at chaos, inconsistency, or irrationality.1
The equilibrium results all stem from Brouwer™s Fixed Point theorem
(Brouwer, 1910): A continuous function from the ball to itself has a
¬xed point. The theorem has been extended to cover correspondences
(Kakutani, 1941) and in¬nite-dimensional spaces (Fan, 1961) and has
proved the fundamental tool in showing the existence of equilibria in
games (von Neumann, 1928; Nash, 1950, 1951), in competitive economies
(von Neumann, 1945; Arrow and Debreu, 1954; McKenzie, 1959; Arrow
and Hahn, 1971), and in coalition polities (Greenberg, 1979; Nakamura,
1979).2
¨
The ¬rst of the inconsistency results is the Godel-Turing theorem on
the decidability-halting problem in logic (Godel, 1931; Turing, 1937): Any
¨
formal logic system (able to encompass arithmetic) will contain propo-
sitions whose validity (or truth value) cannot be determined within the



This chapter is adapted from Norman Scho¬eld, “Equilibrium or Chaos in Prefer-
ence and Belief Aggregation,” in Competition and Cooperation, J. Alt, M. Levi, E.
Ostrom, [eds]. (Russell Sage Foundation: New York 1999): 32“50, with permission
of the Russell Sage Foundation.
The term “social mathematics” was ¬rst used by Marie-Jean-Nicolas, Marquis de
1

Condorcet, in 1785 (see MacLean and Hewitt, 1994).
All of these equilibrium results depend on the intuition that a dynamical system
2

(or “vector ¬eld”) on certain types of spaces (like balls or tori or even-dimensional
spheres) must have singularities (“equilibria”). This intuition allows one to develop
the mathematics using the qualitative theory of global analysis (Smale, 1973; Mas-
Colell, 1985; Scho¬eld, 2003d).

243
Architects of Political Change

system. Recently this theorem has been used by Penrose (1989, 1994) to
argue against Dennett (1991, 1995) that the behavior of the mind cannot
be modelled by an algorithmic computing device. A version of the Turing
theorem has been used more recently to show that learning and optimiza-
tion are incompatible features of games (Nachbar, 1997, 2001, 2005).
¨
There is still controversy over the meaning of the Godel theorems, but
one interpretation is that mathematical truths may be apprehended even
when no formal proof is available (Yourgrau, 1999; Goldstein, 2005).
The second fundamental inconsistency result is Arrow™s Impossibil-
ity theorem (Arrow, 1950a, 1950b, 1951), which shows that apparently
innocuous properties of a social welfare function are suf¬cient to ensure
that it is dictatorial. My reading of these works by Arrow suggests to me
that Arrow was concerned not simply with the possibility of voting cycles,
nor with the intransitivity of domination in voting games (von Neumann
and Morgenstern, 1944). Rather, he was interested in the larger issue
of the interaction between the political and economic realms, the topic
that concerned the political economists and philosophers such as Schum-
peter (1942), von Hayek (1944, 1948), and Popper (1945), in the period
around World War II. If I am correct in my inference, in order to under-
stand Arrow™s theorem it is necessary to set out the fundamental problem
of political economy, namely, the nature and evolution of the social rela-
tionship between human beings. To do this, I comment on my perception
of the main themes of this debate since the time of Hobbes.
Because I understand this debate to focus on the possibility of equi-
librium in contrast to disequilibrium (or disorder), I shall also mention
what I judge to be the third signi¬cant anti-equilibrium discovery of this
century: chaos.
Smale (1966) is responsible for the key mathematical result that relates
to chaos: Structurally stable dynamic systems are not generic when the un-
derlying space has three or more dimensions.3 To illustrate, astronomers
since the time of Laplace (1798) have believed that the solar system is
structurally stable: It was supposed that small perturbations in each plan-
etary orbit (induced by other planets) cannot dramatically change the
nature of the orbit. Although Newton was aware of the problem of per-
turbations (Newton, 1995[1687]), even Poincar´ in his treatise of 1890
e
could not solve the differential equations. However, Poincar´ ™s work in
e
4




A structurally stable system is one that, when perturbed slightly, has identical quali-
3

tative properties. Generic means “almost all.”
See discussion on theories of the solar system in Peterson (1993) and Saari (2005).
4


244
Preferences and Beliefs

celestial mechanics (Poincare, 1993[1892“1899]) led to the beginning of
differential topology and the work of Morse, Milnor, and Smale in this
century. If the solar system were structurally unstable, or indeed chaotic,
then it would be impossible to predict its evolution. It seems indeed that
the system is not chaotic, although subsystems (such as asteroids) are.5
As a result of popular books (Gleick, 1987), we can conceive of natu-
ral phenomena (hurricanes) or even large-scale dynamic systems (such as
climate) as potentially chaotic (Lorenz, 1993). Although still a young sci-
ence, human evolutionary theory suggests that chaotic transformations
in weather may have had a profound effect on the human diaspora out
of Africa (Calvin, 1991; Stanley, 1996; Boaz, 1997). Equilibrium-focused
evolutionary theory may also need a revision (Eldredge and Gould, 1972;
Gould, 2002).
Many scholars of human society believe that society™s evolutionary
progress is intelligible, in the sense that predictions, of at least a qualitative
form, can be made. This, I presume, is the understanding of economists
when they base their reasoning on the fact of equilibrium. Even North
(1990, 1994, 2005), in his discussion of economic development, suggests
that an understanding of institutions allows us to infer something about
the social “laws of motion.” Contrary to North™s suggestion that institu-
tions are the “rules of the game,” it appears to me that institutions are
equilibria. If these equilibria are in constant ¬‚ux, then the dynamic that
describes this motion (if indeed there is one) is just as likely to be chaotic
as to be structurally stable.
It is, of course, possible that this belief, in the structural stability of
society, is sustained by the apparent stability of the “world out there.”
Indeed, the bipolar world from the late 1940s until about 1990 did appear
stable. Since then, the collapse of the Soviet Union, the disintegration of
the Warsaw Pact, tumult in the Balkans, genocide and starvation in Africa,
the troubles in Israel, all suggest that qualitative change is a permanent
characteristic of the world.
To tie the three instability theorems together in a kind of hierarchy, we
¨
may start with Penrose™s argument that the Godel-Turing theorem sug-
gests that, at the ¬ne level of analysis, individuals can display surprising,
or apparently incomprehensible, behavior. Indeed, it is obvious that cog-
nitive psychology can give only a very coarse-grained account of human
motivation. One possible coarse-grained account is that each individual

Chaotic phenomena can, of course, have profound consequences. A chaotic event,
5

an asteroid collision, may have led to the extinction of the dinosaurs.

245
Architects of Political Change

is “approximately” characterized by a preference correspondence (satis-
fying the usual properties assumed in microeconomics). However, game
theory has made it obvious that the beliefs of agents are as important as
(or even more important than) their preferences. Preferences are relatively
easy to model, but beliefs are much more complicated. (In fact, they lie in
function spaces.) Thus, while it is a standard formal procedure to use a
Brouwer Fixed Point theorem to show the existence of optima in prefer-
ences, it is much more dif¬cult to postulate conditions under which stable
beliefs (a “belief equilibrium”) can occur.
Arrow™s theorem suggests that, even when individuals can be described
by their preferences, only under particular circumstances can these prefer-
ences be aggregated to induce a “social vector ¬eld” that is “well behaved”
in an appropriate sense. This is not to say that the social vector ¬eld can
never exist; rather, there may be circumstances under which this ¬eld is
badly behaved (or ill de¬ned) in some sense. Obviously, I am transpos-
ing Arrow™s theorem from the discrete world where it was located to the
continuous world of political economy. By a social vector ¬eld I mean a
method of de¬ning a direction of change compatible with the Pareto una-
nimity condition. If such a vector ¬eld could be de¬ned, then in the usual
political economy world (which is compact and convex), Brouwer ¬xed
point arguments would give a singularity (a “social equilibrium”). The
¬eld could be badly behaved, for example, if it were not de¬ned in some
zone outside the Pareto set. Consequently, following the ¬eld would not
lead into Pareto preferred outcomes. Arrow™s theorem suggests that the
only way to avoid such bad behavior is for one individual to be dictator.6
Suppose now that Arrow™s theorem is avoided by some device. For ex-
ample, consider a world where everyone has strictly economic preferences
and no public goods exist. In such a world, a competitive price equilib-
rium does exist. However, to attain it, we must imagine a price adjustment
process (a vector ¬eld) based on excess demand. As an example by Scarf
(1960) suggests, this vector ¬eld can be cyclic. Indeed, later results by
Mantel (1974), Sonnenschein (1972), and Debreu (1974) show that it can
be anything at all. As Saari (1991) has emphasized, this economic ¬eld
could be chaotic.

To illustrate, voting mechanisms without vetoers (or collegia) can be badly behaved
6

in the sense that voting trajectories (“following” the social vector ¬eld) may lead
away from the Pareto set. The social choice chaos theorem basically suggests that
this is a generic property when choice is based on preferences alone and the voting
rule is non-collegial. See the discussion in Chapters 1 and 2.


246
Preferences and Beliefs

This, of course, does not imply that the world is indeed chaotic. Some
aspects of the political economic world may be chaotic without implying
that the entire human universe is. To use the metaphor of the solar system,
perhaps the overall process of human society is structurally stable, but
contains locally chaotic subsystems.
To illustrate the idea of chaos, it may be worth a detour to mention
von Neumann again, since his work touches on many aspects of social
mathematics (as well as other fundamental areas of quantum mechanics,
group theory, and so on).
Even before his game theory paper of 1928 and the work on gen-
eral economic equilibrium (1945), von Neumann had published results
on completing Hilbert™s program for proving the consistency of classical
¨
mathematics by ¬nitary means. A recent biography of Godel (Dawson,
¨
1997) notes that Godel presented his inconsistency theorem at
¨
Koningsburg in 1930 to an audience that (aside from von Neumann)
failed to grasp its signi¬cance. As far as I know, von Neumann ceased to
work in formal logic after 1930.
Von Neumann met Turing in Cambridge in 1935, and later during Tur-
ing™s visit to Princeton from 1936 to 1937 (Hodges, 1983), but appears to
have paid little attention to Turing™s results on the halting problem. How-
ever, von Neumann does appear to have made use of Turing™s later work on
computation during the Second World War, as well as Turing™s essay on ar-
ti¬cial intelligence (Turing, 1950). Beginning in 1943, von Neumann was
involved in approximate numeric solutions using some form of computing
device. Turing™s notion of a universal machine seems to have been indis-
pensable to the design of British and American decoding devices during the
war and to the construction of the computation machines (Edvac, Eniac,
Maniac) necessary for the solution of nonlinear dynamical problems asso-
ciated with the design of the hydrogen bomb (see Ulam and von Neumann,
1947). Von Neumann took Turing™s idea of a universal computing device
and extended it to a model of the brain (von Neumann, 1958) and of life
(self-reproducing automata) in work later edited by Burks (von Neumann,
1966).
What is interesting about this research is that Ulam, von Neumann™s
collaborator, had found chaos in a stochastic, or Monte Carlo, simula-
tion of a relatively simple dynamical system (Fermi, Pasta, and Ulam,
1955). As far as I know, this is the ¬rst example of a computational model
generating chaos. (It predates Lorenz™s meteorology simulation by seven
years.) Monte Carlo simulation by von Neumann and his associates in


247
Architects of Political Change

numerical weather prediction and in their work on the bomb does not
appear to have observed chaos (Galison, 1997).
In von Neumann™s book with Morgenstern (1944) on cooperative game
theory, the focus (as I understand it) is on trying to “equilibriate” the ob-
vious cyclicity inherent in constant-sum voting games, using such devices
as the von Neumann-Morgenstern solution. Later work in cooperative
game theory also attempted to introduce equilibrium ideas (such as the
bargaining set; see Aumann and Maschler, 1964). These attempts seem
unsatisfactory, and this may be why cooperative game theory is currently
less in¬‚uential than noncooperative game theory (and the powerful notion
of Nash equilibrium).
These observations about chaos bring us back to the argument by
Penrose (1989) that the indeterminacy of the quantum world implies that
the mind is non-algorithmic (see also Popper, 1972, and Popper and Eccles,
1977). The connection between the quantum world and the world of the
mind may be somewhat tenuous: Nevertheless, Penrose™s argument that
the mind is not like a computer is very powerful. More important, the re-
¨
cent extension of Godel™s argument by Nachbar (1997, 2005) suggests that
to play a “game” successfully each agent must already know an impossible
amount about every other agent playing the game. In particular, “algo-
rithmic” agents cannot learn enough about the other agents as the game
progresses.
This is not to deny that computers can play games; but I do deny that
people play games like computers (see also Searle, 1999, for a similar
argument). More generally, I would say that the kinds of games people
play are like poker rather than chess. Predicting how people will play
the game of life is well nigh impossible. Although each of us can gain
some insight into the minds of other people, and may thus believe we
understand something of the social world around us, we can never fully
understand the acts of our fellows. As Arrow (1973: 262) wrote (though
in a somewhat different context than considered here):

To the extent that individuals really are individual, each an autonomous end in
himself, to that extent they must be somewhat mysterious and inaccessible to one
another, there cannot be any rule that is completely acceptable to all. There must
be, or so it seems to me, the possibility of inadjudicable con¬‚ict.


However, to live in society, we do have to understand one another. The
next few sections will attempt to see how we can model this interaction.


248
Preferences and Beliefs

8.2 hobbesian and lockean views of society
Hobbes returned to the England of the Protectorate in December 1652, ten
years after his departure, three years after the execution of Charles I, and
a few months after the publication of Leviathan. Hobbes™s biographer,
Rogow (1986), quotes sources suggesting that during Hobbes™s meeting
with Galileo in Florence from 1635 to 1636, “Galileo gave Hobbes . . . the
¬rst idea that the doctrine of ethics . . . can be brought to a mathematical
certainty by applying the principles of geometry” (109).
As MacPherson (1968) says in his introduction to Leviathan:
The resolutive part of Galileo™s method was an exercise in imagination. What
simple motions or forces could be imagined which, when logically compounded,
would provide a causal explanation of the complex phenomenon which was to
be explained? . . . The resolutive stage . . . consisted in resolving political society
into the motion of its parts”individual human beings. (26)

Although it is the appetites and aversions that move men, the effect is a
“generall inclination of mankind, a perpetuall and restless desire of Power
after power, that ceaseth only in Death. . . . It is manifest, that during the
time men live without a common Power to keep them all in awe, they
are in that condition which is called Warre. . . . And the life of man [is]
solitary, poore, nasty, brutish and short” (Hobbes, 1968: 185).
Hobbes goes on to discuss the nature of contract or “Covenant”:
If a Covenant be made . . . in the condition of meer Nature . . . it is Voyd; But if
there be a common Power set over them both, . . . it is not Voyd. . . . But when a
Covenant is made, then to break it is Unjust. . . . A multitude of men, are made
One person, when they are by one man, or one Person, Represented . . . And if
the Representative consist of many men, the voyce of the greatest number, must
be considered as the voyce of them all. (220)

On the form of the commonwealth, whether monarchy, democracy,
or aristocracy, Hobbes suggests that the difference is not in power, but
in “Convenience, or Aptitude to produce the Peace, and Security of the
People” (241).
In chapter 18, Hobbes compares the bene¬ts of life in the common-
wealth with “the miseries, and horrible calamities, that accompany a Civill
Warre” (238).
In chapter 24, he discusses the economy of the commonwealth”the
distribution of land, the nature of taxes, and, most important, the role
of money, the Sanguini¬cation of the Commonwealth. In this chapter,
Hobbes refers again to his somewhat shocking metaphor: “For by Art is


249
Architects of Political Change

created that great Leviathan called a Common-wealth, or State . . . which
is but an Arti¬ciall Man” (81).
Many political theorists of the recent past (Taylor, 1976, 1982; Sugden,
1980; Axelrod, 1984) have interpreted Hobbes™s argument for Leviathan
in terms of the prisoners™ dilemma. That is, the state of nature, of “Warre,”
is the Nash equilibrium (indeed, the joint dominant strategy in the game).
All players prefer the state of cooperation, of peace, but it is unattain-
able without a covenant. The arguments have often proceeded to suggest
that the “game form” is that of an n-person-iterated prisoners™ dilemma.
In such a game, cooperative equilibria may be possible if they are sus-
tained by appropriate beliefs on the part of the agents. Much of the work
of these theorists can be seen as an extension of Nozick™s famous book
Anarchy, State, and Utopia (1974) to argue, contra Hobbes, that the state
(Leviathan) is unnecessary for security. For example, Sugden argues that
“conventions” (such as language, or driving on one side of the road)
arise spontaneously as solutions to games of coordination and cooper-
ation. But if we think of language as a convention, then it is obvious
enough that it evolves quite rapidly. In Papua New Guinea, where hu-
man settlements are geographically separate, the evolving languages be-
came extraordinarily diverse. (In fact, it has been estimated that there are
about one thousand distinct languages, clustered in thirty phyla, among
a population of about four million.) Although there may be some va-
lidity in Taylor™s (1982) argument that “community” can indeed sustain
cooperation in the absence of a Hobbesian Leviathan, or state, the ar-
gument works only for small communities. Arrovian disorder between
such communities would appear to be generic.7 Moreover, the evolu-
tion of the “equilibria” of these cooperative conventions would seem to
be as indeterminate as the formal models of n-person-iterated prison-
ers™ dilemmas (Kreps et al., 1982). I return to this later when discussing
“belief equilibria.”
Locke™s Two Treatises of Government was published anonymously in
1690. This work is often taken as a response to both the Glorious Revolu-
tion of 1688 and Hobbes™s Leviathan. However, Laslett (1988), in his in-
troduction to the Treatises, suggests that they were written approximately

Just to give an example, Greif (1997) has analyzed the pattern of behavior in twelfth-
7

and thirteenth-century Genoa. In the absence of an outside threat (the Holy Roman
Emperor), Genoa collapsed into a thirty-year civil war. By “chance” the city adopted
the idea of a podesta, a paid pivotal “Leviathan,” with whom the Genoese families
made a covenant. From 1190 to 1300, Genoa was able to engage extensively in trade
with the countries of the western Mediterranean.

250
Preferences and Beliefs

ten years earlier in response to Filmer™s essays, The Natural Power of Kings
Defended against the Unnatural Liberty of the People (1632) and Ob-
servations Concerning the Origins of Government (1652). In the second
treatise, Locke (1988 [1690]) develops further the notion of a contract
but seems to remove the almost metaphysical Hobbesian conception of
Leviathan.

And Thus every Man, by consenting with others to make one Body Politik under
one Government, puts himself under an Obligation to every one of that Society, to
submit to the determination of the majority . . . For if the consent of the majority
shall not in reason, be received, as the act of the whole . . . nothing but the consent
of every individual can make anything to be the act of the whole: But such a
consent is next to impossible to be had. (97)


Locke™s version of the compact has obviously strongly in¬‚uenced the
twentieth-century contractarian visions of Rawls (1972), Gauthier (1986)
and particularly Nozick (1974). For Nozick, property (and especially la-
bor) is a fundamental feature of Lockean liberty. Nozick constructs what
has been called a meta-utopian framework (Gray, 1984), within which
free individuals migrate to preferred communities, agree on public pro-
vision, and live in peace. The formal underpinning of this framework is
that of the “core,” the set of allocations that are coalitionally rational.
But the conditions suf¬cient for the existence of a core (balancedness,
“private” preferences, and so on) are likely to occur only in pure private
goods economies. If power is a feature of the Nozickean political economy
then the appropriate formal model is not the exchange economy but the
constant-sum game. In such a world, the core is generically empty, and
cycles or Arrovian intransitivities are pervasive. Nozick™s anarchic utopia
is thus void.
Gray goes on to describe von Hayek™s (1944, 1948, 1973, 1978) meta-
utopian framework in terms of the idea of “a spontaneous order, of self-
organizing and self-replicating structures [that] arise without design or
even the possibility of design.”
This framework is based on the inference that

unhampered markets display a tendency to equilibrium . . . (In a world of con-
stantly changing beliefs and preferences, of course, equilibrium is never achieved,
but is to be viewed as a[n] . . . asymptote). . . . We ¬nd the spontaneous formation
of self-regulating structures in the growth of language, [in] the development of
law and in the emergence of moral norms.
(Gray, 1984: 31)

251
Architects of Political Change

Although Gray sees Hayek™s ideas as Humean, contra Hobbes™s “con-
structivist rationalism,” it seems to me that the Hayekian vision of how
social order comes into being is very similar to that of the Hobbesian
Leviathan. Although the order is not based on a covenant and may not be
intelligible to human analysis, it would seem to have an “arti¬ciall life.”
Somehow the beliefs of the members of society are “aggregated” in
such a way as to generate the motion of this Leviathan. In an attempt
to determine whether Hayek™s view of order has theoretical justi¬cation,
the next section extends the Arrovian notion of preference aggregation to
that of “aggregation of beliefs.”


8.3 condorcet and social truth
As I intimated earlier, the Galilean logic of motion was developed by
Newton to formally relate matter, motion and space, ¬rst in his article
“Light and Colours” (Newton, 1984 [1672], then in Principia (1687) and
¬nally in Opticks (1704). Voltaire™s volume Newton™s Philosophy (1738)
helped transmit Newton™s underlying philosophy of science throughout
Europe. Part of Newton™s argument was against the “light of Reason” of
Descartes™ Discourse on Method (1637) and for the “light of Nature””
that is, to follow the injunction to reason from the world, to ¬nd its
underlying principles. It is hardly surprising that Newton™s awesome
achievement in natural science sparked attempts by scholars, particularly
in Britain and France, to construct a calculus of the moral or human
sciences.8
Although Adam Smith was probably in¬‚uenced by the French schol-
ars Mandeville, Condillac, Cantillon, and Anne-Robert-Jacques Turgot,
it is Smith™s work in moral philosophy and political economy that is par-

For a discussion of the in¬‚uence of Newton™s philosophy in Europe, and Voltaire™s
8

contribution to this in¬‚uence see Feingold (2004).
The work in the moral and human sciences could include the following:
Mandeville, Fable of the Bees; or Private Vices, Publick Bene¬ts (1924 [1714]).
Cantillon, Essay on the Nature of Commerce in General (1755).
Hume, Essays Moral, Political, and Literary (1985 [1742, revised edition 1748]).
Condillac, Essay on the Origin of Human Knowledge (1746).
Jean-Jacques Rousseau, The Social Contract (1762).
Anne-Robert-Jacques Turgot, Re¬‚ections on the Formation and Distribution of
Wealth (1766).
Adam Smith, Theory of Moral Sentiments (1758) and Wealth of Nations (1776).
See the discussion in Rothbard (1995), Israel (2001), and Buchan (2003).
A recent study by Rothschild (2001) has examined the ideas of and connection be-
tween Adam Smith and Condorcet.

252
Preferences and Beliefs

ticularly remembered. However, I wish to focus not on Smith but on
Condorcet (born 1743). As far as I know, Condorcet was viewed (and is
generally still regarded) as a utopian theorist of little interest other than
as providing provocation for Thomas Malthus™ Essay on the Principle of
Population (1798).
Condorcet, a prot´ g´ and friend of Turgot, was certainly in¬‚uenced
ee
by him and by Adam Smith, whom he met in Paris in 1766. The debt
to Smith is most evident in Condorcet™s Esquisse d™un tableau historique
des progr` s de l™´ sprit humain (edited by Condorcet™s widow, Sophie,
e e
and published posthumously in 1795). The in¬‚uence of this work and
of the Jury theorem (Condorcet, 1994 [1785]) on Madison and Jeffer-
son, has already been discussed in Chapter 4. This theorem was part
of Condorcet™s attempt to construct a grand theory of human behav-
ior, based on collective choice by a society in the presence of risk. As-
suming that there is an external truth (a best choice out of the two al-
ternatives), and supposing that each individual chooses the truth with
probability at least one-half, then majority rule will be correct more of-
ten than the average juror. Moreover, as the jury increases in size, the
probability that it will attain the truth approaches unity. The theorem
assumes that voters are (pairwise) independent in their choices. As might
be expected, however, if the average pairwise correlation between voter
choices is low, then the theorem still holds (Ladha, 1992, 1993; Ladha
and Miller, 1996). Moreover, it is not necessary to assume that each voter
is described by a probability greater than one-half; a suf¬cient condition
for the theorem is that the average probability exceeds one-half (Boland,
1989).
As Condorcet™s biographers (Baker, 1975; McLean and Hewitt, 1994)
have observed, Condorcet believed not in the notion of the “general will”
(as had Rousseau), but in the possibility of the exercise of reason. In
particular, he believed that political representatives would exercise their
judgments (or beliefs) and be less swayed by the passions (or preferences)
than would a mass of voters. In the years following the calling of the
Estates-General (1789), he was active as president of the French Legisla-
tive Assembly, as a member of the National Convention (1792), and as
the architect of the “Girondin Constitution” of 1793. Prior to the trial
of the King, Louis XVI, Condorcet had struggled to institute a constitu-
tional monarchy, and during the trial (in January 1793), he spoke at length
against capital punishment. Chapter 4 has already observed that, with the
expulsion of the Girondins in the Jacobin Terror in 1794, Condorcet was
pursued to his death.

253
Architects of Political Change

Although historians of the period typically emphasize the Lockean ide-
als implicit in the beliefs of Jefferson,9 the evidence presented in Chapter 4
suggests that the in¬‚uence of Condorcet on the Constitution of the United
States was profound. The argument presented there is that Madison™s
“theorem” in Federalist X rests on the postulate that belief heterogeneity
is likely to result in choices that are for the public good. Of course, Con-
dorcet™s Jury theorem is only valid for voting in binary decisions. He was
unable to extend the theorem to three or more choices, and indeed, in at-
tempting to so extend the theorem, he discovered the possibility of voting
cycles. If we consider voting in terms of aggregation of preference, then not
only will an equilibrium generally fail to exist (Black, 1958; Plott, 1967),
but the resulting cycles may ¬ll the entire “policy space.” As suggested
above, this voting indeterminacy may reasonably be considered to be
chaotic. Although these spatial voting theorems and Arrow™s Impossibility
theorem are formally distinct, they do suggest that the greater the degree
of preference heterogeneity, the more likely that the method of preference
aggregation will be chaotic. In contrast, if political and economic decision
making should properly be viewed as belief aggregation, rather than as
preference aggregation, and if the Madisonian postulate is justi¬ed, then
we may infer instead that these processes will be well behaved in some
sense.
There have been attempts to develop models of “belief aggregation”
in economics (Aumann, 1976; Geanakoplos and Polemarchakis, 1982;
McKelvey and Page, 1986), and Arrow (1986) has recently commented
on these in the context of market behavior. These models are conceptu-
ally related to Condorcet™s Jury theorem, and can be seen as attempts to
determine those conditions under which belief convergence occurs. The
basic construction is one in which individuals, each with his or her own
prior and private information, together generate a statistic (essentially a
price vector). If the model that each individual employs is common knowl-
edge, then every individual can compute a posterior belief on the basis of
reasonable inferences about the nature of the other individuals™ private
information. After a few rounds, these posterior beliefs (or subjective
probabilities) converge.


The terms used by Jefferson in, for example, The Draft Constitution for Virginia
9

(June 1776) to describe George III and his “detestable and insupportable tyranny”
(Peterson, 1984: 336) are similar to expressions used by Locke in his Two Treatises
of 1690.


254
Preferences and Beliefs

As Arrow (1986) has observed, however, this result does depend on
seemingly very strong common knowledge assumptions. To illustrate,
consider agents in a typical market trading assets of some kind. Unlike the
standard picture of an exchange economy, the agents cannot really be said
to have preferences for the assets. Whether one wishes to buy or sell an
asset depends not so much on current prices as on expectations (beliefs)
about the probable behavior of the prices. But these beliefs, of course, are
determined by the agents™ interpretation of the other agents™ beliefs. In
other words, unlike the Aumann problem, (which deals essentially with
nature), this market is a game between rational actors. Formally analyz-
ing such a game requires us to model the mental processes and strategic
behavior of each agent. Nachbar™s theorem (1997, 2005) implies that each
agent (in a symmetric game) will adopt strategies that the agent believes
cannot be adopted by the other players.
Of course, this interpretation of the game may be denied. That is, it
could be argued that this market should be viewed as a decision-theoretic
problem, in which each agent plays against nature and attempts to guess
(statistically) how this nature behaves. This argument is based on the as-
sumption that the world is Gaussian, with stochastic events obeying a law
of large numbers, derived from the normal distribution. This may be an in-
valid assumption (Mandelbrot and Hudson, 2004). Indeed, Arrow (1986)
suggests that the presumed advantage of markets (that they are effective
decentralized methods of aggregating beliefs and preferences) rests on an
unreasonable assumption: For the market to work, each agent must have
(at least approximately) a model of every other agent™s thought processes
and a general economic equilibrium calculator to integrate everything.
If we suppose instead that each individual responds, in a “game-
theoretic” fashion, to the overall behavior of the market, then it seems
plausible that the aggregate behavior of the market could be indetermi-
nate. Analyses of much simpler models of collective behavior (Bikhchan-
dani, Hirschleifer, and Welch 1992; Huberman and Glance, 1995) have
found complex bifurcations and cascades.
In his recent comments on the research carried out on complex systems
at the Santa Fe Institute, Arrow (1988) has observed that markets appear
to have both homeostatic and chaotic features.

Equilibrium Theory would tend to suggest that as technology spreads through-
out the world, the per capita national incomes would tend to converge, but any
such tendency is very weak indeed. . . . Instead of stochastic steady states, we
observe that volatility tends to vary greatly over time, quiescent eras with little


255
Architects of Political Change

Newton The world of the large

Darwin The biological world


Individual Collective The social world

Beliefs Popper Condorcet

Preferences von Neumann Arrow

Gödel The world of the mind

Schrödinger The quantum world

Figure 8.1. A hierarchy of models.


period-by-period ¬‚uctuations alternating with eras of rapid ¬‚uctuations. . . . These
empirical results have given greater impetus to the closer study of dynamic models
and the emphasis on application of new results on non-linear dynamic models.
They have also given rise to criticism of the models themselves, and this goes far
back; it suf¬ces to mention the alternative theories of J. M. Keynes. (278)

Some of the work being carried out under the auspices of the Santa
Fe Institute (Holland, 1988; Kauffman, 1993, 1995) emphasizes the no-
tion of complexity, of chaos generating order. These concepts are perhaps
in¬‚uenced by the work of Prigogine (1980) in the physical sciences; and
before him by the ideas of von Neumann (1966). As I suggested earlier,
there appears to be a connection between the ideas of “order out of chaos”
and the non-mathematical, neo-Hobbesian views of Hayek. These recent
ideas about complexity are of very general applicability, and in a later sec-
tion of this chapter I discuss them in the context of some of the abstract
models of the world that we have been considering.


8.4 scientific truth
Paradigm, from the Greek, π±ρ±δµiγ μ±, “pattern”

Figure 8.1 suggests how to relate the models of the world that we
have been discussing. Newton™s laws framed the ¬rst formal, mathe-
matical model of “the world of the large””the interaction of matter
in space. The development of mathematics to deal with this world led
to the new insights in differential geometry and topology of Poincar´ ,e
Smale, and others that we have discussed. This in turn led to the Brouwer
Fixed Point theorem and the various applications in economic theory. For

256
Preferences and Beliefs

convenience, we can view this general class of game-theoretic models of
“the social world” as belonging to the von Neumann research program.
The focus of this program is to describe the interaction of individuals who
are fundamentally described by “preferences,” “utilities,” and so on.
Game theory has been in¬‚uenced by, and in turn has in¬‚uenced, re-
search in the Darwinian or evolutionary research program focused on
“the biological world.” The idea of “¬tness” in the Darwinian research
program is much like that of utility or preference, and the notion of the
game-theoretic equilibrium has been modi¬ed to that of the “evolutionary
stable strategy.”
One might view Popper™s work in the philosophy of science as being
concerned with evolutionary models of knowledge or beliefs. As Popper
(1972) has written: “[T]he growth of our knowledge is the result of a
process closely resembling what Darwin called ˜natural selection™; that is
the natural selection of hypotheses” (261). In other words, Popper was
concerned about how individuals form beliefs about the world, how they
test these hypotheses, and how these beliefs “compete” with one another
through their ability to describe the world. The more recent and related
work of Aumann and others suggests that this process “converges to the
truth.”
Figure 8.1 distinguishes between the Popperian and Condorcetian re-
search programs because I judge there to be an important difference be-
tween the two. Condorcet was interested in collective choice in an un-
certain world: Once individuals have formed their judgments, how could
these differing beliefs be aggregated in a “rational” fashion?
It seems clear that Arrow, in his Social Choice and Individual Values
(1951) and his two earlier papers (Arrow 1950a, 1950b), was also in-
terested in the collective aggregation of values rather than simply tastes
or preferences. However, the formal structure that he imposed on values
was that of transitivity”a property natural to preferences.10 I thus dis-
tinguish between the Condorcetian and Arrovian research programs. As
I have argued above, the importance of Arrow™s Impossibility theorem is
that it suggests that disorder of some kind is a real possibility. In this, it is
very different from the orientation of the three other research programs in
Figure 8.1 (von Neumann, Popper, and Condorcet), which also attempt to
structure the social world. It seems to me that Arrow gave the ¬rst formal


One way to demonstrate Arrow™s theorem (Kirman and Sondermann, 1972) is to
10

show that “order” requires that the family of all decisive coalitions of agents be an
“ultra¬lter” (namely, a family with a single dictator in common).

257
Architects of Political Change

demonstration of the possibility of social disorder of the kind hinted at
earlier in the work of Keynes (1936) and Schumpeter (1942).
To grapple with these themes of order and disorder, it may be worth-
while to consider the context within which Keynes, Schumpeter, Hayek,
and Popper formulated their key ideas. Clearly the terrible political and
economic events of the 1930s must have in¬‚uenced their work. Chap-
ter 7 interpreted Keynes™s argument (Keynes, 1936) to mean that, under
certain conditions, a belief equilibrium can come into being that (con-
trary to the general equilibrium economic model) sustains high levels of
unemployment and low levels of economic activity. Only the state, act-
ing as Leviathan, can change the belief equilibrium to the advantage of all
members of the society. Schumpeter (1942) wrote about the waves of tech-
nological innovations and business cycles that can engulf the economy.
With reason, we may interpret these cycles of economic activity as chaotic
belief cascades.
In contrast, Popper (1945) saw democracy as an “optimal” institu-
tion that was compatible with open competition in ideas and beliefs. In
the same way, he suggested that scienti¬c development follows a pro-
cess of natural selection that is “truth seeking.” Von Hayek (1948), in a
somewhat similar way, saw markets as “truth seeking” in their ability to
generate and aggregate information ef¬ciently. Out of competition in the
market and polity come stable institutions. As the discussion in Chapter 7
emphasized, Keynes had ¬rst to overcome a “core belief ” in the existence
of general economic equilibrium.
This notion of a “core belief” has been raised a number of times in
this book. To try to express what I mean by this, it is worth illustrating
the concept by way of a consideration of Einstein™s “annus mirabilis” of
1905.
Einstein™s Annus Mirabilis
In 1905, Einstein published three papers entitled “On the Electrody-
namics of Moving Bodies,” “On a Heuristic Viewpoint Concerning the
Production and Transformation of Light,” “Does the Inertia of a Body
Depend on its Energy Content?” as well as a fourth, “On the Motion of
Small Particles,” on Brownian motion, all in Annalen der Physik (French,
1979; Calaprice, 2005). These papers are seen by philosophers of science
as truly constituting a scienti¬c revolution. To write them, indeed to con-
ceive of the ideas that they express, Einstein had to deny the profound
conceptual assumption that time and space are absolute (in fact that there
is an “aether” in which light takes its wave-like form). It is well known


258
Preferences and Beliefs

that Einstein was able to do this by thought experiments that were unique
to his imagination. It is also possible that the pathway to the insight came
from Einstein™s realization that Maxwell™s ¬eld equations were not invari-
ant under transformation of a certain kind. The insight led both to special
relativity and the quantum theory. Feyerabend (1970, 1975) has provided
a very interesting discussion of the state of affairs before 1905, which I
contrast with post-1905, in order to articulate some notions about belief
cascades.
According to Feyerabend, there were three different and mutually in-
compatible “paradigms” in the nineteenth century physics: mechanics,
electrodynamics, and heat. Let us refer to these as schools, or research
programs, rather than as paradigms. Each of these schools had its own
well-developed theoretical framework (of beliefs), and, as Feyerabend
emphasizes, they interacted in an essentially “anarchic” fashion. Indeed,
Feyerabend has asserted, “Science is an essentially anarchic enterprise.”
To see what this may mean, we may conceive of the “scienti¬c heart”
of a set of research programs as the combination of all conceivable ac-
tivity spanned by the dominant beliefs in the three schools. Activity can
be disordered (“anarchic”) within this set. We may think of voting as a
metaphor for the interaction of the schools. In this case it is not true that
“anything can happen,” though it will be true that certain features of one
program will be unintelligible to other programs. But certain beliefs com-
mon to all schools will generate boundaries to what is conceivable, and
these boundaries will condition behavior. The heart then is the set of ac-
tivities, together with the supporting beliefs, generated by the boundaries.
In sum, anything inside the heart is possible.
There was a “core belief” within nineteenth century science, that com-
prised the agreed-on commonalities held by all of the three schools: the
belief in absolute time and space. This “core belief,” of course, made sense
within each of the separate “paradigms” of the three schools.
Prior to 1905, however, both Lorentz and Poincare had suspected the
existence of a “quandary,” in a scienti¬c sense, on the relationship be-
tween mechanics and electrodynamics. By overcoming the barrier of the
assumption of absolute time and space, Einstein created a full-¬‚edged
quandary.11 Eventually, it was realized that the rejection of this core

¨
It is also worth mentioning that many years later, Einstein and Godel became close
11

friends at the Institute for Advanced Study at Princeton and continued discussing
solutions of the model of general relativity “without time.” See Yourgrau (1999,
2005).


259
Architects of Political Change

belief transformed the con¬guration, or “heart,” of nineteenth century
physics.
In our own time, there have been numerous attempts to create a new
core belief, by integrating quantized forces with electromagnetism, and
more recently with gravitation. The search for “a theory of everything”
can be seen to be motivated by a non-scienti¬c, aesthetic belief that there
is indeed some conceptual resolution, some core belief, underlying the
various schools within physics. The cascade initiated in 1905 is still un-
derway. Local core beliefs, such as those derived from the integration of
the weak nuclear force and electrodynamics, have been constructed, but
at present the “general scienti¬c core” is empty. The “scienti¬c heart” is
the evolving con¬guration of scienti¬c activities generated by the family
of local core beliefs.


8.5 core beliefs and the heart
As discussed in Chapter 7, there is good reason to accept the valid-
ity of the Arrow-Debreu theorem on existence and Pareto optimality of
economic equilibrium, but only for markets involving commodities, fac-
tors, and well-speci¬ed preferences. Since the theorem has been extended
to economies that may be in¬nite-dimensional, it can incorporate time-
denominated preferences (Zame, 1987). Beliefs, however, are not prefer-
ences. As Keynes noted, if agents in the market engage in enterprise, then
they value assets in terms of “real” economic data. They are character-
ized by preferences (possibly even in an in¬nite dimensional space) and
we may trust in existence of an equilibrium. However, a speculator forms
beliefs about the preferences, and choices, of others. Implicitly the specu-
lator assumes that “he” is different from (almost all) other agents in the
market. As Keynes argued, with a preponderance of enterprise, specula-
tors cause no severe problems for the existence of equilibrium. Suppose,
however, that there is a preponderance of speculators: Each one must pre-
dict the others™ actions, and act in a way different from them. Consider
the situation when a speculator fears that the market may fall; he wants
to escape before the others, so his belief is that he is different in kind from
the others. But all speculators are identical in this regard. The speculator
must reason that his state of mind cannot be a part of belief equilibrium,
since it is not credible that he is indeed different from other speculators,
assuming private information is of no help. Keynes saw this intuitively,
but gave no formal proof. A proof, at least of a version of the hypothesis,
is given in the theorem, mentioned above due to Nachbar (1997, 2005).

260
Preferences and Beliefs

To see the problem, consider a game, such as “scissors, paper, stone,”
involving two players. With equally valued wins and losses, the Nash
equilibrium is for each player to randomize with probability one-third to
each strategy. An enterprising agent may play thus and gain zero in expec-
tation. In the iterated version, a speculator attempts to win by forecasting,
by learning his opponents™ strategy. If his opponent bases his calculations
on “enterprise,” to use Keynes™s term, there is little the speculator can
do but to randomize. With two speculators, the game changes. Player
A attempts to learn whatever Player B is doing, and realizes Player B is
probably trying to learn what Player A is doing. The in¬nite regress does
not close. Although the theorem was suspected earlier, Nachbar™s result
appears to be relevant for a very large class of games.
Two empirical questions are obvious. What ratio of speculators to
enterprisers, in a particular situation, is compatible with equilibrium? In a
complex international asset market, can the “socialization of investment”
at some level available to government, or an international institution,
induce stability?
There is clearly an even more general question. My notion of the “heart
of a constitution” incorporates an implicit set of “core beliefs.” If we
accept Keynes™ chaos hypothesis for asset markets, why not accept it for a
constitution? While it is true that the world of a constitution is generally
not composed entirely of “speculators,”it is also evident, however, that
very different beliefs may “populate” a constitution.
Throughout this book I have used the term core belief to refer to what-
ever belief is in equilibrium, or is collectively agreed upon (in some appro-
priate social choice sense) by the members of the community. If there is a
clear discord between the essential beliefs of the constitution, and some
empirical aspect of reality, then some of the members of the society may
be forced to change their beliefs. If others observe the effects of a small
number switching beliefs, then (acting as rational Bayesians) their propen-
sity to change beliefs will increase. Thus, what I have termed a cascade
can be generated. The conditions under which the cascade can destroy
the previous core belief are unclear and may indeed be unknowable.
To gain some inkling into the stability of a core belief of a constitution,
consider again the notion of a competitive equilibrium in a market. This is
simply a state of the world that cannot be changed to anyone™s advantage
by trade. It depends, of course, on the price equilibrium (of which there
may be many). Such an equilibrium is associated with “stable” states of
mind, or beliefs, by the participants (Hahn, 1973). A more abstract idea
of an equilibrium, but one which does not involve prices, is that of the

261
Architects of Political Change

core of an economy (the set of unbeaten commodity allocations). Under
certain assumptions, the core of an exchange economy will be nonempty
(and will include the competitive equilibrium). Unfortunately, for more
general cooperative games, such as voting, the core (the set of unbeaten
outcomes) is generically empty. However, it is possible to extend the notion
of the core to a more general object that I have called the heart.
The mathematical object, the heart, has been shown to be always
nonempty and to be continuous under certain circumstances (such as
“convexity” of preferences), in the rules of the “game.” The framework
utilized is one in which agents are characterized by preferences and there
is some particular social choice rule, such as voting. It was this notion that
was described in Figure 2.3, and generated by the particular voting rule
in use. However, the formal construct is abstract enough to be relevant in
the more general context of beliefs, and very general social choice rules. In
the world, however, beliefs need not be “convex.” An individual may hold
two con¬‚icting views, assigning to each differing probabilities of truth,
or indeed, as Keynes noted, may be completely uncertain. Because of the
failure of convexity, the heart can fail continuity at certain con¬gurations
of beliefs. By analogy with dynamic systems, the failure of continuity is
called a catastrophe. A cascade is precisely the catastrophic change from
one heart con¬guration to a completely different one. This very simple
notion of a “catastrophic cascade” is adapted from Zeeman™s earlier ideas
(Zeeman, 1974). However, the extension of the idea that I have proposed
is made in the attempt to include more general transformations than those
considered by Zeeman.
The abstract object that I call a heart may not, in fact, be an “equilib-
rium,” if by this we mean that it is associated with unchanging beliefs and
constant behavior on the part of the members of the society. However,
the heart is de¬ned by certain boundaries in the domains of beliefs and
actions. An important feature of the heart is that when the equilibrium or
core is, in fact, nonempty, then the heart and core coincide. On the other
hand, when the core is empty, then behavioral “cycles” are certainly pos-
sible inside the heart. In normal circumstances, such cycles need not prove
destructive to fundamental belief coherence in the constitution. As I have
throughout this book, I use the term core belief to refer to the set of col-
lective beliefs that are mutually compatible within the community. Under
the circumstance of a catastrophe, the core belief may disappear.

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