Wednesday 2 October 2013

Abandoning dichotomies in science

I have recently published a couple of posts arguing against the de-politicisation of mathematics. These thoughts have emerged as I have spent the summer investigating Pragmatic philosophy. I was doing this as part of my primary aim of establishing an ethical basis for Financial Economics.

The problem I had to grapple with was what is known as the fact/value dichotomy, which claims that there is a separation between what we know and our ethical values. Clearly if I want to relate morality to the mathematical science of Financial Economics, in particular my field of Financial Mathematics, I need to abandon the fact/value dichotomy yet remain within mainstream thinking. This can be done by adopting Pragmatism, which is founded on the denial of the ‘spectator theory of knowledge’, that we can stand back from what we observe and, either through Empiricism or Cartesian Rationalism, identify certain, objective truths. Having adopted this stance, Pragmatism must navigate a difficult path between scepticism – nothing is justified belief – and relativism – all beliefs can be justified. 

As a Financial Mathematician, Pragmatism has a number of attractive features. It rejects the belief that we can be certain of anything, which resonates with people involved in the markets, and under such circumstances attempts to define how to act. As well as rejecting the fact/value dichotomy, a strategy is to embrace pluralism, in the context of finance this implies we should avoid investing in super-portfolios; situations where distinct agents adopt identical strategies so that there is no diversity in the market. Another is to reject a dichotomy between means and ends, this is an emergent theme in financial mathematics manifested as ‘forward utility’ functions. Finally I am very interested in Pragmatic views that knowledge is all about communication: we have ideas about ‘something’, but this does not make our ideas knowledge, our ideas need to be confirmed/denied with reference to a third party’s ideas about the ‘thing’. On this basis ‘communicative action’ becomes essential to society. I think there are links between theories of ‘communicative action’ and ideas of how markets should operate, so they are seen as positive aspects of society, not destructive.

In arguing that mathematics should be politicised I take my self out of orthodox views that scientists should aim to be ‘honest brokers’, presenting policy makers with options that they can choose. Pragmatism is emphatic in stating that scientists are not able to be ‘honest brokers’. Given that scientists cannot provide objective assessments, of climate change for example, I think Pragmatism argues that we should engage in rational discourse that does not involve insincerity (hiding things) and dogma (rejecting hypothesis out of hand). With regard to the topical discussion of climate science I think this piece gets to the heart of the matter: the IPCC is looking for consensus, as a result it attempts to silence dissent, rather than ‘honestly’ addressing the concerns of anyone who might disagree with its arguments.

I am still working towards my primary objective, which has morphed into establishing that the norm of reciprocity is the foundation of Financial Economics. I will post the four sections of the argument (with some enhancements) over the next few weeks. The full paper is on SSRN and I genuinely welcome constructive comments

1 Introduction
The processes of structured finance employing ‘special purpose vehicles/ structured investment vehicles’ (SPVs / SIVs) to fund activities, whether by industrial corporations, like Enron; governments, such as the UK government’s Private Finance Initiative; or banks, through asset backed securities, has had a significant impact on modern business practice. However, along side its growth, structured finance has become associated with financial crises, particularly the Financial Crisis of 2007—2009 ([14], [9], [1]). Recurring themes associate the Crisis with financial innovation generating complex risks (e.g. [20, p 55], [17, p 564], [52, p 769], [80, p 14]) and the inability of the mathematical techniques employed by financial economics to address these issues (e.g. [10], [20], [17], [80, p 14], [52], [16], [40], [25]). Amongst those who identify a problem with mathematics, there are two classes: those who can see a possible solution in mathematics (e.g. [10], [16], [40]) and those who don’t and advocate tighter market regulation (e.g. [20], [17], [52], [80]).
While SPVs are frequently presented as twentieth century innovations, their fundamental character of transforming an uncertain future cashflow into a fixed and insured cashflow was exhibited in the Contractus Trinus (the ‘triple’ or ‘German’ contract). [63, Ch 10] and [22] have given detailed accounts of the contract and the scholastic debate about their legitimacy which eventually led to their condemnation of usury in 1586 (Detestabilia avaritia). Securitisation and collateralisation manifested themselves as the corpo/sopracorpo structures that emerged in the thirteenth century (e.g. [65, p 554]) and the trading of securitised assets has been widespread since the eighteenth century, particularly through the reinsurance markets (e.g. [54, p 38]).
Mathematics is frequently presented as being an alien encroaching into economics (e.g. [84]). However the foundation of European mathematics is in Fibonacci’s 1202 Liber Abaci, a text for merchants [75], and the subsequent mathematisation of the physical sciences was stimulated by the mathematical analysis of financial phenomena (e.g. [39], [47]). The emergence of mathematical probability, at the heart of all science, is out of the ethical analysis of commercial contracts (e.g. [32], [77], [8], [78]). Rather than mathematics encroaching on economics, the historical account suggests that economics has generated mathematics that is then used in other domains. The issues that many of the critics of the contemporary use of mathematics in economics raise are not relevant to mathematics, as conducted throughout history, but to modern mathematics. The nature of mathematics has changed in the twentieth century; pre-modern mathematics developed in the vernacular of financial practice and between the eighteenth and twentieth centuries was motivated by observation of natural phenomena. In the second half of twentieth century a theoretical, formalist-deductivist, approach dominated mathematics, and this was adopted by orthodox economics. While this approach to mathematics has been rejected in the physical sciences [35] it seems to persist in economics (e.g. [84], [53, Ch 10]).
This sketch suggests that while financial technology has not changed significantly over the centuries, attitudes to risk-taking and mathematical practice have. Contemporary attitudes to risk-taking and mathematical approaches to financial problems before the nineteenth century have the common feature of being explicitly ethical. Authoritative assessments of the causes of The Crisis that have looked beyond the field of economics have focussed on the ethical nature of the financial failures. The Financial Crisis Inquiry Commission (FCIC) concluded that in the lead up to The Crisis there had been a “systemic breakdown in accountability and ethics” [26]. The UK’s Parliamentary Commission on Banking Standards [67] pointedly titled their comprehensive report of 2013 “Changing Banking for Good”, emphasising that the direction of change should be in an explicitly moral direction. The argument in both reports is that improving ethical behaviour is a key component of improving financial stability. The role of mathematics is peripheral but significant in that it legitimised financial innovation by creating a false sense of confidence (e.g. [26, p 44], [67, vol. 2, para. 60]): mathematics speaks with an indubitable authority that need not be questioned [53, Ch 10].
In light of these observations the purpose of these articles is to investigate links between contemporary financial economics and ethics in order to make a contribution to mitigating financial crises. This theme has been addressed by a variety of authors, for example, Kevin Jackson [45] tackles it tangentially by addressing failures in the curricula of Business Schools, an issued examined in detail by Jason West [85]. Pre-dating the events of 2007, James Horrigan, George Frankfurter and Elton McGoun have examined the underlying ideology of financial economics ([44], [31], [30]).
The relative paucity of literature on ethics in financial economics, as compared to scholarship on ethics in other technology based professions, probably comes about because the discipline is explicitly mathematical and mathematics strives to be infallible by maintaining a strict fact/value dichotomy. Therefore, in order to achieve its objective the paper will abandon the fact/value dichotomy in financial economics. This path is justified by adopting a Pragmatic approach, which is characterised by arguing that knowledge has no certain, infallible, foundations and because scientists are part of the system they observe, there can be no real distinction between what is and what ought to be. A consequence of adopting a Pragmatic approach is that the historical evolution of beliefs and the role that practice has in generating theory are an important themes running through the paper. [59, Introduction]
Pragmatism addresses the question of ‘what is’; the ‘fact’, the paper addresses ‘what ought to be’; the ‘value’, by taking a Virtue Ethics approach, as employed in the seventeenth and eighteenth centuries and is a growing area of interest (e.g. [28]).
As a consequence of taking this approach is that this paper concludes that contemporary financial economics has an implicit foundation in ethics, specifically Justice expressed as balanced reciprocity. This is the central argument of the paper. This conclusion is arrived at by showing that one of the fundamental theory of financial economics, the Fundamental Theorem of Asset Pricing (hereafter ‘FTAP’), has its basis in the virtue ‘Justice’. The FTAP is the mathematical theory underpinning modelling frameworks such as Black-Scholes-Merton, Cox-Ross-Rubinstein, Heath-Jarrow-Morton and the LIBOR Market Models and is the central theory in contemporary mathematical approaches to pricing derivatives. Its significance is in unifying various strands in financial economics: Samuelson and Merton’s use of stochastic calculus; CAPM, developed by Treynor and Sharpe; martingales, employed by Fama in the development of the Efficient Markets Hypothesis; Arrow and Debreu’s concept of incomplete markets and in accomplishing this unification it represents a Kuhnian paradigm for financial economics.
Arguing that virtue ethics are implicit and embedded in contemporary financial economics is unorthodox; it is more normal to argue that markets are socially destructive (e.g. [50], [72] ) or have the potential for corruption if not constrained (e.g. [20, p 55], [17, p 564], [52, p 769], [80, p 14]), and so financial economics is immoral in facilitating this corruption. These attitudes have a powerful influence on how investigations of the causes of The Crises are framed. In order to address these framing issues, we discus the changing social attitudes to markets in order to provide some context to the thesis that financial economics is implicitly ethical.
2 Fact
Determining what is is part of epistemology, and epistemological theories can be broadly separated into two classes, foundational and coherentist. “Foundational theories attempt to ground knowledge in a solid base such as sense experience [Empiricism] or a priori reasoning [Realism]. In contrast, coherentists argue that there are no foundations for our beliefs, whose justification derives from how well they fit together with each other.”[79]
Realism argues that there is an ‘intelligible’ universe, of immutable truths, and a ‘sensible’ universe, that is actually experienced and undergoes change. ‘Truth’ transcends experience and can be established only through abstract thinking (Rationality). Realism, in the Christian and Islamic traditions, can be traced to Plato’s Theory of Forms (or Ideals) and was central to Descartes’ and Kant’s philosophy. In this framework, there is a hierarchy of knowledge with mathematics being closer to ‘truth’ than experimentation. Beliefs in the immutability and indubitability of mathematics became embedded in western philosophy with the Neo-Platonists, such as Augustine of Hippo, who associated mathematics with a transcendental deity [5, p 46].
Contemporary Empiricism argues that there are two types of truth: tautologies, established through formal mathematics or logic; and factual statements that can be verified by employing the ‘scientific method’ to guide observation and analysis. A principal of Empiricism is that while ‘Truth’ might be unachievable, the scientific method will converge towards a close approximation of true facts. European Empiricism has its roots in Greek Epicureanism and became dominant in British philosophy through Francis Bacon, John Locke, David Hume and J. S. Mill. Logical Positivism, a form of Empiricism, emerged in Vienna in the early twentieth century and became significant in North America in the 1940s.
While Empiricists reject the metaphysics of Realism, they generally do not challenge the status of mathematics and created a special class of truth related to Hilbert’s Formalism. To appreciate the distinction between Realism and Empiricism, a Realist might claim that “2 + 2 = 4 was true at the time of the dinosaurs”, implying the mathematics is independent of human thought (synthetic a priori); an Empiricist would claim the statement is a tautology: 2 := 1 + 1,4 := 1 + 1 + 1 + 1 and so 2 + 2 = (1 + 1) + (1 + 1) = 4 (analytic a posterior).
Within economics, Realism is associated with Neo-classical theories that employ equilibrium and rationality and resort to ceteris paribus arguments to explain why economic facts (what is experienced) rarely conform to Neo-classical theory [4]. Contemporary economics in the Empirical spirit includes experimental and behavioural economics (e.g. Vernon Smith, Daniel Kahneman).
Realism and Empiricism are foundational theories built on the idea that ‘Truth’ is a static relationship to some reality that is external to the thinker. Pragmatism, on the other hand, argues that ‘Truth’ is just what ‘competent, rational enquiry’ produces. Pragmatism emerged in the late nineteenth century with Charles Peirce, William James and John Dewey and developed more recently by Richard Rorty, Hilary Putnam and Robert Brandom, amongst others. While closely associated with American philosophy, there have been Pragmatic strands in French thought, associated with Greek Sophism, notably the ‘occasional Pragmatism’ of Henri Poincaré [42] while Émile Durkheim acknowledged the usefulness of Pragmatism in destroying “the cult of truth” ([51], [24, pp 69-72]). In Britain, Pragmatism has been associated with the Cambridge School, particularly with (the later) Wittgenstein and Huw Price. Pragmatism overlaps Empiricism (e.g. Peirce, Quine) and Realism (e.g. Brandom, Putnam) [73, pp xvi—xvii].
Pragmatism does not assign a special status to mathematics, in the way that Realism and Empiricism do, Putnam argues that
we learn what mathematical truth is by learning the practices and standards of mathematics itself, including the practices of applying mathematics. [70, p 66]
while Poincaré observed that
The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious. It is through it that the mathematical world remains in touch with the real world, and even if pure mathematics could do without it, we should still have to have recourse to it to fill up the gulf that separates the symbol from reality. [68, p 449]
[The definition of ‘intuition’ here can be read as ‘The action of looking upon or into; contemplation; inspection; a sight or view.’ (OED 1), from the Latin intuitus: to look, rather than the philosophical definition ‘The immediate apprehension of an object by the mind without the intervention of any reasoning process’ (OED 3).]
Pragmatism is being associated with a revival of ‘classical economics’ [56], is close to Pasinetti’s description of the Cambridge School of Keynesian Economics [66], relates to Deirdre McCloskey’s economics founded on rhetoric (discourse) [57], has been linked to behavioural economics [49] and institutional economics [7]. Pragmatic approaches are distinguished by acknowledging ethical features of economic behaviour and emphasising the role of uncertainty ([46], [23]). For example, Friedman’s argument in The Methodology of Positive Economics appears to share principles of Pragmatism [49, p 2]: “[Positive economics’] performance is to be judged by the precision, scope, and conformity with experience” [34, p 4]. However, Friedman’s rejection of a normative dimension to economics and a faith in the ability to verify stable economic theories makes it incompatible with Pragmatism.
3 Value
Ethical frameworks, in the Western tradition, are usually classed as being Deontological, Consequentialist or Virtuous. Deontology can be typified as “Thou shalt / shalt not” and guides action on the basis of laws, rules or principles. Since an individual cannot be subject to a law unless it has been promulgated, Deontology is linked to with philosophical systems that are based on ‘divine’ or ‘natural’ law, such as Realism and Stoicism [3, p 14]. The practical problem with Deontological Ethics is that basic rules such as “Thou shalt not kill” have caveats while other prohibitions become redundant, or need revising, as society evolves. In the context of contemporary economics, Deontological Ethics has been employed in financial regulation (e.g. Pillars I & II of Basel II) and has been criticised for being over-bureaucratic and rigid while susceptible to ‘gaming’; adhering to the letter of the law but not the spirit. [82, pp 23—26]
Consequentialism attempts to judge the value of an action in terms of its consequences. This approach has its roots in ancient Chinese Mohism and Greek Epicureanism, developed in opposition to Platonism and Stoicism. The approach became fully developed in the nineteenth century with a trio of British philosophers, Bentham, Mill and Sedgewick, who argued that one should “Act always in such a way as to promote the greatest happiness to the greatest number”.
On the basis of Consequentialism and David Hume’s distinction of ‘what is’ and ‘what ought to be’, ‘value—neutrality’ was established in economics: since we have ‘objective access’ to the empirical world’ and are ‘rational beings’, we are able to calculate the consequences of our economic actions [86]. A problem with this value-neutrality, described by Robert Heilbroner, is that it misses the critical fact that
the objects observed by the social scientist all possess an attribute that is lacking in the objects of natural universe. This is the attribute of consciousness — of cognition, of “calculation”, of volition [41, p 133]
The importance of ‘volition’ had been recognised by Oskar Morgenstern, who objected to perfect foresight based on calculation because
always there is exhibited an endless chain of reciprocally conjectural reactions and counter-reactions. This chain can never be broken by an act of knowledge but always through an arbitrary act — a resolution. [58, quoting Mogernstern on p 129]
Practically this means that while we could incorporate the possibility of a Japanese earthquake into the modelling of asset prices, it would be impossible to account for the behaviour of Nick Leeson in destroying Barings’ Bank.
As well as questioning the basic ability to predict in a social context, Consequentialism has been criticised because obviously immoral acts, such as the execution of the innocent, could be justified either by the hope of good consequences or the fear of bad [3, p 14]. In response to these problems, many argue that ethics should focus on the judgement of the agent taking the action that has consequences, or Virtue Ethics.
Virtue Ethics, in the European tradition, is associated with Aristotle, in particular Nicomachean Ethics in which virtues are the “characteristics that enable individuals to live well in communities” [69, p 247]. Aristotle’s ethics do not distinguish reason and emotion, as Hume did in the eighteenth century, nor do they define absolute standards, rather Virtue is a consequence of personal reflection [81, pp 6—8]. This opens Virtue Ethics to the criticism that it cannot be codified into a set of rules that any person could apply to determine ethical action in any situation. However, this criticism assumes such a reduction is possible, and implicit in this is that the environment is stable and predictable. The advantage of Virtue Ethics is precisely that it can accommodate unforeseen circumstances.
Virtue Ethics is often associated with Catholicism, the four ‘Cardinal’ virtues; Courage; Justice; Temperance; and Prudence, and three, so-called, ‘Christian’ virtues: Faith; Hope; and Charity, however all these virtues existed in pre-Christian Greek and Roman philosophy, which influenced both Judaic and Islamic thought. Chinese (e.g. [83]) and Indian philosophy both have their own versions of Virtue Ethics that can be mapped onto the European framework. Particularly relevant is the first century Mahayana Buddhist Vimalakirti Sutra that tells the story of how a virtuous merchant instructs both kings and monks.
While it is conventional to associate Deontology with Realism and Consequentialism with Empiricism, it is not so well established to associate Virtue Ethics with Pragmatism, but there are links, notably through John Dewey [15] and in the discussion of reciprocity [64]. More broadly, Aristotle argued that excellence of character [ethike] derives from ‘habituation’ [ěthos] [13, 1103a15—20]. This can be related to the technical term ‘Pragmatism’, which is derived from the Greek word describing ‘deed, act, affair, matter, business’ [pragma] and both words are more closely associated with ‘practice’ than ‘theory’.
With these observations in mind, Khalil makes the point that “true [Pragmatic] inquiry cannot take place in an ivory tower” [49, p 2] and discourse is central to Pragmatism. Putnam admires Jürgen Habermas’ position on ‘communicative action’. Habermas defines a ‘norm’ as a “universally valid statement of obligation”, which some might equate with a ‘virtue’, where as a ‘values’ are culturally specific. The “binding universal norm” is ‘communicative action’, “norms of communication governed by the ideal of rational discourse” and the ideal of rational discourse is governed by
the norm of sincerity, the norm of truth-telling, and the norm of asserting only what is rationally warranted ... [and] is contrasted with manipulation. [71, pp 113-114]
While Putnam is describing society in general, these ‘virtues’ could well apply to guiding financial markets in particular.
Putnam observes that the problem of leading an ethical life is a fact of life that cannot be solved ex cathedra, by philosophy external to the individual such as with Deontology and Consequentialism. Rather, ethical disagreements are resolved through ‘communicative action’ in a social context and the norms that govern this ‘communicative action’ have the features of ‘virtues’ (i.e. tempering, justice, faith, charity and prudence). However, in advocating pluralism Pragmatism, like Virtue Ethics, has to defend itself from the criticism of Relativism (e.g. [73], [55, p 53], [27]).

4 The Morality of Markets
Albert Hirschman has provided a description of four different views on the relationship between markets and morality: doux-commerce, self-destruction, feudal-shackles and feudal-benefits [43]. The idea that commerce improved society was prevalent throughout the eighteenth century. In 1704 technical text on commerce argues “Commerce attaches [men] to one another through mutual utility”; while in The Rights of Man (1792) Thomas Paine writes “[Commerce is a pacific system, operating to cordialise mankind”. In the intervening years Montesquieu, Hume, Condorcet and Adam Smith all agreed that commerce was a powerful civilising agent, promoting honesty, industriousness, probity, punctuality, and frugality, in contrast to the excesses of absolute monarchies.
Following the Industrial Revolution, these attitudes all but disappeared and were replaced by views that blamed the collapse of morality on the influence of capitalism. Commerce was seen as commodifying human interaction, “custom is replaced by contract”, and on this basis Romantics saw capitalism as being un-natural and undermined traditional hierarchies while Marxists believed that commerce’s alienation of the proletariat along with capitalism’s instabilities would lead to revolution. Others believed that the success of capitalism, founded on frugality and probity, would be so great that society would eventually become dissolute, seeking instant gratification, echoing the rise of Republican Rome and the fall of Imperial Rome.
Both the doux and self-destructive views of commerce represented capitalism as a powerful force driving social change. When capitalism did not collapse, the emphasis changed and capitalism was not seen as strong but weak: the bourgeoisie were unable to escape traditional social forces. The United States of America, not bound by “feudal—shackles” seemed to have an advantage over Europe between 1914 and the sixties. Capitalism, led by America, seemed to rediscover its confidence in solving society’s problems after the Second World War. But this confidence was lost in the economic malaise of the seventies. Because America did not have the feudal past of Europe it did not have social and ideological diversity and so reforms, such as Roosevelt’s New Deal, were vulnerable to a “tyranny of the majority”; America missed the feudal—blessings. Daniel Friedman has recently presented the relationship between markets and morals as a difficult marriage: “where markets sabotaged morals, and morals hurt markets” [33, p 4]. In the aftermath of The Crisis, and of particular interest to this project, Johan Graafland has related contemporary economic literature to the doux-commerce and self-destruction theses in the context of Aristotelian Virtue Ethics [36].
Marion Fourcade and Kieran Healy [29] have recently returned to Hirschman’s characterisation and argue that it is still valid today, but have added a fifth characterisation: Moralized Markets. In their paper Fourcade and Healy identify the four strands of Hirschman’s thesis in recent scholarship starting with doux-commerce summarising Deirdre McCloskey’s argument that markets nurture “bourgeois virtues” as
Commerce teaches ethics mainly through its communicative dimension, that is, by promoting conversations among equals and exchange between strangers. [29, p 287]
Researchers performing empirical studies on the Ultimatum Game (introduced the year of Hirschman’s thesis, by [38]), argue that commerce fosters co-operation, particularity amongst strangers while others support Hayek’s argument that “Capitalism makes you free”. Finally, some economists look for evidence that markets are the best motor for innovation. In opposition to these strands, economists are arguing that instead of virtue we have envy, instead of co-operation there is coercion, freedom does not equate to populism and creativity is being stifled by copyright.
While economists seem to focus on the robust nature of markets, able to create or destroy society, sociologists tend to study the feebleness of markets. Following Weber, some authors argue that markets are consequences of cultural legacy, of institutions. The new Moralized Markets thesis goes further, it characterises markets as ‘cultures’, not simply a consequence of culture, which “are explicitly moral projects, saturated with normativity.” [29, pp 299-300].
Fourcade and Healy identify three strands of the Moralized Markets thesis. Firstly, there is the view that markets have a role in creating moral boundaries, as McCloskey argues. This approach follows Durkheim, who argued that morality is not fixed by some ‘Ontological’ ethical standard (that is, one fixed and derived from a single issue [70, p 19]); rather, morality is defined by the group.
The second strand builds on the first by turning to the sociology of science, where an emphasis is placed on impartiality in evaluating scientific knowledge (i.e. it studies failures as well as successes). A key theme in this approach is to study what Michael Callon called the ‘performativity of markets’, that economic theory drives economic behaviour, rather than economic theory describes economic behaviour, in the words of Donald MacKenzie, financial economics is “An engine not a camera”. These views are close to the Pragmatic attitude, that Empiricism and Rationalism fail by not acknowledging that scientists are an active part of the system they observe [6, pp 35—37, 50—53].
While the second strand of the Moralized Markets thesis focuses on behaviour at the micro level, the third strand considers economic rules at the macro level and how they are saturated with normative considerations. For example, when Friedman made the case for positive economics it was “to make correct predictions” [34, p 4] he ignored the question of what determines ‘correct’, and this driven by mutable normative values. For example determining ‘correctness’ has changed with the emergence of the value ‘efficiency’ and the decline of ‘social cohesion’.

5  The Morality of Gambling
Gambling is today regarded as profane, but this was not always the case. For the Greeks, the brothers Zeus, Poseidon and Hades cast lots to divide up the universe. The Hindus believe the world was a game of dice played between Shiva and his wife and at the heart of the epic tale Mahabharata is an, unfair, dice game between the Kauravas and the Pandavas.([74, p 27], [11, p 1—5]). Divination by casting lots played an important role in Judaism and the Bible refers to the ‘judgement’ of Urim and Thurim, which scholars today think were two dice ( Exodus 28:30, Leviticus 27:20-21, Samuel I 14:41 see [11, p 2]).
Gambling was often associated with sacrificial practises that were widespread and are generally known by their Native American name, potlach. Potlach involved the destruction of goods, and seems to have evolved in nomadic groups because they could not store what was not needed and gambling was a means avoiding waste by re-distributing goods before any excess was destroyed. Similar ceremonies are described in Vedic scriptures ([48, pp17-19], [37, p 56]).
The role gambling plays in archaic societies has been studied by Jon Altman and William Mitchell. Altman studied an Australian aboriginal group around 1980 [2]. The community had access to social security payments and there was often a surplus left over after essentials had been bought. However, some individuals were excluded from social security payments by the government and there was an “inter—household variability in access to cash”. This variability was seen as a subjective discrimination within the community by the Australian government and gambling “acted effectively to both redistribute cash ... [and] provided a means for people with no access income to gain cash” [2, pp 60-61]. This was important in non-hierarchical communities because it meant that one arbitrary bestowal of money was not corrected by another subjective distribution, such as redistribution by a chief. William Mitchell has considered the role that gambling plays in disrupting hierarchical social structures, such as the Indian caste system, by studying the Wape in New Guinea [60]. The conclusion was that the non-hierarchical society of the Wape was maintained through gambling.
The pervasive nature of gambling in archaic communities, appearing in the Vedic scriptures, potlach ceremonies, aboriginal Australia and New Guinea and the Hazda [74, p 27] can be explained because it is an objective, ‘fair’, mechanism for the redistribution of wealth. What needs to be recognised is that this process remains valid only so long as no single entity accumulates enough wealth that it can bankrupt all the others.
Gambling had been outlawed in the medieval period, usually because time spent gambling could be better used [11, p 58]. However, building on Roman practice, lotteries began to be used as means of raising public-finance in the later Medieval period. The first private lottery appeared in the sixteenth century in Italy and the mechanism spread to France and England [12, pp 133—138]. The practice culminated in The Million Adventure lottery set up by the English government and drawn in November 1694 [61, p 34].
The seventeenth century economist, William Petty, observed that lotteries were “a tax upon unfortunate, self-conceited fools” and from the start of the eighteenth century gambling became increasingly associated with “the waste of time and money; the neglect of familial and business duties; the erosion of social trust; and the severed link between hard work, talent and gain.” [19, p 161]. However, by the end of the century ‘gambling’, in the form of insurance, had become a legitimate practice if based on rational foundations ([87], [18]) and in 1774 the Life Assurance Act distinguished between legitimate insurance and illicit gambling and became known as the Gambling Act.
Gabrielle and Reuven Brenner argue that the de-legitimisation of lotteries, and gambling in general, comes about because during the seventeenth and eighteenth centuries there was significant social and economic change. In this environment gambling and speculation provided the unlanded with a means to climb up the social ladder [12, pp 98—104]. While the lotteries enabled this disruptive social mobility, they were also a necessary tool of public finance that prevented the stagnation and crises suffered by states reliant on taxation [62]. By the start of the nineteenth century, finance had developed to such an extent that governments could tax more effectively, notably the incomes of the middle classes, and borrow from the middle and upper classes, notably by regulating and employing the life-insurance industry.
The prohibitions on gambling had an important impact on the development of finance. In 1851, following a dispute between two counterparties in a forward contract, English law established that there needed to be ‘intent to deliver’ for a derivative to avoid being classed as an illegitimate gamble [76, pp 211—213]. While English courts avoided becoming involved in derivative markets, U.S. courts were much more active in restricting speculative behaviour and were vigorous in prosecuting “idlers who made profit even while they slept” [21, p 62, quoting Fabian]. One case, brought by the Chicago Board of Trade (CBOT)against Christie-Street Commission Company, which was offering its customers bets on the grain futures prices published by the CBOT, eventually reached the U. S. Supreme Court, who ruled in 1905 that
People will endeavour to forecast the future, and to make agreements according to their prophecy. Speculation of this kind by competent men is the self—adjustment of society to the probable. [21, p 71]

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