Archive for the 'Uncertainty' Category

Gray on Akerlof and Shiller

Published
by
peter
on 2009-11-25
in Global Economic Crisis, Uncertainty and economics
. 1 Comment

Philosopher John Gray has a review in the LRB of Akerlof and Shiller’s new book on the errors of mainstream economics, a review which mentions the sadly-neglected economist George Shackle.  Shackle, unlike most academic economists, actually worked in industry and Government and had made investment decisions, and knew whereof he wrote. 

If Akerlof and Shiller’s grip on the history of economic thought is shaky, they also fail to grasp why Keynes rejected the idea that markets are self-stabilising. Throughout Animal Spirits they portray him as reintegrating psychology with economic theory. No doubt this was one of Keynes’s goals, but it is not his most fundamental revision of economic orthodoxy. Among his other accomplishments he was the author of A Treatise on Probability (1921), in which he tried to develop a theory of ‘rational degrees of belief’. By his own account he failed, and in his canonical General Theory of Employment, Interest and Money (1936) he concluded that there was no way anyone could make forecasts. Future interest rates and prices, new inventions and the likelihood of a European war cannot be predicted: there is no ‘basis on which to form any calculable probability whatever. We simply do not know!’ For Keynes, markets are unstable less because they are driven by emotion than because the future is unknowable. To suggest that the source of market volatility is unreason is to imply that if people were fully rational markets could be stable. But even if people were affectless calculating machines they would still be ignorant of the future, and markets would still be volatile. The root cause of market instability is the insuperable limitation of human knowledge.

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Great mathematical ideas

Published
by
peter
on 2009-09-23
in Logic, Mathematics, Probability theory and Uncertainty
. Closed

Normblog has a regular feature, Writer’s Choice, where writers give their opinions of books which have influenced them.   Seeing this led me recently to think of the mathematical ideas which have influenced my own thinking.   In an earlier post, I wrote about the writers whose  books (and teachers whose lectures) directly influenced me.  I left many pure mathematicians and statisticians off that list because most mathematics and statistics I did not receive directly from their books, but indirectly, mediated through the textbooks and lectures of others.  It is time to make amends. 

Here then is a list of mathematical ideas which have had great influence on my thinking, along with their progenitors.  Not all of these ideas have yet proved useful in any practical sense, either to me or to the world – but there is still lots of time.   Some of these theories are very beautiful, and it is their elegance and beauty and profundity to which I respond.  Others are counter-intuitive and thus thought-provoking, and I recall them for this reason.

  • Euclid’s axiomatic treatment of (Euclidean) geometry
  • The various laws of large numbers, first proven by Jacob Bernoulli (which give a rational justification for reasoning from samples to populations)
  • The differential calculus of Isaac Newton and Gottfried Leibniz (the first formal treatment of change)
  • The Identity of Leonhard Euler:  exp ( i * \pi) + 1 = 0, which mysteriously links two transcendental numbers (\pi and e), an imaginary number i (the square root of minus one) with the identity of the addition operation (zero) and the identity of the multiplication operation (1).
  • The epsilon-delta arguments for the calculus of Augustin Louis Cauchy and Karl Weierstrauss
  • The non-Euclidean geometries of Janos Bolyai, Nikolai Lobachevsky and Bernhard Riemann (which showed that 2-dimensional (or plane) geometry would be different if the surface it was done on was curved rather than flat – the arrival of post-modernism in mathematics)
  • The diagonalization proof of Gregor Cantor that the Real numbers are not countable (showing that there is more than one type of infinity) (a proof-method later adopted by Godel, mentioned below)
  • The axioms for the natural numbers of Guiseppe Peano
  • The space-filling curves of Guiseppe Peano and others (mapping the unit interval continuously to the unit square)
  • The axiomatic treatments of geometry of Mario Pieri and David Hilbert (releasing pure mathematics from any necessary connection to the real-world)
  • The algebraic topology of Henri Poincare and many others (associating algebraic structures to topological spaces)
  • The paradox of set theory of Bertrand Russell (asking whether the set of all sets contains itself)
  • The Fixed Point Theorem of Jan Brouwer (which, inter alia, has been used to prove that certain purely-artificial mathematical constructs called economies under some conditions contain equilibria)
  • The theory of measure and integration of Henri Lebesgue
  • The constructivism of Jan Brouwer (which taught us to think differently about mathematical knowledge)
  • The statistical decision theory of Jerzy Neyman and Egon Pearson (which enabled us to bound the potential errors of statistical inference)
  • The axioms for probability theory of Andrey Kolmogorov (which formalized one common method for representing uncertainty)
  • The BHK axioms for intuitionistic logic, associated to the names of Jan Brouwer, Arend Heyting and Andrey Kolmogorov (which enabled the formal treatment of intuitionism)
  • The incompleteness theorems of Kurt Godel (which identified some limits to mathematical knowledge)
  • The theory of categories of Sam Eilenberg and Saunders Mac Lane (using pure mathematics to model what pure mathematicians do, and enabling concise, abstract and elegant presentations of mathematical knowledge)
  • Possible-worlds semantics for modal logics (due to many people, but often named for Saul Kripke)
  • The topos theory of Alexander Grothendieck (generalizing the category of sets)
  • The proof by Paul Cohen of the logical independence of the Axiom of Choice from the Zermelo-Fraenkel axioms of Set Theory (which establishes Choice as one truly weird axiom!)
  • The non-standard analysis of Abraham Robinson and the synthetic geometry of Anders Kock (which formalize infinitesimal arithmetic)
  • The non-probabilistic representations of uncertainty of Arthur Dempster, Glenn Shafer and others (which provide formal representations of uncertainty without the weaknesses of probability theory)
  • The information geometry of Shunichi Amari, Ole Barndorff-Nielsen, Nikolai Chentsov, Bradley Efron, and others (showing that the methods of statistical inference are not just ad hoc procedures)
  • The robust statistical methods of Peter Huber and others 
  • The proof by Andrew Wiles of The Theorem Formerly Known as Fermat’s Last (which proof I don’t yet follow).

Some of these ideas are among the most sublime and beautiful thoughts of humankind.  Not having an education which has equipped one to appreciate these ideas would be like being tone-deaf.

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Epistemic modal logic at the CIA

Published
by
peter
on 2009-07-01
in Decision theory, Intelligence and Uncertainty
. Closed

Jim Angleton

A recent issue of the TLS ran a review by Terence Hawkes of the biography by Michael Holzman of Jim Angleton, head of counter-intelligence at the CIA.  Holzman’s book, although mostly written from secondary sources, is a fine summary of Angleton’s life and career.  It is marred, however, by (a) Holzman’s annoying (academic) habit of quoting something or somebody and  then repeating, verbatim, key words from that very quotation in the following paragraph, as if we readers were idiots, unable to read for ourselves or contemplate an idea for longer than a paragraph.  And, (b) by a casual sloppiness about dates.  Call me old-fashioned, but I think a historian should not simply say “in  May that  year”  when the last mention of the specific year was some tens of pages and several anecdotes or set-pieces back.   No doubt Holzman always knows which of the 71 years of Angleton’s life and the various ones before or since he is currently referring to, but this is rarely obvious to the reader of this book, even to a careful reader.   In view of the subject matter and Holzman’s theme (that Angleton’s training in so-called practical criticism was invaluable to his career in counter-intelligence), one has to wonder if such sloppiness is deliberate.

Holzman also does not tell us much about the actual theory and practice of counter-intelligence, despite the title and the claims he makes up front.   In particular, his treatment of the Nosenko case is misleading, partly he believes the official CIA line and because he does not refer to the most recent publication on the case, namely the book by Bagley. Hawkes seems to have followed Holzman in his garden-path-up-straying.

Unlike literary criticism, espionage is not only about what to believe, it is also about what to do.  It may be the case that Yuri Nosenko was a genuine Soviet defector, as Holzman claims CIA eventually came to believe.  Others closely involved in the case, such as retired CIA agent Tennent Bagley (2007) have argued compellingly that Nosenko was in fact a KGB plant, not a genuine defector.

Whether or not Nosenko was a genuine defector, and whether or not CIA leadership believed him to be a genuine defector, CIA would also need to concern itself with what impact a revelation of their beliefs would have on KGB, as I have argued before, and thus on what proposition to seek to have KGB believe about CIA’s beliefs in the matter.   If CIA were seen by KGB to accept Nosenko’s testimony (inconsistent and incomplete, by his own admission) too quickly, KGB may not accept as genuine any CIA profession of belief in his bona fides.  So, some delay and equivocation in decision-making was called for.  If CIA professed to believe that Nosenko was a plant or allowed KGB to conclude that CIA believed Nosenko to be a plant, then CIA risked signalling to KGB that they (CIA) were also rejecting all the testimony he arrived in the west with, which included detailed protestations of KGB non-involvement in the assassination of President John F. Kennedy.    Whether or not CIA believed that KGB were involved in that assassination, they may or may not have wished to let KGB know what they believed, at least at that particular moment.  In any case, perhaps a clever (and cunning) CIA would seek to have KGB believe that Nosenko was believed, in order to see how the game played itself out.

 So, one possible course of action for CIA was to signal to KGB that they accepted Nosenko as a genuine defector, but to signal also that they came to this decision only slowly and painfully.   How better to do this than to interrogate the man at length and (allegedly) harshly, and then, after years of apparent indecision and multiple internal investigations (some of which may even have been genuine), decide to accept him publicly as a true defector.   This public acceptance – consultancy fees, letters, flags, medals, and all – even now, four decades later, may have absolutely no connection whatever with what CIA leadership really believed then or, indeed, what they believe now.

It’s not only litcrit that gets an outing in these events.  If any philosopher reading this wonders about the practical usefulness of dynamic epistemic modal logic, wonder no more.

References:

Tennent H. Bagley [2007]:  Spy Wars.  New Haven, CT, USA:  Yale University Press.

Terence Hawkes [2009]: “William Empson’s Influence on the CIA.”  Times Literary Supplement, 2009-06-10.

Michael Holzman [2008]:  James Jesus Angleton, the CIA and the Craft of Counterintelligence.  Boston, MA, USA: University of Massachusetts Press.

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Black swans of trespass

Published
by
peter
on 2009-04-08
in Decision theory, Forecasting, Uncertainty and economics
. Closed

gould-blackswan

Nassim Taleb has an article in the FinTimes presenting ten principles he believes would reduce the occurrence of rare, catastrophic events (events he has taken to calling black swans).  Many of his principles are not actionable, and several are ill-advised.  Take, for instance, # 3:

3. People who were driving a school bus blindfolded (and crashed it) should never be given a new bus.

If this principle was applied, the bus would have no drivers at all.   All of us are driving blindfolded, with our only guide to the road ahead being what we can apprehend from the rear-view mirror.  Past performance, as they say, is no guide to the future direction of the road.

Or take #6:

6. Do not give children sticks of dynamite, even if they come with a warning.  Complex derivatives need to be banned because nobody understands them and few are rational enough to know it. Citizens must be protected from themselves, from bankers selling them “hedging” products, and from gullible regulators who listen to economic theorists.

Well, what precisely is “complex”?  Surely, Dr Taleb is not suggesting the banning of plain futures and options, as these serve a valuable function in our economy (enabling the parceling and trading of risk).  But even these are too complex for some people (such as those farmers, dentists, and local government officials currently with burnt fingers), and surely such people need protection from themselves much more so than the quant-jocks and their masters on Wall Street.  So, where would one draw the line between allowed derivative and disallowed? 

Once again, it appears there has been a mis-understanding of the cause of the recent problems.  It is not complex derivatives per se that are the problem, but the fact that many of these financial instruments have, unusually, been highly-correlated.  Thus, the failure of one instrument (and subsequently, one bank) brings down all the others with it — there is a systemic risk as well as a participant risk involved in their use.   Dr Taleb, who has long been a critic of the unthinking use of Gaussian models in finance, I am sure realises this.

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The decade around 1664

Published
by
peter
on 2009-03-29
in Culture, History, Probability theory, Prophecy, Science and Uncertainty
. Closed

We noted before that one consequence of the rise of coffee-houses in 17th-century Europe was the development of probability theory as a mathematical treatment of reasoning with uncertainty.   Ian Hacking’s history of the emergence of probabilistic ideas in Europe has a nice articulation of the key events, all of which took place a decade either side of 1664:

  • 1654:  Pascal wrote to Fermat with his ideas about probability
  • 1657: Huygens wrote the first textbook on probability to be published, and Pascal was the first to apply probabilitiy ideas to problems other than games of chance
  • 1662: The Port Royal Logic was the first publication to mention numerical measurements of something called probability, and Leibniz applied probability to problems in legal reasoning
  • 1662:  London merchant John Gaunt published the first set of statistics drawn from records of mortality
  • Late 1660s:  Probability theory was used by John Hudde and by Johan de Witt in Amsterdam to provide a sound basis for reasoning about annuities (Hacking 1975, p.11).

Developments in the use of symbolic algebra in Italy in the 16th-century provided the technical basis upon which a formal theory of uncertainty could be erected.  And coffee-houses certainly aided the dissemination of probabilistic ideas, both in spoken and written form.   Coffee houses may even have aided the creation of these ideas – new mathematical concepts are only rarely created by a solitary person working alone in a garret, but usually arise instead through conversation and debate among people with partial or half-formed ideas.  

However, one aspect of the rise of probability in the mid 17th century is still a mystery to me:  what event or phenomena led so many people across Europe to be interested in reasoning about uncertainty at this time?  Although 1664 saw the establishment of a famous brewery in Strasbourg, I suspect the main motivation was the prevalence of bubonic plague in Europe.   Although plague had been around for many centuries, the Catholic vs. Protestant religious wars of the previous 150 years had, I believe, led many intelligent people to abandon or lessen their faith in religious explanations of uncertain phenomena.   Rene Descartes, for example, was led to cogito, ergo sum when seeking beliefs which peoples of all faiths or none could agree on.  Without religion, alternative models to explain or predict human deaths, morbidity and natural disasters were required.   The insurance of ocean-going vessels provided a financial incentive for finding good predictive models of such events.

Hacking notes (pp. 4-5) that, historically, probability theory has mostly developed in response to problems about uncertain reasoning in other domains:  In the 17th century, these were problems in insurance and annuities, in the 18th, astronomy, the 19th, biometrics and statistical mechanics, and the early 20th, agricultural experiments.  For more on the connection between statistical theory and experiments in agriculture, see Hogben (1957).  For the relationship of 20th-century probability theory to statistical physics, see von Plato (1994).

References:

Ian Hacking [1975]:  The Emergence of Probability: a Philosophical study of early ideas about Probability, Induction and Statistical Inference. London, UK: Cambridge University Press.

Lancelot Hogben [1957]: Statistical Theory. W. W. Norton.

J. von Plato [1994]:  Creating Modern Probability:  Its Mathematics, Physics and Philosophy in Historical Perspective.  Cambridge Studies in Probability, Induction, and Decision Theory.  Cambridge, UK:  Cambridge University Press.   Cambridge Studies in Probability, Induction, and Decision Theory.




Evaluating prophecy

Published
by
peter
on 2009-01-19
in Argumentation, Computer technology, Decision theory, Forecasting, Prophecy and Uncertainty
. 1 Comment

With the mostly-unforeseen global financial crisis uppermost in our minds, I am led to consider a question that I have pondered for some time:   How should we assess forecasts and prophecies?   Within the branch of philosophy known as argumentation, a lot of attention has been paid to the conditions under which a rational decision-maker would accept particular types of argument. 

meteor

 For example, although it is logically invalid to accept an argument only on the grounds that the person making it is an authority on the subject, our legal system does this all the time.  Indeed,  the philosopher Charles Willard has argued that modern society could not function without most of us accepting arguments-from-authority most of the time, and it is usually rational to do so.  Accordingly, philosophers of argumentation have investigated the conditions under which a rational person would accept or reject such arguments.   Douglas Walton (1996, pp. 64-67) presents an argumentation scheme for such acceptance/rejection decisions, the Argument Scheme for Arguments from Expert Opinion, as follows:

  • Assume E is an expert in domain D.
  • E asserts that statement A is known to be true.
  • A is within D.

Therefore, a decision-maker may plausibly take A to be true, unless one or more of the following Critical Questons (CQ) is answered in the negative:

  • CQ1:  Is E a genuine expert in D?
  • CQ2:  Did E really assert A?
  • CQ3:  Is A relevant to domain D?
  • CQ4:  Is A consistent with what other experts in D say?
  • CQ5:  Is A consistent with known evidence in D?

One could add further questions to this list, for example:

  • CQ6:  Is E’s opinion offered without regard to any reward or benefit upon statement A being taken to be true by the decision-maker?

Walton himself presents some further critical questions first proposed by Augustus DeMorgan in 1847 to deal with cases under CQ2 where the expert’s opinion is presented second-hand, or in edited form, or along with the opinions of others.

 Clearly, some of these questions are also pertinent to assessing forecasts and prophecies.  But the special nature of forecasts and prophecies may enable us to make some of these questions more precise.  Here is my  Argument Scheme for Arguments from Prophecy:

  • Assume E is a forecaster for domain D.
  • E asserts that statement A will be true of domain D at time T in the future.
  • A is within D.

Therefore, a decision-maker may plausibly take A to be true at time T, unless one or more of the following Critical Questons (CQ) is answered in the negative:

  • CQ1:  Is E a genuine expert in forecasting domain D?
  • CQ2:  Did E really assert that A will be true at T?
  • CQ3:  Is A relevant to, and within the scope of, domain D?
  • CQ4:  Is A consistent with what is said by other forecasters with expertise in D?
  • CQ5:  Is A consistent with known evidence of current conditions and trends in D?
  • CQ6:  Is E’s opinion offered without regard to any reward or benefit upon statement A being adopted by the decision-maker as a forecast?
  • CQ7:  Do the benefits of adopting A being true at time T in D outweigh the costs of doing so, to the decision-maker?

In attempting to answer these questions, we may explore more detailed questions:

  • CQ1-1:  What is E’s experience as forecaster in domain D? 
  • CQ1-2: What is E’s track record as a forecaster in domain D?
  • CQ2-1: Did E articulate conditions or assumptions under which A will become true at T, or under which it will not become true?  If so, what are these?
  • CQ2-2:  How sensitive is the forecast of A being true at T to the conditions and assumptions made by E?
  • CQ2-3:  When forecasting that A would become true at T, did E assert a more general statement than A?
  • CQ2-4:  When forecasting that A would become true at T, did E assert a more general time than T?
  • CQ2-5:  Is E able to provide a rational justification (for example, a computer simulation model) for the forecast that A would be true at T?
  • CQ2-6:  Did E present the forecast of A being true at time T qualified by modalities, such as possibly, probably, almost surely, certainly, etc.
  • CQ4-1:  If this forecast is not consistent with those of other forecasters in domain D, to what extent are they inconsistent?   Can these inconsistencies be rationally justified or explained?
  • CQ5-1: What are the implications of A being true at time T in domain D?  Are these plausible?  Do they contradict any known facts or trends?
  • CQ6-1:  Will E benefit if the decision-maker adopts A being true at time T as his/her forecast for domain D? 
  • CQ6-2:  Will E benefit if the decision-maker does not adopt A being true at time T as his/her forecast for domain D? 
  • CQ6-3:  Will E benefit if many decision-makers adopt A being true at time T as their forecast for domain D?
  • CQ6-4:  Will E benefit if few decision-makers adopt A being true at time T as their forecast for domain D?
  • CQ6-5:  Has E acted in such a way as to indicate that E had adopted A being true at time T as their forecast for domain D (eg, by making an investment betting that A will be true at T)?
  • CQ7-1:  What are the costs and benefits to the decision-maker for adopting statement A being true at time T in domain D as his or her forecast of domain D? 
  • CQ7-2:  How might these costs and benefits be compared?  Can a net benefit/cost for the decision-maker be determined?

Automating these questions and the process of answering them is on my list of next steps, because automation is needed to design machines able to reason rationally about the future.   And rational reasoning about the future is needed if  we want machines to make decisions about actions.

References:

Augustus DeMorgan [1847]: Formal Logic.  London, UK:  Taylor and Walton.

Douglas N. Walton [1996]:  Argument Schemes for Presumptive Reasoning. Mahwah, NJ, USA: Lawrence Erlbaum.

Charles A. Willard [1990]: Authority.  Informal Logic, 12: 11-22.

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Retroflexive decision-making

Published
by
peter
on 2009-01-18
in Corporate culture, Decision theory, Probability theory, Uncertainty and economics
. 1 Comment

How do companies make major decisions?  The gurus of classical Decision Theory – people like economist Jimmie Savage and statistician Dennis Lindley - tell us that there is only one correct way to make decisions:  List all the possible actions, list the potential consequences of each action, assign utilities  and probabilities of occurence to each consequence, multiply these numbers together for each consequence and then add the resulting products for each action to get an expected utility for each action, and finally choose that action which maximizes expected utility.   

There are many, many problems with this model, not least that it is not what companies – or intelligent, purposive individuals for that matter – actually do.  Those who have worked in companies know that nothing so simplistic or static describes intelligent, rational decision making, nor should it.  Moreover, that their model was flawed as a description of reality was known at the time to Savage, Lindley, et al,  because it was pointed out to them six decades ago by people such as George Shackle, an economist who had actually worked in industry and who drew on his experience.  The mute, autistic behemoth that is mathematical economics, however, does not stop or change direction merely because its utter disconnection with empirical reality is noticed by someone, and so - TO THIS VERY DAY – students in business schools still learn the classical theory.  I guess for the students it’s a case of:  Who are we going to believe – our textbooks, or our own eyes?    From my first year as an undergraduate taking Economics 101, I had trouble believing my textbooks.

So what might be a better model of decision-making?  First, we need to recognize that corporate decision-making is almost always something dynamic, not static – it takes place over time, not in a single stage of analysis, and we would do better to describe a process, rather than just giving a formula for calculating an outcome.   Second, precisely because the process is dynamic, many of the inputs assumed by the classical model do not exist, or are not known to the participants, at the start, but emerge in the course of the decision-making process.   Here, I mean things such as:  possible actions, potential consequences, preferences (or utilities), and measures of uncertainty (which may or may not include probabilities).     Third, in large organizations, decision-making is a group activity, with inputs and comments from many people.   If you believe – as Savage and Lindley did – that there is only one correct way to make a decision, then your model would contain no scope for subjective inputs or stakeholder revisions, which is yet another of the many failings of the classical model.    Fourth, in the real world, people need to consider – and do consider – the potential downsides as well as the upsides of an action, and they need to do this – and they do do this – separately, not merged into a summary statistic such as “utility”.   So, if  one possible consequence of an action-option is catastrophic loss, then no amount of maximum-expected-utility quantitative summary gibberish should permit a rational decision-maker to choose that option without great pause (or insurance).   Shackle knew this, so his model considers downsides as well as upsides.   That Savage and his pals ignored this one can only assume is the result of the impossibility of catastrophic loss ever occurring to a tenured academic.

So let us try to articulate a staged process for what companies actually do when they make major decisions, such as major investments or new business planning:

  1. Describe the present situation and the way or ways it may evolve in the future.  We call these different future paths scenarios.   Making assumptions about the present and the future is also called taking a view.
  2. For each scenario, identify a list of possible actions, able to be executed under the scenario.
  3. For each scenario and action, identify the possible upsides and downsides.
  4. Some actions under some scenarios will have attractive upsides.   What can be done to increase the likelihood of these upsides occurring?  What can be done to make them even more attractive?
  5. Some actions under some scenarios will have unattractive downsides.   What can be done to eliminate these downsides altogether or to decrease their likelihood of occurring?   What can be done to ameliorate, to mitigate, to distribute to others, or to postpone the effects of these downsides?
  6. In the light of what was learned in doing steps 1-5, go back to step 1 and repeat it.
  7. In the light of what was learned in doing steps 1-6, go back to step 2 and repeat steps 2-5.  For example, by modifying or combining actions, it may be posssible to shift attractive upsides or unattractive downsides from one action to another.
  8. As new information comes to hand, occasionally repeat step 1. Repeat step 7 as often as time permits.  

This decision process will be familiar to anyone who has prepared a business plan for a new venture, either for personal investment, or for financial investors and bankers, or for business partners.   Having access to spreadsheet software such as Lotus 1-2-3 or Microsoft EXCEL has certainly made this process easier to undertake.  But, contrary to the beliefs of many, people made major decisons before the invention of spreadsheets, and they did so using processes similar to this, as Shackle’s work evidences.

Because this model involves revision of initial ideas in repeated stages, it bears some resemblance to the retroflexive argumentation theory of philosopher Harald Wohlrapp.  Hence, I call it Retroflexive Decision Theory.  I will explore this model in more detail in future posts.

References:

D. Lindley [1985]:  Making Decisions.  Second Edition. London, UK: John Wiley and Sons.

L. J. Savage [1950]: The Foundations of Statistics.  New York, NY, USA:  Wiley.

G. L. S. Shackle [1961]: Decision, Order and Time in Human Affairs. Cambridge, UK:  Cambridge University Press.

H. Wohlrapp [1998]:  A new light on non-deductive argumentation schemes.  Argumentation, 12: 341-350.

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Epideictic arguments

Published
by
peter
on 2008-11-06
in Argumentation, Culture, Decision theory, Politics, Rhetoric and Uncertainty
. 1 Comment

Suppose you are diagnosed with a serious medical condition, and you seek advice from two doctors.  The first doctor, let’s call him Dr Barack, says that there are three possible courses of treatment.   He labels these courses, A, B and C, and then proceeds to walk you methodically through each course – what separate basic procedures are involved, in what order, with what likely side effects, and with what costs and durations, what chances of success or failure, and what likely survival rates.   He finishes this methodical exposition by summing up each treatment, with pithy statements such as, “Course A is the cheapest and most proven.  Course B is an experimental treatment, which makes it higher risk, but it may be the most effective.  Course C . . .” etc.

The other doctor, let’s call him Dr John, in contrast talks in a manner which is apparently lacking all structure. He begins a long, discursive narrative about the many different basic procedures possible, not in any particular order, jumping back and forth between these as he focuses first on the costs of procedures, then switching to their durations, then back again to costs, then onto their expected side effects, with tangential discussions in the middle about the history of the experimental tests undertaken of one of the procedures and about his having suffered torture while a POW in Vietnam, etc, etc.  And he does all this without any indication that some procedures are part of larger courses of treatment, or are even linked in any way, and speaking without using any patient-friendly labelling or summarizing of the decision-options.

Which doctor would you choose to treat you?  If this description was all that you knew, then Doctor Barack would appear to be the much better organized of the two doctors.   Most of us would have more confidence being treated by a doctor who sounds better-organized, who appears to know what he was doing, compared to a doctor who sounds dis-organized.   More importantly, it is also evident that Doctor Barack knows how to structure what he knows into a coherent whole, into a form which makes his knowledge easier to transmit to others, easier for a patient to understand, and which also facilitates the subsequent decision-making by the patient.  We generally have more confidence in the underlying knowlege and expertise of people able to explain their knowledge and expertise well, than in those who cannot.

If we reasoned this way, we would be choosing between the two doctors on the basis of their different rhetorical styles:  we would be judging the contents of their arguments (in this case, the content is their ability to provide us with effective treatment) on the basis of the styles of their arguments.  Such reasoning processes, which use form to assess content, are called epideictic, as are arguments which draw attention to their own style. 

Advertising provides many examples of epideictic arguments, particularly in cultures where the intended target audience is savvy regarding the form of advertisements.  In Britain, for instance, the film director Michael Winner starred in a series of TV advertisements for an insurance company in which the actors pretending to be real people giving endorsements revealed that they were just actors, pretending to be real people giving endorsements.   This was a glimpse behind the curtain of theatrical artiface, with the actors themselves pulling back the curtain.  Why do this?  Well, self-reference only works with a knowledgeable audience, perhaps so knowledgeable that they have even grown cynical with the claims of advertisers.   By winking at the audience, the advertisers are colluding with this cynicism, saying to the audience, “we know you think this and we agree, so our advert is pitched to you, you cynical sophisticates, not to those others who don’t get it.”

The world-weary tone of the narration of Apple’s “Future” series of adverts here is another example of advertisements which knowingly direct our attention to their own style.

Apple Future Advertisement – Robots

And Dr Barack and Dr John?  One argument against electing Senator Obama to the US Presidency was that he lacked executive experience.  A counter-argument, made even by the good Senator Obama himself, was that he demonstrated his executive capabilities through the competence, professionalism and effectiveness of his management of his own campaign.   This is an epideictic argument.

There is nothing necessarily irrational or fallacious about such arguments or such modes of reasoning; indeed, it is often the case that the only relevant information available for a decision on a claim of substantive content is the form of the claim.   Experienced investors in hi-tech start-ups, for example, know that the business plan they are presented with is most unlikely to be implemented, because the world changes too fast and too radically for any plan to endure.   A key factor in the decision to invest must therefore be an assessment of the capability of the management team to adjust the business plan to changing circumstances, from recognizing that circumstances have in fact changed, to acting quickly and effectively in response, through to evaluating the outcomes.   How to assess this capability for decision-making robustness?  Well, one basis is the past experience of the team.  But experience may well hinder managerial flexibility rather than facilitate it, expecially in a turbulent environment.  Another way to assess this capability is to subject the team to a stress test – contesting the assumptions and reasoning of the business plan, being unreasonable in questions and challenges, prodding and poking and provoking the team to see how well and how quickly they can respond, in real time, without preparation.   In all of this, a decision on the substance of the investment is being made from evidence about the form — about how well the management team responds to such stress testing.   This is perfectly ratonal, given the absence of any other basis on which to make a decision and given our imperfect knowledge of the future.

Likewise, an assessment of Senator Obama’s capabilities for high managerial office on the basis of his competence at managing his campaign was also eminently rational and perfectly justifiable.   The incoherent nature of Senator McCain’s campaign and the panic-struck and erratic manner in which he responded to suprising events (such as the financial crisis of September 2008) was similarly an indication of his likely style of government; the style here did not produce confidence in the content.  For many people,  the choice between candidates in the US Presidential campaign was an epideictic one.

Refs and Acks

The medical example is due to William Rehg.

William Rehg [1997]: Reason and rhetoric in Habermas’s theory of argumentation,  pp. 358-377 in:  W. Jost and M. J. Hyde (Editors): Rhetoric and Hermeneutics in Our Time: A Reader. New Haven, CN, USA: Yale University Press.

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Kaleidic moments

Published
by
peter
on 2008-10-27
in Prophecy, Uncertainty and economics
. Closed

Is the economy like a pendulum, gradually oscillating around a fixed point until it reaches a static equilibrium?  This metaphor, borrowed from Newtonian physics, still dominates mainstream economic thinking and discussion.  Not all economists have agreed, not least because the mechanistic Newtonian viewpoint seems to allow no place for new information to arrive or for changes in subjective responses.   The 20th-century economists George Shackle and Ludwig Lachmann, for example, argued that a much more realistic metaphor for the modern economy is a kaleidoscope.  The economy is a “kaleidic society, interspersing its moments or intervals of order, assurance and beauty with sudden disintegration and a cascade into a new pattern.” (Shackle 1972, p.76).    

The arrival of new information, or changes in the perceptions and actions of marketplace participants, or changes in their subjective beliefs and intentions, are the events which trigger these sudden disruptions and discontinuous realignments.   Recent events in the financial markets show we are in a kaleidic moment right now.  If there’s an invisible hand, it’s not holding a pendulum but busy shaking the kaleidoscope.  

Reference:

Geoge L S Shackle [1972]: Epistemics and Economics.  Cambridge, UK:  Cambridge University Press.

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Banking on Linda

Published
by
peter
on 2008-06-28
in Decision theory, Probability theory and Uncertainty
. 3 Comments

Over at “This Blog Sits”, Grant McCracken has a nice post about a paradigm example often used in mainstream economics to chastise everyday human reasoners. A nice discussion has developed. I thought to re-post one of my comments, which I do here:

“The first point — which should be obvious to anyone who deals professionally with probability, but often seems not — is that the answer to a problem involving uncertainty depends very crucially on its mathematical formulation. We are given a situation expressed in ordinary English words and asked to use it to make a judgement. The probability theorists have arrived at a way of translating such situations from natural human language into a formal mathematical language, and using this formalism, to arrive at an answer to the situation which they deem correct. However, natural language may be imprecise (as in the example, as gek notes). Imprecision of natural language is a key reason for attempting a translation into a formal language, since doing so can clarify what is vague or ambiguous. But imprecision also means that there may be more than one reasonable translation of the same problem situation, even if we all agreed on what formal language to use and on how to do the translation. There may in fact be more than one correct answer.

There is much of background relevance here that may not be known to everyone, First, note that it took about 250 years from the first mathematical formulations of uncertainty using probability (in the 1660s) to reach a sort-of consensus on a set of mathematical axioms for probability theory (the standard axioms, due to Andrei Kolmogorov, in the 1920s). By contrast, the Second, even now, the Kolmogorov axioms are not uncontested. Although it often comes as a suprise to statisticians and mathematicians, there is a whole community of intelligent, mathematically-adept, people in Artificial Intelligence who prefer to use alternative formalisms to probability theory, at least for some problem domains. These alternatives (such as Dempster-Shafer theory and possibility theory) are preferred to probability theory because they more are expressive (more situations can be adequately represented) and because they are easier to manipulate for some types of problems than probability theory. Let no one believe, then, that probability theory is accepted by every mathematically-adept expert who works with uncertainty. Historical aside: In fact, ever since the 1660s, there has been a consistent minority of people dissenting from the standard view of probability theory, a minority which has mostly been erased from the textbooks. Typically, these dissidents have tried unsuccessfully to apply probability theory to real-world problems, such as those encountered by judges and juries (eg, Leibniz in the 17th century), doctors (eg, von Kries in the 19th), business investors (eg, Shackle in the 20th), and now intelligent computer systems (since the 1970s). One can have an entire university education in mathematical statistics, as I did, and never hear mention of this dissenting stream. A science that was confident of its own foundations would surely not need to suppress alternative views. Third, intelligent, expert, mathematically-adept people who work with uncertainty do not even yet agree on what the notion of “probability” means, or to what it may validly apply. Donald Gillies, a professor of philosophy at the University of London, wrote a nice book called, “Philosophical Theories of Probability” (Routledge, London, 2000), which outlines the main alternative interpretations. A key difference of opinion concerns the scope of probability expressions (eg, over which types of natural language statements may one validly apply the translation mechanism). Note that Gillies wrote his book 70-some years after Kolmogorov’s axioms. In addition, there are other social or cultural factors, usually ignored by mathematically-adept experts, which may inform one’s interpretations of uncertainty and probability. A view that the universe is deterministic, or that one’s spiritual fate is pre-determined before birth, may be inconsistent with any of these interpretations of uncertainty, for instance. I have yet to see a Taoist theory of uncertainty, but I am sure it would differ from anything developed so far. I write this comment to give some context to our discussion. Mainstream economists and statisticians are fond of castigating ordinary people for being confused or for acting irrationally when faced with situations involving uncertainty, merely because the judgements of ordinary people do not always conform to the Kolmogorov axioms and the deductive consequences of these axioms. It is surely unreasonable to cast such aspersions when experts themselves disagree on what probability is, to what statements probabilities may be validly applied, and on how uncertainty should be formally represented.”

The differential calculus, invented about the same time in the 17the century as Probability, was already rigorously formalized by the mid-19th century. Dealing formally with uncertainty is hard, and intuitions differ greatly, even for the mathematically adept.

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