THE PHILOSOPHY OF RISK
MARTIN SEWELL
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RISK
• In my (Bayesian) mind, risk is uncertainty.
• Uncertainty is best described using a probability
distribution, and the broader the distribution, the
greater the uncertainty.
• We live in a largely deterministic universe; the only
truly random processes involve phenomena which
are aspects of quantum mechanics.
• However, the movement of just three bodies can
be chaotic (therefore unpredictable), so in practice
life is full of uncertainty, and risk.
BAYESIANISM
• Normative—how rational agents should behave.
• A Dutch book is a gambling term for a set of odds and bets that
guarantees a profit, regardless of the outcome of the gamble.
• At the very least, one who practices self-consistent reasoning should not
be susceptible to having a Dutch book made against them.
• If an individual is not susceptible to a Dutch book, their previsions are said
to be coherent.
• A set of betting quotients is coherent if (Ramsey 1926; de Finetti 1937;
Shimony 1955) and only if (Kemeny 1955; Lehman 1955) they satisfy the
axioms of probability.
• Bayes’ theorem is merely the calculus for updating a probability in the
light of new evidence, so the validity of the formula itself is not
controversial, but it does presuppose the applicability of probability.
• By definition, an individual is a Bayesian to the extent that they are willing
to put a probability on a hypothesis.
• Science is essentially applied Bayesian inference (Sewell 2012).
WE ARE POOR BAYESIANS
• The finite frequency theory of probability defines the
probability of an outcome as the frequency of the
number of times the outcome occurs relative to the
number of times that it could have occurred.
• For our ancestors in the environment of evolutionary
adaptedness, a quick count of the number of predators
approaching was likely to have been a useful heuristic
for survival, which may explain why we make fewer
errors when dealing with relative frequencies than when
we are faced with (Bayesian) probabilities.
• Fast and frugal frequency-based probability, rather than
Bayesian methods, has evolved (Gigerenzer and
Hoffrage 1995; Cosmides and Tooby 1996). This leads to
failing to take sufficient account of, or even ignoring,
prior probabilities, which is known as base rate neglect.
KNIGHTIAN UNCERTAINTY
The American economist Frank Knight was the first to
explicitly make a conceptual distinction between risk
and uncertainty (Knight 1921):
• risk—outcome governed by a known probability
distribution
• uncertainty—outcome governed by an unknown
probability model
UNKNOWN UNKNOWNS
On 12 February 2002 United States Secretary of Defense, Donald Rumsfeld,
made the following statement during a press briefing where he addressed
the absence of evidence linking the government of Iraq with the supply of
weapons of mass destruction to terrorist groups:
‘[T]here are known knowns; there are things we know that we
know. There are known unknowns; that is to say there are
things that, we now know we don’t know. But there are also
unknown unknowns—there are things we do not know, we
don't know.’
Rumsfeld was ridiculed at the time for obfuscation, but it actually makes
sense.
BLACK SWAN EVENTS
In his book The Black Swan: The Impact of the Highly
Improbable (Taleb 2010), Nassim Taleb defines a Black
Swan event as having the following three attributes:
• Rarity—It is an outlier, as it lies outside the realm of
regular expectations, because nothing in the past can
convincingly point to its possibility.
• Extreme impact—It carries an extreme impact.
• Retrospective (though not prospective) predictability—In
spite of its outlier status, human nature makes us
concoct explanations for its occurrence after the fact,
making it explainable and predictable.
NASSIM TALEB
Taleb (2010) claims that:
• History is dominated by Black Swan events—
unexpected high-impact rare events that are
beyond the realm of normal expectations.
• The probability of these high-impact rare events is
very small and cannot be calculated.
• Due to psychological biases people are blind to
uncertainty and unaware of the hugely significant
role of these rare events in historical affairs.
ELIE AYACHE
• Traditionally, taking a Bayesian perspective, we
map probabilities onto states of the world.
• In his book The Blank Swan: The End of Probability
(Ayache 2010), Elie Ayache replaces probability
with a market-generated price:
contingent claims → market → prices
ELIE AYACHE: AN ASSESSMENT
• Ayache proclaims the ‘end of probability’, but the
subjective Bayesian Bruno de Finetti has already
famously noted that ‘probability does not exist’.
• Where markets exist, Ayache’s thesis makes sense,
e.g. bookies odds imply that
P(Brazil win 2014 FIFA World Cup) = 0.22
P(England win 2014 FIFA World Cup) = 0.05
• However, markets do not always exist when we are
interested in a probability, e.g. P(rain tomorrow).
• We need probability in order to conduct science.
RISK AVERSION
• Risk aversion exists when an individual prefers a
guaranteed payoff to an uncertain payoff with the
same expected value.
• Wealth is generated by a multiplicative process.
• In order to maximize growth of wealth, one must
maximize the expected value of the logarithm of wealth
after each period (Kelly 1956; Breiman 1961).
• If one is risk neutral in terms of log(wealth), because the
log utility function is concave, it follows that one must
exhibit a small degree of risk aversion regarding wealth.
• Normatively, we have a tendency towards slight risk
aversion with respect to utility generated by a
multiplicative process.
PROSPECT THEORY
Prospect theory (Kahneman and Tversky 1979; Tversky and Kahneman
1992) provides a descriptive account of decision making under risk.
Probability
Low
Moderate
High
Gains
risk seeking
risk averse
risk averse
Losses
risk averse
risk seeking
risk seeking
People tend to be risk averse, and will pay for insurance, but can also
be risk seeking for low probability events, such as playing the lottery.
ENLIGHTENMENT THINKING
• The British philosopher John Gray argues that Enlightenment thinking aimed to
supplant Christianity with a scientific view of the world, but could do so only if it was
able to satisfy the hopes it had implanted (Gray 2008).
• The Enlightenment belief that humanity is an inherently progressive species is a byproduct of Christianity.
• Human knowledge increases in a cumulative fashion, science progresses and
allows us to improve our material conditions.
• Thanks to economic growth modern societies become richer.
• However, we cannot expect improvements in ethics, politics, society or humanity.
Theories of such progress are myths, which rely on a teleological view and answer
the human need for meaning.
• History is not a movement in the direction of a universal goal or a march to a better
world, human history has no overall meaning.
• Gray (2008) states that humans are not becoming more civilized and that conflicts
are becoming more savage, in contrast Pinker (2011) evidences the fact that
violence is diminishing.
• The basis of all of our Western Civilisation utopias (ideologies) is the false elevation
of humans to be above and separate from nature. We’re only animals, albeit
intelligent ones.
• Such ideologies assume that man is good but has been rendered bad by some
historical condition that must be overcome.
THE PARADOX OF INCREASING RISK
• Technological progress has led to increasing efficiency.
• David Ricardo’s law of comparative advantage has led to
increasing globalization.
• The above two points have led to fewer supply chain
disruptions.
• Nassim Taleb argues that reducing vulnerability to small shocks
may increase the severity of large ones.
• Hyman Minsky claims that in a capitalist economy stability is
inherently destabilizing.
• An analysis of the Dow Jones Industrial Average shows that the
long term trend in stock market volatility has been upwards
since about 1960, so it could be that risk, in general, is
increasing.
• Examples of recent Black Swan events include the terrorist
attacks in the US on 11 September 2001 and the 2008–2012
global financial crisis.
THE FUTURE: SOCIAL DISCOUNT RATE
• How much do we care about the future?
• How much should we care about the future?
• If we wish to perform a cost-benefit analysis on a
future public sector project (such as climate
change mitigation), we must choose a discount
rate that reflects society’s preference for present
benefits over future benefits.
THE SOCIAL DISCOUNT RATE:
A PRESCRIPTION
• Although humans are simply vehicles that have evolved as if
to help ensure that their genes survive in perpetuity, all that is
required of individuals is that their ultimate motivation is to
reproduce, so we seek to maximize gene replication within our
lifetime, but not beyond.
• During a lifetime, generally the risk that a reward will not be
available decreases as one approaches the time that the
reward is expected, which leads to a hyperbolic discount
function.
• This account is descriptive, but as we cannot transcend our
genes (Moxon 2010), a prescriptive social discount rate must
accommodate our motivational set, so optimally coincides.
• An individual’s discount function is hyperbolic and reaches
100% at the end of their lifetime. An equitable social discount
function should average the population's individual discount
functions.
THE MEDIA AND BIASES
• Our ancestors living in the environment of evolutionary adaptedness
would only experience or witness events taking place within the
environment of their own tribe.
• Our minds evolved during a time when the number of times that we
experienced an event would have been fairly representative of the
probability of it recurring. Of course, ‘extreme’ events have always been
more memorable than mundane events.
• What is the effect of newspapers and other media reporting news?
• News, by definition, is unpredictable (otherwise, it would have been
reported yesterday).
• If we cannot predict something, it will be a surprise. So news is surprising,
the most likely to be reported news, therefore, is the most surprising.
• This means that rare events, such as a man being killed by a shark, are
likely to be heavily reported. While, for example, dying of diabetes is
much more common, but goes unreported.
• The media creates a biased impression of the world around us.
AVAILABILITY
• Availability (or saliency) (Tversky and Kahneman 1973) is
a cognitive heuristic in which we rely upon knowledge
that is readily available, rather than examine other
alternatives or procedures. That is, we make decisions
based on how easily things come to mind (which is
usually something that is likely to be newsworthy).
• Modern man is far more likely than his ancestors to hear
about events that he is unlikely to experience (such as
an airplane crash).
• This likely biases our judgement of risks, overestimating
the probability of high-impact low probability events.
CONCLUSIONS
• Probability does not exist, but is necessary if we wish to
remain self-consistent and conduct science (science is
essentially Bayesian inference).
• Don’t expect risk to decline.
• Avoid naive optimization at the expense of robustness
(Taleb 2010)—Mother Nature includes redundancy, e.g.
two eyes, two lungs, two kidneys.
• We can’t change human nature in any radical sense, so
it is better not to try.
• In-group/out-group biases are natural and market forces
are inevitable, so elude the control of government.
• Don’t expect or force people to make sacrifices in the
present for the sake of the distant future.
• It is our utility relative to others that matters.
REFERENCES
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MOXON, Steve, 2010. Culture is biology: Why we cannot ‘transcend’ our genes—or ourselves. Politics and Culture, 1.
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