Obiter dicta by Professor Gavin Brown AO
Beyond the eftest
16 August 2002
Having comported myself with dignity and every appearance of skill throughout this season's Australian Vice-Chancellors' Committee AFL tipping contest, I have fallen flat on my face with a sequence of disastrous selections in the latest round. The professionals who frame the odds for sporting events have my respect and I use their probabilistic skills as a background for my own decision making. This serves me well at Randwick but not at Colonial Stadium.
Every so often, however, it is a pleasure to see them get things wrong. Such an occasion was Sydney University's victory over Eastwood which has taken our first grade team to the top of the rugby championship table. It may surprise some readers that there is vigorous official betting on club rugby and that Eastwood were hot favourites to win last Saturday.
In a strictly logical sense it is wrong to claim that the odds-makers made a mistake. The occurrence of an event does not change the probability of its having happened. It may have no bearing on the probability of its happening again. Consider, for example, a standard six-sided die which is known to be unbiased. If we have made the outcome "a number less than five" strong favourite, then we are not proved wrong when a six is thrown. Neither would we change our stance in consequence.
Where the underlying structure is less clear-cut then it is as much art as science to determine truth. One cannot entirely refute the hypothesis that my selections were accurate but the results aberrant while, at the same time, Uni's win was not only deserved but predictable. I may choose to believe both!
Variations on this theme formed part of a recent after-dinner conversation with Lord Mustill who gave the Inaugural Clayton-Utz lecture on International Arbitration. His Lordship, who trained in mathematics as an undergraduate, discussed with me the traps and ambiguities which can arise when expert witnesses are cross-examined in court concerning the probability of outcomes. There is a potential to mislead which can be either wilful or unconscious.
Similar problems attend the whole question of Risk Management in NSW universities and, by the time this piece appears, the topic will have been addressed in a major ICAC report.
Naturally one uses case studies of mistakes and undesirable outcomes. This is an entirely legitimate tactic to raise awareness and to encourage the examination and improvement of protocol and process. On the other hand one must always be aware that Risk Management really does involve risk and we should be deeply suspicious of any system which apparently fails to throw up unanticipated outcomes. Moreover we need to have the courage to balance the cost of prevention against the risk and cost of post hoc remediation.
I have a hazy recall of another time and place where the issue was car-parking. A single officer issued tickets and collected money. Audit recommended the employment of a second officer to avoid corruption. A few years later the pair were caught colluding.
That is petty but pithy. On a grander scale governments have had vivid recent reminders of the existence of evil – terrorism and corporate fraud – and we all face a delicate task of optimisation to balance quality of life and handiness with security and effectiveness.