Infernal Ramblings
A Malaysian Perspective on Politics, Society and Economics

On the Balance of the Probabilities

Written by johnleemk on 12:36:33 pm Feb 4, 2007.

Far too often, we humans have a tendency to make decisions on the basis of extreme and unlikely possibilities, rather than considering statistical probabilities. This fundamental failing often has little ill consequence in our personal lives, but can be disastrous if applied as a matter of policy.

Let us take that quintessential example of the man afflicted by that oft-fatal disease known as "love". The odds that the attraction between him and his female (or, in certain rare cases, male) interest will be mutual are exceedingly small. Furthermore, the probability that this interest will not end up in some amount of permanent heartbreak for one or more parties is also rather minuscule. Nevertheless, this does not deter the poor fellow from pursuing the opportunity, because man is not governed by mathematics.

Or, rather, if man is that homo economicus that economists have often proposed as a behavioural model for mankind, his mathematical calculations produce a result rather different from the one a computer would produce. It is difficult to grasp the behaviour of man and present it in logical terms, but I think a number of explanations can be proposed.

One is that man knows that the probabilities are very small, but is prepared to bet on them anyhow, despite all the immense financial and emotional costs involved, because he figures that: first, the reward of finding the right match would be so substantial as to warrant the large costs involved in finding a mate; second, he can afford to bet on the probabilities. Even if the odds that a particular person would be the right one are in the vicinity of 1/100 (a rather generous estimate, I would venture - the real probability is likely much lower, but for the purposes of this example, it does not matter), if the man tries a hundred girls, at least one of them is bound to be the right one. (Man's hopes are also driven by the fact that in reality, most of us don't bother aiming for the perfect girl, but rather settle for some appropriate approximation instead of holding out for perfection, where the odds are clearly too small to warrant such an extensive search.)

Other possible theories I might suggest include an application of the "sunk cost" fallacy. Basically, once a man has had his heart broken, having experienced both the rewards and costs of love, he decides that he has invested too much in the fairer sex to see it all go to waste. As a result, he continues to bear the expenditure associated with soulmate-searching simply to justify the costs he has already sunk into the venture. Or, an alternative hypothesis might bring to bear the idea that the opportunity cost of not entering the market for a mate is simply too high - again, in other words, that the rewards associated with love so far outweigh the costs of being lonely forever that the guy will go through anything to find the right one.

Whatever the case may be, this is really an interesting paradox that has puzzled economists and mathematicians for ages - only it has been in a different form. This paradox is this: the odds that any vote in a particular election will be the one that decides it are very, very small (almost virtually zero). Any vote that isn't the deciding vote - the one that tips the scales - is essentially worthless. Since the odds that your vote will decide the election (and thus be worth something) are practically nil, statistically speaking, it is far wiser to stay home and not bother wasting your petrol to drive to the polling station than to participate in the democratic process. (For more, see Wikipedia's article on public choice theory.)

This is a very striking problem that has bothered economists for ages - it may seem rather odd at first glance, but mathematically, the paradox is real. Why do people vote when mathematically speaking, their vote is worthless? Numerous hypotheses along the lines of those I set out above for our other problem have been proposed. I personally am partial to the idea that the benefits of being the deciding vote are so great that despite the near-zero chance of being the decider, people vote anyway. Nevertheless, this hypothesis has its problems - after all, in many democracies, people complain that they can find little to no difference between two candidates, so why would they care enough to vote?

Another idea along similar lines which I also find favour with is that the opportunity cost of not being the deciding vote is so great that if your vote could have been the decider, but you chose not to vote, you would be kicking yourself to no end - even if you would derive little actual benefit from having cast your vote. Or, you could just do as some people have done and say, "Screw homo economicus - real men obviously bear no resemblance to this caricature created by economists".

Whichever idea you choose to align yourself with, this would be a mere pretty parlour game if not for the unfortunate fact that when it comes to issues of law and policy, people often find themselves thinking about unlikely possibilities instead of real probabilities. As you would probably learn in a simple statistics class, we can never hope to attain perfection. All we can do is set a target standard, and set a maximum tolerable deviation from this standard. Some deviation will always have to be expected.

I would say that a lot of useles bureaucracy and red tape, both in the public and private sector, have resulted simply because people have been thinking too much about fringe possibilities and making the system "foolproof" rather than considering the typical situation one is likely to encounter. And, of course, I don't think any attention was paid to defining acceptable standards for deviation from the ideal result. How often should the system work properly? In 99 out of 100 cases? 999 out of 1000? Such a question is far too often neglected when we give our laws and policies some thought, and the result is that we end up saddled with a system that makes life difficult for those 999 out of 1000 cases that proceed just fine, when in reality an acceptable standard for the deviation might have been one screw-up for every 10,000 cases.

A real example I encountered was when I was debating some policy proposal for the English Wikipedia. I forget what exactly it was about, but I think it had something to do with dispute resolution. At any rate, the proponents of the proposal argued very strenuously for it on the grounds that we had a lot of "rogue admins" whose antics would trouble us to no end unless we implemented the policy they advocated. My response was along these lines: the number of actual "rogue admins" is very small - no more than a handful of such cases have ever come to light, and they have been adequately dealt with by the present system. The threat they pose is exceedingly limited, because the technology Wikipedia runs on allows us to recove almost any data deleted and undo any mishaps that they might have effected. Some small costs might be imposed because one or two offended editors in the Wikipedia community would take umbrage at the rogue's actions and take their contributions elsewhere, but this seems to be an acceptable cost.

On the other hand, if the policy proposal was implemented, the 99% of administrators who were not "rogue" would be forced to jump through procedural hoops and the like to get anything substantial done. Weighing the probabilities, it seemed just silly to implement the idea, when it would provide little benefit while imposing a great cost on the honest members of the community, who far outnumbered the dishonest. Fortunately, the proposal was defeated - but not before I was surprised by how many people can get away with such ignorant thinking.

This may seem of little relevance to you, but something very similar happened when the legal structure of Malaysia was being drafted. The Reid Commission which drafted the Federal Constitution had originally provided for Parliament to impose restrictions on the freedom of speech, as long as it was "reasonable". The question of what constituted a reasonable restriction would of course be left to the courts. This clause was accepted by all members of the Reid Commission, except one - Justice Abdul Hamid of Pakistan. Hamid wrote a scathing dissent to the Commission's proposals, lambasting the suggestion that the question of reasonableness was one that should be settled by the judiciary. He argued that considering the subjective nature of the term "reasonable", it was a real possibility that the interpretation of what was "reasonable" would be carried out incorrectly by the courts. In particular, he feared, it might not conform with what Parliament had intended. As a result, he argued that Parliament be given unlimited power to restrict the freedom of speech, stating that it would be better to allow Parliament to be the judge of what constituted "reasonable".

In law, this actually raises a very interesting and complicated question - just what is the position of judges in the legal system? Are they mere arbiters of the law, giving effect to the intention of Parliament, or should they be allowed to effectively legislate from the bench by deciding on questions such as what constitutes a "reasonable" restriction? This is a question I will seek to answer in a future article, but suffice it to say that for our purposes now, judges can and should have some practical legislative power. The judiciary exists as a check on the powers of the executive and legislative branches of government. If the executive drafts the law, approves it, and arbitrates it, how can there be any justice? That is why we have separation of powers - to prevent the concentration of untrammeled power in the hands of a few.

Hamid's suggestion was clearly ill-thought out, because if he had used his noggin a little, he would have realised that his position betrayed a fundamental mistrust of the judicial system. He simply did not trust the courts to avoid making a mistake in interpreting the law. He did not trust them to refrain from excessive activism and taking a far too extreme and liberal approach to the law. He just did not see how many checks exist within the judiciary itself to prevent such mishaps from occurring. The hierarchy of the court system does not exist for show - it provides clear routes of appeal if either party to a case thinks that a judge has erred in deciding it. This system has worked very well for centuries, and there is no reason that it should continue to do so in the future.

It is true, of course, that insane and unthinkable decisions will emerge from the courts and emerge from the highest court of the land, unscathed. But how can we expect perfection from any mortal system? The existing judicial system we inherited from England has thrived for centuries because it has an accepted standard of deviation from the ideal decision. Cases which deviate from what we consider a just result will always exist, but provided their numbers lie below a certain limit, they are a tolerable annoyance. Furthermore, the ability of the highest court of the land to overrule itself in the future will mean that even these decisions should some day be ironed out, once their negative impact is clear.

This was Hamid's failing. He did not trust the courts to be fair and impartial arbiters of what would be "reasonable" impositions and what would not. His strongly-worded dissent, which contained a number of other pro-executive proposals and a suggestion that Islam be made the official religion of the new country, was taken up by the Alliance government - and the rest is history. The rest of the Reid Commission stood down, and allowed Hamid's dissent to stand. The result has been a Constitution that cannot even protect that basic fundamental freedom of speech, simply because some wise guy thought it would be better to allow one branch of government to decide what is a "reasonable" infringement of that right. This is why our already emasculated courts have always had such trouble dealing with cases on the fundamental freedoms our Constitution theoretically grants us - because thanks to Hamid, they have no real authority to handle the question of their constitutionality. As long as Parliament approved it, even if any sane man can see that the imposition is totally unreasonable, it must stand.

We should never allow theoretical fringe possibilities to dominate our thinking. The actual odds that these possibilities will materialise are small - so infinitesimally small that in most cases, they can be safely written off as acceptable deviations from our ideal standard. While we should always keep an eye out for those possibilities that, should they materialise, will destroy our system, we cannot allow minuscule odds to dominate our thinking in our planning. The typical possibility is almost always far more mundane, and the question of how to handle this typical possibility is what we should spend more time grappling with.

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