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What are the odds?

My associates on the Fink Tank (my column providing a statistical take on football) have introduced me to a riveting new website.

Called Politimetrics, it seeks to provide the probability that, for instance Hillary Clinton would reduce unemployment if elected.

Here's a short introduction to their method:

Who is the party candidate who would stand the most chances to win the presidency if designated as a candidate during the primaries?

Who is the candidate to the presidency who would be most likely to conduct a successful economic policy if elected to the White House? 

To compute this information, Politimetrics.com uses prices from two prediction markets from our partner Intrade. For instance we compute the probability that Clinton will decrease the unemployment rate, by (roughly) dividing the price of the event "Clinton will be elected and she will decrease the unemployment rate" by the price of the event "Clinton will be elected".

Technically, this gives us the conditional probability that "Clinton will decrease the unemployment rate IF she is elected". Comparing this to the same probability for other candidates allows voters to make more informed choices.

Naturally your faith in these probabilities depends upon your faith in the accuracy of prediction markets.

But I think their approach is fascinating.

How seriously should we take the terrorist threat?

Econlog repeats the claims of John Mueller that the threat from terrorism is being taken too seriously. Bryan Caplan, the brilliant analyst who is one of the two men behind Econlog, argues that we have enough data now to be clear that the risk posed by terrorists is small in the scheme of things.

Mueller's arguments deserve to be taken seriously, but I am not convinced:

First, the probability of an event is not really the thing you should be worrying about. In his excellent book Fooled by Randomness, the mathematician and Wall Street trader Nassim Nicholas Taleb discusses what he calls the issue of asymmetry. He explains (rather impatiently since he regards the issue as obvious) that you may believe, say, that financial markets will probably go up, while you behave, sensibly, as if they will go down. The reason? Because you think it very likely that they will go up a little, but, in the unlikely event that they go down, you think they will go down a great deal.

“How could people miss such a point?” he complains. “Why do they confuse probability and expectation, that is probability and probability times the payoff?” The probability of, say, a nuclear terrorist attack might be tiny but the consequences, the “payoff” as it were, would be huge. It is expectation, not probability, that should determine policy towards terrorism.

The second problem with Mueller’s paper is simple: the low incidence of terrorist outrages occurred when there was already a firm policy in place to prevent it. His argument, the “bloody nuisance” argument, depends on the idea that, without additional measures domestically and internationally, the number of terrorist incidents is unlikely to rise greatly.

There is, however, lots of evidence that crime doesn’t work like that. Instead of falling gently or rising gently in response to policy measures, crime behaves like a contagious disease. Potential offenders catch the idea of offending from each other. And just like a disease that starts with only a few people and becomes an epidemic, once it reaches a tipping point the amount of criminal behaviour explodes.

Bad statistics are a crime

The BBC news website this morning says:

Crime in England and Wales has remained stable during the past year, according to Home Office figures.

We're going to have to put up with this sort of stuff all day I suspect. But, really, what does it mean? Overall crime figures are meaningless because they assume all crimes are equal. In fact, within a stable number of overall crimes crime may be improving or getting worse.

Let me give you an example.

Say that one year your car was broken into three times, the next year you were mugged twice at knifepoint, and then, in year three you were murdered.

The BBC (and the rest of the media) would record this as a fall in crime. Indeed it is. In the fourth year the crime rate would be zero.

The statistics and strategy behind suicide bombings

I first came across M.Daniele Paserman on a football website. He'd done some interesting work on valuing goal scorers.

Now Chris Dillow draws attention to a rather different Paserman paper - the mathematical relationship between suicide bombing and Israeli targeted killings. Here's the paper's conclusion:

In this paper we assess the effectiveness of suicide attacks and targeted killings in the Second Intifada.

We find evidence that the targeted killings of Palestinian leaders by Israel
reduce realized Palestinian violence. We find, however, that intended Palestinian violence is increasing at low levels of targeted killings, but decreasing at higher levels.

There is little evidence to suggest that suicide bombings against Israelis reduce the number of subsequent Palestinian fatalities. Rather, we find that suicide attacks that kill at least one Israeli lead to subsequent increased incidence and levels of Palestinian fatalities.

Our results do not support the notion that suicide attacks and targeted killings follow the “tit-for-tat” pattern that is commonly postulated in the literature.

Chris draws the conclusion from this that suicide bombing is a bad military strategy. But this is only true if the Palestinian leadership minds how many people die. The deaths may help put pressure on the Israeli government. Increasing the reprisal attacks may, perversely be part of the plan.

Anchoring and the Iraq War

Anjana Ahuja has done a terrific job unpicking the row over the Lancet's claim that there have been 650,000 civilian deaths in Iraq, a shocking number.

The Lancet research has taken quite a battering. But this doesn't mean that it isn't important work.

Why? Anchoring.

Once a figure is established in the public mind, there is room for some adjustment. But not all that much. Gordon Brown relies on anchoring to make Tory criticisms of his budget seem risky and inappropriate.

If the Lancet's critics are right and part of the motivation for publication was political, then the job has been well done.

Lone parents and gun crime

The mighty Chris Dillow is worried.

He thinks that Ross Clark's piece on gun crime this morning might be misinterpreted. He fears that people will read Ross and think that single parenthood causes gun crime. He then takes readers through a series of calculations that, he says, strongly suggests that single parenthood is not a cause of gun crime.

Here are the steps:

Assume that every one of the 11,084 gun crimes in 2005-6 was committed by a different 16-24 year old.

Assume that each of these gunmen was one of the 560,000 16-24 year olds brought up in a single parent household.

Even with these ridiculously heroic assumptions it means that only 2 per cent of 16-24 year olds from a lone parent household commits a gun crime [11,084 is 2 per cent of 560,000]. 98 per cent don't.

Hey presto! Lone parenthood does not cause gun crime.

Erm, wait a second.

First of all, I am not sure about Chris's figures. What he shows is not that only 2 per cent of 16-24 year olds from lone parent households commits a gun crime, it is that only 2 per cent commit a gun crime in any given year.

Using his heroic assumptions, you could argue that the number should be multiplied by eight. During the years the young people are between 16 and 24, there are 11, 084 gun crimes committed in each of the eight years.

This would mean that 16 per cent of 16-24 year olds from a lone parent household commits a gun crime at some point in their youth. That seems quite a large proportion to me!

Of course, it's all nonsense. And not just because of the heroic assumptions.

No one suggests that being the child of a single parent makes you certain to commit a crime. Or that all single parent households turn out children more likely to be criminals than if the parents of those children were still together.

The only questions are whether, on average, being in a single parent household makes you more likely to commit a crime. And whether reducing single parenthood would reduce gun crime. An affirmative answer to these two questions is completely consistent with every figure Chris cites.

What Ross Clark said was:

Those involved with gun crime tend to have grown up fatherless and in the absence of good male role models have gravitated towards gangs.

This can be true even if only a tiny proportion of those who grow up fatherless join gangs or are involved in gun crime.

Ringo and power law

Today is the last day to sign the Ringo petition. It has done respectably well in terms of signatures. The theory underpinning it has, I would say, performed spectacularly.

I offered (still offer) Ringo's knighthood as a rare example of something on the Downing Street site that could actually be acted upon.

My argument was that the site would soon fill up with petitions the Government could do nothing about since they opposed existing policy, cost too much money or were simply mad. Even if a petition garnered a million signatures, it might be advancing a proposition that the rest of the population did not agree with, or, if they did, was in direct conflict with the programme of the elected government.

And lo, so it came to pass.

I'd love someone with a spare hour or four to do some work on the petition site. Am I wrong, or do the signatures to petitions distribute themselves exactly according to a power law? It seems to the naked eye that 80 per cent of the signatures are on 20 per cent of the petitions and that there is a very long tail of petitions with hardly any supporters.

If this is right, it would suggest that there is nothing particularly remarkable about the road pricing petition, merely that it is the first of a series of such petitions that will lead the site.

Why we lost the Ashes

I don't do cricket statistics but I'd like to make an observation about the Ashes. Not about losing them again, but about winning them last time.

You can win the Ashes once in 18 years without being the better side when you win it. The higher scoring a sport is and the more games that are played the more likely it is that the best side will win.

Cricket is a high scoring game and a five game series is very likely to be won by the best side. But not certain.

Our victory last time, instead of being a great national revival was simply a feature of randomness. Even when we won the Ashes, Australia were the better team. This time that fact simply reasserted itself.

The mathematics of the Saudi decision

The Attorney General, Lord Goldsmith, says that in the Saudi case we needed to balance the rule of law and the public interest. This is a very dangerous statement, for the rule of law and the public interest are not different things. They are two parts of the same thing.

This is all about maths.

The purpose of the rule of law is to ensure that, in a vast range of different circumstances and over a long period of time, the interest of the public is served on average.

The result of following the rule of law may be that in an individual incident some harm may be done to some people (those hoping for aerospace jobs might be an example) and may, just possibly, not be balanced with the good that results to others (those wishing to rid the world of bribery for instance). But over time, on the whole, this does not happen.

The result of the Government balancing the rule of law and public interest in each individual case may be better in an individual case but is, without question, worse in the end.

The rule of law may not be superior in each individual case, but it is better for all cases when they are considered together. And it only works that way because it is applied to all cases considered together. The only way the rule of law can succeed is if it is applied blindly.

It is not therefore necessary to consider the rights and wrongs of the particular Saudi case in order to judge whether the decision was the correct one. The rule of law must prevail if we are not to live with the consequences of arbitrary justice.