Car insurance? How big are your feet?

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was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

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[Appeared in The Times, 25th February 2011]

If I weren’t such a mean dad, I would pay the £1500 to insure my 20-year old daughter to drive my car. If she magically swopped a chromosome and became a boy, it would cost me £2300. Next Tuesday it is likely that the EU Court of Justice will make it illegal to take gender into account when fixing insurance premiums, which means that my daughter would have to pay even more, and the chances of her ever driving my car will disappear entirely.

The EU Advocate General has stated that current practice appears to break EU discrimination laws. Is this reasonable? I would expect to pay more for my travel insurance if I chose to try and climb Everest rather than lie on the beach, but I don’t choose my gender and so why should it affect my premiums? On the other hand insurance only works by placing people into groups of broadly similar risk, and if low and high-risk groups get put in together, the premiums go up, low-risk people stop buying insurance and the system falls apart.

And there is sound statistical evidence that females and males have very different risk profiles. Boys are more accident–prone from a young age: sadly, around 210 children under 15 are killed in all types of accidents each year in England and Wales but the gender split even at this early age is not 50:50; around 130 are boys and around 80 are girls. These differences don’t stop when they get behind the wheel - males commit 90% of driving offences and insurers know that young males claim twice as much per policy as young females.

Women are also the safer bet at the other end of the age spectrum, with my life expectancy being 3 years less than a woman my age. But this time the male benefits from the difference, since I would pay less for a pension annuity as the insurers do not expect to have to pay me as long. This is likely to be outlawed as well. Of course men could get a discount if they started smoking, but even I am not sufficiently mean to do this.

This is a messy legal and ethical area, in which the insurers’ wish to set premiums on statistical grounds can lead to some odd consequences. Drivers who make no-fault claims, for example if someone runs into their parked car, get fed up when they are charged higher premiums in future. Insurers are not, in general, allowed to ask the results of genetic tests, but can ask for family history of diseases. They can’t ask about ethnicity but can ask postcode, which can mean much the same thing.

Maybe insurers will find a similar way round this problem – all they need to find are proxies that could tell them the gender of the applicant without actually asking. Maybe they could ask about preferences for handbags or hoodies? How many shoes you own? Or your shoe size?

The last measure has been seriously considered in a report commissioned by the Association of British Insurers, but they concluded it would probably be considered indirect discrimination. Unless, I suppose, they could prove that people with big feet are more likely to hit the wrong pedal, but even then there is probably some obscure EU law protecting persecuted large-footed minorities. They may get away with asking for height and weight if they could show that these directly increased risk, perhaps from not being able to see over the dashboard.

Even more efficient would be to ask for testosterone levels, since this might provide an even finer risk stratification than gender. If this is too intrusive then perhaps you might get asked for the lengths of your ring and index fingers, since the ratio of their lengths is associated with testosterone exposure in the womb. Males tend to have longer ring than index fingers, and a bigger difference in their lengths has been related to many classic ‘male’ behaviours, such as aggressive financial trading and increased convictions for traffic offences.

If this bonkers judgement goes through, then what next? Men my age can, rarely, get breast cancer, so am I being discriminated against by not being screened (even though it would be a complete waste of time and money)? Perhaps age-discrimination legislation will mean the EU will ban asking how old you are when setting insurance premiums, and then we might be asked for age-related proxies, such as whether we let out a loud sigh when settling in an armchair, or enjoy watching the Two Ronnies.

So when in future you have a daughter with a long ring finger and big feet, apart from heeding the traditional advice not to put her on the stage, you could also save on driving lessons since you won’t be able to afford the insurance anyway.

Free tags: 


David, I see your point entirely but I think the problem here is that the grouping according to gender (although convenient for insurers) is inapproriate for the problem at hand. Yes a greater proportion of young men make claims, but this is not because they are young men rather than young women. You can think of there being two groups of drivers for each gender: one likely to create claims and another that doesn't. The former group happens to be larger in young men but that is for reasons quite separate from their gender, perhaps their level of education, or maturity. It's these factors that the insurers should be getting a handle on rather than the too broad a surrogate of gender. Yes, I know these questions would be more obtrusive but that's why the insurers have opted to discriminate against young male drivers - it's easier than coming up with a more appropriate model. Gender is the proxy here, not big feet or finger lengths. Similar arguments can, of course, be made about annuities at the opposite end of the age spectrum. Far from being bonkers, the statement made by the Advocate General is a very logical step in starting to address a reticence on the part of insurers to delve more deeply into the problem of accurately assessing risk when setting premiums. As an aside, if you combine low and high-risk groups, premiums don't go up for everyone, they should decrease for those in the higher-risk groups. Assuming a 50/50 split acrioss the sexes you're daughter's premiums should only go up to £1900 and I should make a saving of £400 insuring my perfectly sensible son.

Steve, I get your point, well made on But no background factor causes age and sex, so I don't see how it can be a proxy. OK it is 'upstream' and possibly influences risk through other factors such as reckless behaviour, but no factor can be found that 100% discriminates between those at 'high risk' and those at 'low risk'. So insurance companies are perhaps being a bit lazy in using age and sex, and more refined factors could perhaps be found with some intrusive measurement, although for overall survival gender comes in as a factor whatever adjustment is made for other measurable factors, and so removing this would be mixing groups of demonstrably higher and lower risk, which undermines the principle of insurance. Anthony Edwards has got a nice quote on this: 'Insurance is about the lucky supporting the unlucky, not the low risk subsidising the high risk'

Clearly this gender equality business can be taken too far (e.g. screening for breast cancer), and many in 'the media' are using the car insurance example to hang this argument on. But I am not sure it works. For the simple reason that gender is too crude a tool to use here, (young) men are paying more because prob(claim|young man) > prob(claim|young woman). On the surface this seems reasonable. But both probabilities are quite low (correct me if I'm wrong, please). So prob(no claim|young man) ~ prob(no claim|young woman). Yet the majority of young men - who make no claims - are footing the bill for a small minority who make all the claims. This change in the law is now saying that both men and women share the bill for the small minority make all the claims, irrespective of their gender distribution. Put this way I don't think it is so unfair: why should a safe, young male driver bear a greater part of the cost of the few unsafe drivers, than a young woman driver, simply because that minority of unsafe drivers is more male than female? I think whether it sounds unfair depends on how you tell the story.