[T2.4] Statistical reasoning

Examples and fallacies

There are many pitfalls in reasoning about risks. See if you can tell which of the following arguments are correct, and which are fallacies.

The life expectancy in Hong Kong is 77 years for men and 83 years for women. So a man who is forty years old today can expect to live another 37 years, and a woman of the same age can expect to live another 43 years. Correct or fallacy?
The death rate from cancer in Hong Kong has more than doubled from 73 per 100,000 population in 1961 to 160 per 100,000 population in 1999. So living in Hong Kong has become more unhealthy in recent years. Correct or fallacy?
Between May 1995 and October 1996, 14 people in Britain died of CJD (Creutzfeldt-Jakob disease), which may have been caused by eating beef infected with BSE (bovine spongiform encephalitis, or "mad cow disease"). The utility of dying of this disease is very low! The utility of eating beef is at most only very slightly higher than the utility of eating pork or chicken. Hence those British people who continued to eat beef after 1996 were acting irrationally, since they were lowering their expected utility. The British government eventually banned the sale of certain beef products. This ban can be justified in terms of maximizing the overall expected utility of British people. Correct or fallacy?
Insurance companies make a profit on all the kinds of policy they offer, so the expected value of buying a travel insurance policy is negative. For the average traveller, then, if you want to minimize your expected financial losses, you shouldn't buy insurance. Correct or fallacy?
According to Christianity, if you believe in God and live your life as a Christian, you will be rewarded with an eternal life of bliss (heaven). Heaven has an extremely high, perhaps infinite, utility. On the other hand, if there is no afterlife, your utility after death will be zero (since you no longer exist!). Consequently, the expected utility of being a Christian is given by the utility of heaven multiplied by the probability that heaven exists. The expected utility of not being a Christian is at most zero; whether or not heaven exists, you don't go. So however small the probability is that heaven exists, the expected utility of being a Christian is greater (perhaps infinitely greater) than the expected utility of not being a Christian. So if you want to maximize your expected utility, you should be a Christian. Correct or fallacy?