## Occasional reflections on Life, the World, and Mathematics

### Parliamentary mortality

An article in the New Statesman raised the question of whether the Conservatives could lose their hold on power via by-elections over the next few years only to dismiss the possibility because by-elections simply don’t happen frequently enough. The reason? Reduced mortality rates. Quite sensible, but then this strange claim was made:

In 1992-7, the last time that the Conservatives had seven by-elections in a parliament, life expectancy was 15 years lower than it is today.

Ummm… If life expectancy had increased by 15 years over the last 20 years, we’d be getting close to achieving mortality escape velocity. In fact, the increase has been about 5 years for men and 4 years for women.

But that raised for me the somewhat morbid question: How many MPs would be expected to die in the next 5 years? Approximate age distribution of MPs is available here. It’s for the last parliament, but I’ll assume it remains pretty similar. It’s interesting that Labour had twice as large a proportion (25% vs 12%) in the over-60 category. In addition, I’ll make the following assumptions:

1. Within coarse age categories the distribution is the same between parties. (This is required to deal with the fact that the numbers by party are only divided into three age categories.)
2. Since I don’t have detailed mortality data by class or occupation, I’ll simply treat them as being 5 years younger than their calendar age, since that’s the difference in median age at death between men in managerial occupations and average occupations.
3. I assume women to have the same age distribution as men.
4. I’m using 2013 mortality rates from the Human Mortality Database.

My calculations say that the expected number of deaths over the next 5 years is about 6.4 Conservatives and 6.5 Labour. So we can estimate that the probability of at least 7 by-elections due to deceased Tory MPs is just a shade under 50%.