# Morbid electoral maths

## What’s the distribution of by-elections likely to be?

Stephen Bush answers a very pertinent question: might the government fall before 2022 because of by-election losses? His conclusion is: probably, no. I think, approaching the question from another direction, he is right.

Or, at the least, Tory MPs shuffling off their mortal coils are unlikely to bring down the government.

Using this 2017 parliament list of MPs, we can scrape out ages for 580 of them from Wikipedia. Here’s the distribution of Tory and Labour MPs’ ages — Labour has more slightly older MPs than the Tories.

If you match their ages and genders to the GAD lifetables, you get estimates — from among those 580 — of expected numbers of MPs’ deaths over the next 5 years. These numbers are likely to be too high, because MPs’ life expectancies are surely higher than the national averages.

• From the MPs whose ages we have, the Tories can expect 7 by-elections. But only 1 in a seat with a majority of below 10% and 2 in seats with majorities of below 20%.

We have age coverage of 87% of their MPs — we’re missing 40 of them. But it’s very hard to come up with plausible numbers that lead you to a world where mortality gets you get half-a-dozen Tory by-elections in plausibly winnable seats that you would need to wipe out the government’s majority.

There are 17 seats that they hold with a majority of under 20% where we do not know the ages of the MPs. To get a further 4 by-elections from them, say, these MPs would had the same average life chances as the average British 78-year-old man. The missing entries, however, tend to be for newer MPs who tend to be younger than the rest.

It is possible that Tory MPs might resign for other jobs, but (a) government means ministerial office might remain a temptation; (b) the expected change in PM means those currently out in the cold might not feel dispirited, and (c) the lack of a healthy majority/poll lead makes it less likely that Tory MPs in vulnerable seats will slope off.

For the completionists among you:

• Labour can expect 8 by-elections. But not-quite-1 in a seat with a majority of below 10% and 3 in seats with majorities of below 20%. We have age coverage of 89% of their MPs — we’re missing 31 of them.

One modest curiosity of this: yet another benefit of having more women MPs. Because of their longer life expectancy, the Tories would expect 8 by-elections, not 7, if they were all men. And Labour would expect 10, not 8.