Is the Cabinet Office mathematically illiterate?

Too many civil servants, politicians and celebrities are receiving honours, a report by a group of MPs has said.

I am sure this is true. How many "Sir" Bufton Tuftons are there at the top of the civil service for example? Proportionately many more than in my view deserve it and the MPs agree:

"We believe that no-one should be honoured for simply 'doing the day job', no matter what that job is," the committee said.

But the Cabinet Office has come out to bat defending the current way of doing things:

The Cabinet Office denied honours were dominated by politicians and celebrities, with 72% of the awards in the last honours list going to people who were actively involved in charitable or voluntary work.

Wow! 72%! That's almost three quarters! Fantastic! So I guess we should all just shut up about it.

Oh, but hang on a minute. The Cabinet Office seems to have made a fundamental mistake here.

I don't have the exact figures but I am sure if we were to get together a list of the top civil servants, politicians and celebrities who are the ones in the frame for those 28% of remaining honours each year the total would not come to more than about 20,000. It can't really. There are only 650 MPs and about 800 Lords. Then there are senior members of local government and quangos. On top of that we have senior civil servants, again surely numbering in the hundreds or low thousands at a maximum. The celebrities are also going to be limited to the top or "most famous" in their field. If anything 20,000 is probably being generous as the pool from which those to be honoured in these fields can be plucked.

Now contrast that with the pool of "ordinary" people who do things like volunteering in their local community, who do things for charities and who go the extra mile in their jobs as teachers, nurses and all sorts of other vital services. Again it's hard to come up with an exact figure but it must surely be well over a million. Local communities have lots of people who do all sorts of things that go unrewarded and it's hardly a stretch to say that 1/60 people across the country should be eligible for some sort of recognition like this. So let's say 1,000,000 to be conservative.

Now back to that 72% figure. The most recent honours list awarded them to roughly 800 people in the UK. So roughly 220 went to "The Great and the Good" and about 580 went to everyone else.

Or to put it another way, if you are one of the 20,000 then you had a roughly 1% chance of getting an award. And if you are one of everyone else then you had a roughly 0.05% chance of getting one. So you are around 20 times more likely to get an honour if you are a politician, senior civil servant or celebrity than if you are someone who has devoted lots of time to going the extra mile in your local community.

That the Cabinet Office would even try to make this argument suggests that either they are mathematically illiterate or institutionally incapable of recognising the massive bias in their own systems.