# The Mathematics and Language of Politics

Mike Rath
21st December 2015 at 15:00

When people suggest that all students should be studying mathematics and English up to the age of 18, I always wonder what sort of maths and English would be most helpful at that age.  In my opinion, there are many areas of modern day politics that are designed to confuse the electorate, so I would advocate a focus on interpreting political speak for 16-18 years olds.  Here are some expressions that I would suggest need redefining for a better understanding for students.

1. Hardworking people, hardworking people, hardworking people, hardworking people

Do you ever wonder why this Government uses the expression “hardworking people” so often?  Strangely enough, it was cleared up for me by a comment made by Nick Clegg when he was Deputy Prime Minister.  He said that only one vote in sixty affects the outcome of an election.  I was intrigued to find out if that really was the case and, if so, why.  I tried a simple bit of mathematics to check it.

What he was talking about was that the voters that matter were the ones who might be persuaded to vote differently from a previous election.  An interesting result of that thought is that the least interesting voters to a party are their own members, since you would assume they would keep voting for their party.

I have assumed that about 100 seats change hands during a typical election.  I think it was actually more in 2015 due to the situation in Scotland, but I will stick to the 100 for now.  Since there are 650 seats in all, then that says that only 1 seat in 6½ changes hands.  Now within those 1 in 6½ seats that change hands, there is still a vast majority of party faithful who will always vote the same way, so I suggest that the fraction of voters who change parties within those seats could be a similar 1 in 6½. So you have 1 in 6½ seats in which 1 in 6½ voters change their votes.  6½ × 6½ is 42¼ (that is, 6×7 + ½×½) so that suggests that 1 in over  40 of voters change.  However, we know that only two-thirds of the electorate vote, so that out of every 60 voters, 20 don’t vote and 1 in 40 of the remaining voters change.  Therefore out of every 60 potential voters, according to my way of looking at it, only 1 voter has a vote that could change a general election.

The next question is about who these 1 in 60 voters are?  If you divide the electorate into three sections – high earners, middle earners, low earners – then it is reasonable to assume that high earners will generally vote Conservative and low earners will generally vote Labour.  This means it is not unreasonable to assume that those likely to change votes are middle earners.  Do you see where this is going?

At this point I would direct you to the Institute for Fiscal Studies Director Paul Johnson and his original analysis of what would have been the result of the tax credit shambles.  He commented that the losers would be the poorest and possibly some of the richest – and the ones to gain would be middle-earners!  Now why would the Government favour only those they call the hardworking people, the hardworking people, the hardworking people ….. ?

2. “Efficiency savings”

Statistics is not my strong point, but I am vaguely aware of the Normal Distribution curve.  One of the key things this curve tells us is that, in a very large population such as the population of the UK, there is no such thing as a perfect system.  Now why is that important?

This means that any system set up in the UK is bound to have faults.  This is what keeps certain newspapers and certain political figures happy, because they can always find examples of individuals – anything from immigrants to “benefit cheats” – who are at one extreme of this normal distribution curve – while the fact that the other 99.9% are behaving reasonably doesn’t count!

When a Government decides to change a system, it also wants a good excuse for doing so.  The normal distribution curve suggests that most new systems will be no more successful than the previous system – in other words, it will once again not be 100% efficient.  They must therefore find some “good” reason for a change.  We now have the use of the term “efficiency savings” to suggest that the new system can offer more for the same – or, in the present day, more for even less!

3. “We want all schools to be outstanding”

Naturally, as a mathematician I have a problem with this desire.  Let me offer a similar idea to explain my concern.

“We want all workers to be paid above average salary”.  Of course, if this happened, then it would no longer be “the average salary”, so the pay would not be “above average”!

The same is true of schools.  The word outstanding means “exceptionally good” which would suggest “way above average” so, if all schools were outstanding, paradoxically individual schools would no longer stand out!!