In the modern world, a huge amount of important information is summarised as numbers, percentages, charts and tables. And, as an ex maths teacher in high schools, I can assure you a good portion of our population struggle to digest information in this form. And that makes them ripe for manipulation by the unscrupulous.

A nice political example of this came about last year when the minister of finance gave a response in parliament purporting to show that the top 10% of our households (by income) pay 70% of our tax. Were that true, it would be a startling figure. And, given that tables were produced that apparently backed up the claim, those of a certain political persuasion were falling over themselves to pass on the news. The figure appeared in newspaper columns, blogs, letters to the editor and the newsletters of financial sector firms. Doubtless it also made its way into the conversations at the sorts of dinner parties I don’t get invited to. You can see the appeal. One of the most significant political acts of our current government came in their first term, when they dropped the top tax rate back form 38% to 33%, so providing a nice little bonus payment to that sector of society that, you might imagine, least needed it. Meanwhile, its budget balancing austerity kick meant those more likely to be struggling were bearing more of the burden via, an increase in sales tax. That’s a fairly outrageous move, and you can imagine that even some of the primary beneficiaries might be feeling a bit embarrassed about it. How heartening then to discover that they are already paying the lion’s share. No need to feel awkward then, back to the holiday home for a well earned rest.

Trouble is, predictably enough, the figure isn’t close to true. A dirty mathematical trick was pulled, relying upon the assumption that the majority of those checking the tables wouldn’t much understand percentages. So let me explain. The easy way of calculating tax burden would be to rank households by earnings, look at the contribution made by each decile and divide that by the total to get the percentage contribution. Do this and it shows the top 10% pay about 37% of the income tax take, a touch over half of the claimed amount. So, how to transform this more accurate figure to fit the myth?

Well, it was noted that the bottom earning households, while they pay some tax, in total receive more back in terms of income support. Maybe they’re retired and drawing national superannuation, for example, or a solo parent at home looking after their children and receiving assistance, or in some cases on such a low wage that working for families payments for their children balance out the tax contribution. If you take sales tax payments into account, then about a third of households are in this category, and for all our system’s flaws, we are at least still civilised enough to provide some support to those who need it most.

That means the other two thirds of households do in effect pay all of the available tax. We might attempt to increase this figure by providing more jobs, higher wages or perhaps a more stable social environment, but the elderly, the students, the sick are always going to be with us, so there’ll never be 100% household contribution, and nor should there be.

Now for the sleight of hand. Look at the net tax contribution of the top 10%, and compare this to total net taxation, that is all the tax that is taken in, after transfers to superannuitants and the like are deducted. Do this, and you see the figure is equivalent to seventy percent of the tax available after transfers have been made. If you gave up on math early on in your high school years, that might seem the same as saying the top income bracket pay seventy percent of all tax, but it isn’t. Here’s why not.

The top ten percent of households earn $150 000 a year or more. If we look at households between $80 000 and $150 000, which is just over a quarter of households, then we see they pay about the same amount as the top ten percent. So by this measure, the top ten percent pay 71% of our tax, the next 25% pay 69%? Hang on, can’t be right. Aren’t percentages meant to add up to 100? Yes they are, if we are talking about percentages of something. And here we’re not. We’re taking money paid in tax, and comparing it to the amount of tax left over after some of that tax has been distributed to beneficiaries. Essentially we’re calculating a percentage contribution to a list that includes negative numbers, and that’s a cheat. And at this point we’re not entitled to say 70% of anything. People know that by using the figure, they are implying that they’re paying most of the tax, and they’re not. Nothing like.

An analogy might help. Imagine every household in your street has its net wealth assessed. Half the houses are in debt, they have negative wealth, and the other half have positive wealth. In total, the amounts almost cancel out, so that the net worth of the street is a paltry $10. Now imagine a child in one of the houses does indeed have $10. Can that child reasonably claim to having 100% of the wealth in the street, even though her neighbours are bona fide millionaires? No, that’s more than stretching the truth. It’s misleading.

So what are the actual figures? In terms of gross tax, it’s 37%. If we look only at those households that pay tax, then the top ten percent of them pay about 30% of true tax take(counting beneficiaries as zero, rather than negative, tax payers). Or, the top ten percent of all households by this measure pay maybe 40% of it.

Trouble is, if the true tax burden for the figure is in the ball park of only one third, they don’t sound quite like a put upon group in desperate need of a tax break anymore, do they? So, if you’re the ones giving that tax break, your best hope might just be to tell a little untruth and figure most people will get tangled up in the numbers. And even though the cheat is easily exposed, the trouble is that the lie is out there, circulating about through the minds and mouths of those too self-interested to challenge it. Next time you hear it, I do hope you speak up.