IT MAY be a coincidence that the stories about the chairman of the Conservative Party and the chairman of the BBC hit the headlines at the same time. But it is far from a coincidence that they have been linked together. When you look for the highest common factor — to borrow a metaphor from maths — something revealing emerges.

But, first, another coincidence. Just before the news broke that the Tory Party chairman, Nadhim Zahawi, had had to pay nearly £5 million after a “careless and not deliberate error” in his tax returns — along with the accusation that the BBC chairman Richard Sharp had helped to facilitate an £800,000 loan guarantee to Boris Johnson just before Mr Sharp was appointed to his BBC post — there was a discussion of John Rawls’s A Theory of Justice on Radio 4’s In Our Time.

Described as perhaps the most influential book in 20th-century political philosophy, it tackles the question how a democracy can reconcile personal liberty, equality of opportunity, and societal fairness. Rawls’s radical idea is that inequalities are acceptable in society — but only when they play to the advantage of the poor, not the rich.

Rawls’s instinct is that the most privileged are the least suitable people to make decisions about society. He offers a thought-experiment, which he calls the “veil of ignorance”. This suggests that we can agree a fair and impartial social contract only if we are not biased by our personal interests. The child who cuts the cake cannot be the one to allocate the portions. “You cut, I’ll choose,” must be the rule.

That is an approach which, to use today’s political jargon, combines transparency and accountability. The common factor with both Mr Zahawi and Mr Sharp is that they both felt that key information could be withheld from their peers and the public.

HM Revenue and Customs clearly determined that Mr Zahawi was deficient in the information that he offered them about the £27 million that he had placed in an off-shore trust fund. They didn’t just demand due tax, with interest; they also fined him. Then it became clear that he hadn’t given the full facts to the Prime Minister, who has ordered an inquiry. Next, it emerged that Mr Zahawi’s expensive lawyers had been sending threatening letters to a tax lawyer who had been raising questions about the affair.

Mr Sharp is now facing an investigation by Whitehall’s appointments commissioner into how he got his job as BBC chairman. Sir Peter Riddell, the commissioner who interviewed Mr Sharp for the job, has said that Mr Sharp should have disclosed the part he played in introducing someone to Mr Johnson who could offer him a loan guarantee. This is especially so since questions had been raised by the Cabinet Secretary, Simon Case, who had told Mr Sharp to end his involvement in brokering the loan — and told Mr Johnson the same thing.

Mr Sharp has insisted that there was no conflict of interest — a claim that Mr Zahawi will find it harder to sustain, since he negotiated with HMRC at a time when he was Chancellor of the Exchequer, and therefore head of the very tax authority investigating him.

What is most worrying is that all this was kept from the voting public. It all gives “veil of ignorance” a rather different meaning.