TRADE unions must meet a 50 per cent turnout threshold in a ballot to be permitted to take strike action. This deliberately restrictive legislation can lead to absurd situations.

Consider a union branch with 100 members. If 48 members vote for strike action, and 1 member votes against, a total of 49 votes have been cast. No strike is possible. Instead, if 26 members vote for strike action, and 24 members vote against, then 50 votes have been cast and there is a majority for strike action. So a strike is legal in this second case, even though the strength of support is far weaker.
 
However, practical issues of striking aside, a more recent strike revolves around statistical arguments. This strike involves scientists and other academics — science doesn’t happen in a vacuum — but it also has wider relevance.

From November 25 until December 4, members of the University and College Union (UCU) have been on strike at universities across Britain. Among other issues such as working conditions and equality, members have been on strike over an ongoing argument about their pensions, most of which are within the Universities Superannuation Scheme (USS). The success or failure of this strike will have huge repercussions for other workers and their pensions.
 
USS is a huge pensions scheme: in total, its value is estimated to be more than £60bn. The dispute centres around planned contribution increases. These depend on how much USS will need to pay out in the future. If this is predicted to be more than the value of the assets, then the scheme is said to be in “deficit.”

An analogy might be made with “balancing the books” for an individual or a household — but this analogy is only superficial and disguises the complexity of valuation. Predicting the value of managed funds decades into the future is difficult, depending on many different assumptions. However, there are good and bad ways of doing it. Academic research into statistical modelling and inference is essential, particularly for a scheme with nearly 200,000 active members paying in.
 
With this in mind, you would have thought that the USS board would be happy to publish full details of the valuation for academics to pore over. One academic who has found the opposite is Professor Jane Hutton, a medical statistics expert at the University of Warwick. In 2015, she became a non-executive member of the board of trustees of USS.

The chair of the board said at the time that he looked forward to working with her over what he predicted would be “an exceptionally busy period.” That prediction did indeed come to pass: UCU is now calling for his resignation.
 
Professor Hutton encountered repeated difficulties in getting hold of documents she requested, despite being a trustee. She also found cases of bad statistical modelling at the heart of the valuation which has been used to justify changes to the scheme. For example, something which needs to be modelled in a valuation is retirement rates. If scheme members retire early, this affects both how much they pay into the scheme and what they take out. Fortunately, USS holds a great deal of data on previous members and their retirement rates.

Any sensible valuation would use as much of this information as possible, eg what percentage of academics retire at the age of 63? Yet a routine practice for actuaries is to round up percentages to the nearest unit of 5 per cent. This might not sound important, but it can be.

Small errors may each seem inconsequential in themselves: if the estimate of this small component could only lead to a total error in the valuation of 0.2 per cent, surely this is nothing to worry about?
 
However, if there are multiple errors in many assumptions, they can combine. In mathematical terms, if each assumption introduces a small error that could change the overall prediction by 0.2 per cent, then for five assumptions the total potential error already hits 1 per cent (often used as an arbitrary threshold for what counts as a “prudent” set of assumptions).

Therefore, even small steps in the process such as rounding retirement rates must be checked to be confident that the total valuation is “prudent.”
 
When Professor Hutton challenged the rounding of the retirement age, she was told that the reason was to avoid spurious accuracy. As she points out, to say that 100/600 is 16.67 per cent is not “spuriously” accurate: it’s just accurate. Reporting it as 20 per cent is wrong.

That’s why in GCSE Maths students are told never to round during calculation, but only when reaching their final answer. It’s worrying that those responsible for valuing a huge pension scheme made such mathematical errors.
 
This October, USS fired Professor Hutton from the board of trustees. They claimed this move was “completely separate” to her role as a whistleblower raising serious concerns with the pensions regulator and others about the valuation process.

Professor Hutton has been admirably unapologetic. She continues to host a page on “actuarial ethics” on her personal website with worked examples showcasing bad practice she has encountered. In recognition of her work, she was recently commended by the judges of the Standing up for Science prize.
 
However, there are many others still trying to get straight answers from USS. Those involved in negotiations have publicly expressed their frustration.

UCU negotiator Sam Marsh has explained how after the pensions regulator recently asked to see particular documents, USS dragged its heels. As he explained on Twitter, despite the request coming close to serious industrial action it took USS nine full days to respond, only doing so last week after two days of strike action.
 
It seems highly likely that there will be more strikes this academic year, demonstrating the real-world impact of bad statistics.

Despite claims about lack of impact, the 2018 UCU strike succeeded in setting up a Joint Expert Panel to assess the situation — its recommendations are what USS is now refusing to implement, necessitating further action.

When those in power try to use statistics to pretend they are “simply stating facts,” it is more important than ever that the mathematically literate scrutinise their claims. Strikes work: in a trade union, the whole is greater than the sum of its parts.