The Cabinet Office has published its impact assessment of the government bill to ban conversion practices – acts which attempt to change someone’s sexuality or ‘gender identity’.

It projects that introducing a ban on LGBT conversion practices will yield benefits worth an impressive £783 million over the next ten years. The catch is that this estimate is based on a survey that found one in ten LGBTQ+ people have experienced an exorcism.

There is only one possible outcome of a report based on such a cascade of assumptions: nonsense. If the data is so poor that your estimate might be out by a factor of ten or more, you should confess that you haven’t a clue

Using this survey, the Cabinet Office has estimated that 4.7 per cent of LGBTQ+ people experience conversion practices every year. This contrasts rather sharply with the government’s own 2018 National LGBT survey which found that only 2 per cent of LGBT people had undergone conversion therapy over their entire lifetime.

The difference between these figures is dramatic. It’s not straightforward to compare an annual figure with a lifetime figure. If 4.7 per cent of LGBT adults were selected at random each year to receive conversion therapy, you would expect 78 per cent in surveys to have experienced conversion therapy at some point in their life. But let’s be more conservative and guess that conversion therapy lasts five years, which reduces the number of different people who receive the therapy in total. In that case you would expect about 26 per cent to have experienced it by the time of the survey. This gives a factor of 13 difference between the lifetime figure implied by the Stonewall survey and the National LGBT survey. Enough to change a £783 million bonanza to a £60 million damp squib.

To turn their estimate on the frequency of conversion therapy into a financial value, the report does three very reasonable things. First, it gets an estimate for the total number of LGBT people who have experienced conversion therapy, using the above survey figure and the last census.

It then puts a price tag of £10,500 on the cost of one year of depression, using standard government rules to put a financial value on quality of life. There’s no perfect way to do this, but when considering costs and benefits of policies it is helpful to use a consistent benchmark across government departments.

Finally, it divides their initial estimate of the benefit by four to acknowledge optimism bias: this is the tendency to overestimate the benefits of new policies.

The report also does two very unreasonable things.

It assumes that the differences in levels of depression among 21- to 25-year-old LGBT people in San Francisco will be repeated across the population in the UK. In the US, levels of depression are 2.2 times higher among 18- to 25-year-olds compared to the rest of the population, so this introduces an exaggeration factor of about two.

It also assumes that a conversion therapy ban will entirely eliminate the differential in levels of depression experienced by those who have undertaken conversion therapy and those who have not.

Is it really plausible to say that banning conversion therapy alone will transform the lives of LGBT people in unsupportive families in this way? Even if Stonewall’s figures are correct, will the homophobic parents who are currently feeding their children ‘purifying substances’ to cure their gayness now start taking them to Pride? It is impossible to estimate the impact of this error, but it is surely more than the correction for optimism bias.

There is only one possible outcome of a report based on such a cascade of assumptions: nonsense. If the data is so poor that your estimate might be out by a factor of ten or more, you should confess that you haven’t a clue.

This is not the approach taken by the Cabinet Office. Instead, they pluck from the air a guess that they may have wrongly estimated the prevalence of conversion therapy by about 10 per cent in either direction. On this basis, they give a range of plausible estimates of the benefits as £699.9 million to £866.6 million. This is pure pseudo-science. When you are pulling numbers out of your arse, you cannot simply cite the magic incantation ‘plus or minus 10 per cent’ to make your numbers reasonable.

It would be disturbing enough if this was mere innumeracy. However, it is hard not to suspect there may also be some motivated reasoning behind this report.

The most likely source of error is the choice to use a survey by Stonewall. The authors made this choice despite knowing that Stonewall’s data implies that in the UK there is one LGBT exorcism for every two religious wedding ceremonies that takes place here.

I know this because Footnote 49 of the impact assessment mentions the piece I wrote for The Spectator pointing this out. They summarise my argument, rather disingenuously, as follows:

‘the article concluded that Opinium’s sample and weighting was unlikely to be at fault, but that responses about exorcism may be ‘satisficing’ (rushing to complete the survey without paying sufficient attention) or be motivated by wider anti-religious sentiment.’

In fact, I argued that satisficing is an implausible explanation. It wouldn’t explain why trans respondents were four times as likely to say they have been exorcised as other respondents. I said nothing about anti-religious sentiment. What I actually concluded was, ‘the most likely explanation of Stonewall’s findings seems to be that respondents were either fibbing or fantasising.’

Survey respondents are not stupid. They understand the political consequences of their responses. Proposals to ban conversion therapy are a touchstone issue in our culture wars. There is a clear incentive for respondents to give the answer that will produce the policy change they want, even if the answer isn’t, strictly speaking, true. Indeed, the philosophical foundations of trans activism come from postmodern theory which takes issue with the whole concept of truth. A postmodernist would be acting in bad faith if they favoured ‘honesty’ over their commitment to social justice. If a man tells you he is a woman, it is unwise to take everything else he says at face value.

When I wrote my article, my intention was to show the absurdity of attempting to draw any conclusions from Stonewall’s data. I obtained the ludicrous figure of one exorcism for every two religious wedding ceremonies by looking at the five-year data in Stonewall’s report rather than the lifetime figures. Stonewall’s survey finds that 8.2 per cent of LGBTQ+ people experienced exorcism over the last five years compared to 10 per cent over a lifetime (already a ridiculous figure). By playing on this obvious inconsistency, I was able to produce the ridiculous estimate of exorcisms. When I did this, I did it for comic effect. What I did not consider was that I might be giving civil servants ideas.