Gloomy forecasts for the post-Brexit economy, and a psychological tendency to gamble rather than accept certain losses, may boost public support for a giant leap away from the EU – despite the fact that most experts are advising a cautious small step.

Parliamentary rebels have tempered their demands for a vote on the final Brexit deal and abandoned an earlier House of Lords attempt to keep the UK in the European Economic Area. Attempts to maintain membership of the customs union and single market by Brexit’s opponents have seemingly failed.

But in keeping up pressure to stay as close as possible to the EU, they risk driving Britain further away from it. Anti-Brexiteers now risk colliding with one of the harshest lessons of behavioural economics – once people are determined to leave, any scare about the next step may just prompt them to run further away.

Most independent studies point to bigger economic losses the more the UK distances itself from present EU trade arrangements. So does the Treasury’s own analysis, unless the UK gains a remarkably generous bespoke deal.

But the same studies also suggest there will be losses even from the smallest step away. And the error around these calculations gets bigger as they move further from present arrangements, so that the gloomier forecasts are also hazier. This allows Leave campaigners to agree with “Remoaners” that an ultra-soft Brexit is worse than remaining – and to draw the opposite conclusion: that only the most radical departure will do.

Double or nothing

People are generally risk-averse when it comes to potential gains. They tend to opt for guaranteed receipt of a certain amount (say, £50), rather than the chance to gamble for a larger amount (say, a 50% chance of getting £100) while getting nothing at all if they lose the bet. The expected outcome (to someone who’s risk-neutral) is £50 in both cases. But, as the proverb goes, a bird in the hand is worth two in the bush.

By contrast, most people are risk-preferring when it comes to potential losses. Instead of definitely losing £50 they would prefer to gamble on a 50% chance of losing £100 and a 50% chance of not losing anything. Although the mathematically expected loss is £50 in each case, most of us will run the risk of worsening that loss if that brings a comparable chance of escaping it altogether.

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The evidence that people routinely gamble to avoid guaranteed losses, while playing safe with guaranteed gains, was assembled by cognitive psychologists and turned into an elegant “Prospect Theory” by Amos Tversky and Daniel Kahneman – who won the economics Nobel for it in 2002.

An important consequence of this asymmetry is that people may react differently to a choice that is functionally the same, if it is re-framed in terms of losses rather than gains. You might, for example, prefer the surefire gain of £50 if you perceive the alternative (gaining £100 or £0, with equal probabilities) as a lottery.

But if you are loss-averse, you might also part with £50 – calling it an insurance premium – to avoid risking an equally probable loss of £100 or £0. So, stating post-Brexit outcomes in terms of GDP loss, compared to the status quo, may have worked out to the Brexiteers’ advantage.

The Remainers’ dilemma

Faced with a certain loss from the “soft” option, those (the majority) who voted for Brexit will inevitably be drawn towards the “hard” alternative. It might be a huge gamble, but it seems worth taking if it brings some chance of ultimate gain, against the certain loss from a soft Brexit.

While the hard Brexit risk may be very high – with potentially even bigger economic losses, according to leaked government analysis – a bigger break creates room for radically different and rosier scenarios. It’s always possible that, after a transitory tussles with Brussels, a clean break from EU rules sparks a British social and economic renaissance.

This could come from fully embracing globalisation and free markets (the preference of those on the Right), or from a return to social, industrial and economic policies lost to past liberalisation (preferred by those on the Left). These are opposing and incompatible approaches, but they coalesced to swing the referendum in 2016.

For those with no wish to stay, a giant leap with the distant possibility of landing on higher ground will tend to seem much more appealing than a small step that’s bound to lead downhill. And developments since the referendum may be reinforcing a pattern of preferences by which voters who never wanted to Leave now embrace the “hardest” way of doing so, once they’ve definitely lost the option to Remain.

Behavioural trouble

This isn’t the first time that Prospect Theory has loomed behind Brexit-related decisions. The original Leave vote in 2016 can be explained as a battle of gain/loss framing, which the Brexiteers won by exploiting discontent with people’s present situations.

Remainers unsuccessfully tried in 2016 to persuade voters that EU membership brought a net gain – through trade, unrestricted travel and work opportunities. They wanted the UK to stick with these sure gains, rather than gamble on a step into the unknown outside the EU which might result in great loss.

The Leave campaign successfully re-framed EU membership as a sure loss – of money (since the UK is a net contributor), sovereignty (since the EU sets rules) and external links (since the common external tariff blocks the UK from doing its own trade deals). Convinced that they were losing under the current arrangement, many voters saw leaving as a way to avoid this sure loss, even if not entirely believing Brexiteer predictions of instant gains once outside.

So having persuaded a majority of referendum voters that they could only avoid a certain loss by leaving, hard Brexiteers will now exploit the same behavioural trait to propel the UK as far away from the EU as it can go. The risk for Remainers is that by framing the soft Brexit option as damage limitation, they may simply propel people towards the hard alternative – as the only way their decision to Brexit can possibly do them any good.