When the day comes to write the obituary of this curious coalition, a day that many feel can't come too soon, it won't be "the big society" that it is remembered for creating. It seems unlikely to be "fairness" either. There may, however, be a large section on "the nudge unit", otherwise known as the cabinet office's behavioural insights team. Set up in the summer of 2010 shortly after this government came to office, and well known to be a pet project of David Cameron's, it is essentially a little band of academics looking for ways to run the country better. (There used to be nine of them, but there are now 13, mostly economists and psychologists.)

In part, the unit owes its reputation to Cameron, and to its nickname, a reference to the 2008 book Nudge by Richard Thaler and Cass Sunstein, who are not formal members but set out many of its guiding principles. But only in part. Because its work has been quite startling, drawing so much interest from private companies and foreign governments who want to pay for its ideas that it is now going into business by itself. Yesterday, plans were announced to start a joint-venture company, owned in equal thirds by the government, a private investor, and the staff themselves.

The idea behind the unit is simpler than you might believe. People don't always act in their own interests – by filing their taxes late, for instance, overeating, or not paying fines until the bailiffs call. As a result, they don't just harm themselves, they cost the state a lot of money. By looking closely at how they make their choices and then testing small changes in the way the choices are presented, the unit tries to nudge people into leading better lives, and save the rest of us a fortune. It is politics done like science, effectively – with Ben Goldacre's approval – and, in many cases, it appears to work.

Jobcentres

What is it actually like to walk into a jobcentre for the first time, hoping to find work? People who don't know probably hope they won't find out, but by considering the question carefully in a Jobcentre Plus in Loughton, Essex, the nudge unit has been able to make what look like some very valuable adjustments. For one thing, they found that within the first half hour many new jobseekers were being required to complete as many as nine different forms. And, having done so, they did not get to speak to an adviser straight away, but instead had to wait two weeks while their details were processed.

So in a trial, more than 2,000 jobseekers were split into two groups. One continued to be treated in the same way; the other was dealt with under a new system. This new system ensured that each person had a proper conversation during their first visit about getting back to work, that they were encouraged on each subsequent visit to make clear plans for the following two weeks (instead of being asked to account for what they'd done in the preceding two), and if they were still unemployed after eight weeks their "psychological resilience and wellbeing" was enhanced with techniques such as "expressive writing" and "strengths identification".

Thirteen weeks after signing on, the second group were 15-20% less likely to be on benefits compared with the first.

Status: Expanded to larger trials in Essex and the north-east.

Car tax

Not every nudge is friendly. People who don't pay their road tax can be fined up to £1,000 and have the vehicle clamped or towed away – yet many still don't do it, even after their car has been photographed without its tax disc by a DVLA camera. A letter reminding them that the payment is due does help, but even this gets only an 11% response.

The nudge unit suggested some changes, based on a few principles of psychology (and indeed marketing): that people respond better when things are made simple, and that personalised and visual messages make a bigger impression. As a result, in December 2011 the DVLA began testing some new letters on drivers who had been photographed more than once. One batch continued as before, another was simplified and included a big headline saying "Pay your tax or lose your [make of car]", and a third added a photograph of the recipient's untaxed car for good measure. The second group prompted roughly double the number of payments compared with the first. The third group tripled it.

Status: Bigger trials are planned.

Income tax

A subtler approach had equally dramatic effects on income tax. As things stand, people have a relatively long time – around nine months – between the end of the tax year in April and the deadline for payments at the end of the following January. Many of us consider this a dull job, and put it off, but how much procrastination is normal? After what date do we start to become feckless and disorganised in comparison with our peers?

On the advice of the nudge unit, Her Majesty's Revenue and Customs tested some new styles of reminder letter, which included a startling statistic: that most people living in the recipient's town or postcode had already paid. Rates of repayment in the test groups rose by around 15%. According to estimates from the HMRC, if this was repeated on a national scale, it would generate approximately £30m of extra revenue from savings in the cost of tax collection. The same method was also more effective than statements about the cost of non-payment to public services.

Status: Scaled up to almost everybody; the results appear to be repeated.

Court texts

When people have been fined in court, they don't always pay up. As you might imagine, sending a letter doesn't make a lot of difference – only about 5% comply. But if you send them a text message, as the nudge unit found in a trial in the south-east last year, the results are dramatic. If you send them a text message with their name in it, they are spectacular, increasing the response rate to around 33%. Applied nationwide, it would cut bailiff interventions by around 150,000 and save the government about £30m.

Status: National rollout planned.



Loft insulation

For years, by offering financial help to insulate people's lofts, thereby reducing their energy consumption and their bills, successive governments had been trying to give money away – and failing. But in 2011, the nudge unit realised that money wasn't the problem. What held people back was all the clutter that they knew was stored up there.

So in a trial, people were offered not subsidised insulation, but subsidised loft clearance – with unwanted items being taken to local charity shops – on the condition that they got the space insulated afterwards. The scheme cost people more, but they loved it, and uptake rates tripled. If the insulation was subsidised as well, it became a fivefold increase. Another approach was less successful, but equally revealing. When offered a still greater discount for every friend or neighbour they roped in, people took no interest. You cannot put a price, it appears, on being seen to be a loft-botherer.

Status: B&Q (the original partner) expanded the loft clearance scheme.