In such cases, the government’s first step is to send a letter asking for payment within six weeks, after which sterner, more expensive measures are taken. The tax collection authority wondered whether this letter might be improved. Indeed, it could.

The winning recipe comes from Robert B. Cialdini, an emeritus professor of psychology and marketing at Arizona State University, and author of the book “Influence: The Psychology of Persuasion.”

People are more likely to comply with a social norm if they know that most other people comply, Mr. Cialdini has found. (Seeing other dog owners carrying plastic bags encourages others to do so as well.) This insight suggests that adding a statement to the letter that a vast majority of taxpayers pay their taxes on time could encourage others to comply. Studies showed that it would be even better to cite local data, too.

Letters using various messages were sent to 140,000 taxpayers in a randomized trial. As the theory predicted, referring to the social norm of a particular area (perhaps, “9 out of 10 people in Exeter pay their taxes on time”) gave the best results: a 15-percentage-point increase in the number of people who paid before the six-week deadline, compared with results from the old-style letter, which was used as a control condition.

The tax authorities estimate that this initiative, if rolled out across the country, could generate £30 million of extra revenue annually. And note that sending an effective letter doesn’t cost any more than sending a bad one. Did I mention that the entire budget for the team is less than £1 million?

In some domains, team members have different intuitions about what will work best, so randomized trials can be used to determine which interventions are most successful — and also to decide who has to buy the first round of drinks at the pub.

One example was an effort to encourage homeowners to utilize a government program that offers subsidies for installing better insulation in their attics, locally known as lofts. An experiment tested the existing standard offer against either a group discount offer (you get this deal if enough of your neighbors also sign up) and an attic cleanup program provided at the supplier’s cost.