Problem solving is improved by having more engaged minds.

The researchers were able to provide concrete evidence for these ideas by running a series of experiments in which participants were asked to solve what is known as "the knapsack problem." In the knapsack problem, participants are given a large number of items to pack into a knapsack that cannot possibly hold all of the items; their job is to try to figure out how to maximize the number of "valuable" items they can fit into the knapsack.

"These aren't always the most expensive items," says Bossaerts. "For instance, if you're packing the knapsack to go on a trip, one of the items you would consider most valuable would probably be a toothbrush."

Participants in Bossaerts's knapsack experiment had to solve one set of problems under a regime that worked in much the same way as a traditional patent system, with a $66 reward for whoever figured out the solution first.

The second set of problems was to be solved in a kind of free-trading market regime. Each item that could go into the knapsack was given a different price, and each participant was given five securities per item at the beginning of the experiment. They were then encouraged to buy and sell their securities for the various items, stocking up on shares of items they believed were likely to be included in the problem's solution, and getting rid of shares of items they thought would be left out of the knapsack.

Once the solution was revealed, the securities of the left-behind items became worthless, while the participants who had bought up shares of the included items were allowed to keep their earnings of $1 a share. While nobody won the full $66 as in the patent groups, several people in the market groups were able to benefit financially from coming up with a workable solution to the problem.

That solution didn't even have to be the optimal one, Bossaerts notes. "They didn't have to fully solve the problem to benefit financially," he explains. "They could solve only part of the problem--figure out a few items they believed would be in the solution, or those they thought wouldn't be there--and focus buying and selling those."

This resulted in a large number of different people trying different ideas each time the game was played. Allowing people to benefit even if they only tackle a part of a problem might well lead to more collaboration, and to the faster development of a final solution to the whole problem, Bossaerts adds. "This is important, because the nature of knapsack problems is such that one can only be sure that the optimal solution has been found after one has tried everything," he says.

To 'win' in the patent group, on the other hand, required coming up with the right answer first, which seemed to remove the incentive for the large majority of participants to even attempt solving the problem.

This brings to mind the work done on the benefits of heuristic diversity in group problem solving. No team member has to solve the whole problem, or even be able to solve the whole problem, to benefit from discovery. These folks were concerned with patents and markets - a special case of problem solving - and they are still investigating why their system seems to work.

studies have shown that more than 50 percent of people think they're better than the median--a statistical impossibility, but one that can be exploited in the marketplace to generate trade. . .

Bossaerts's next step is to try to collect data to explain why the market system works. "Our conjecture is that it's due to this idea of overconfidence, that most people think they are better than most other people. But this study wasn't able to test that idea specifically, so we're hoping to do that in future studies."

All the children are above average.