Decision makers are frequently called upon to make choices between gains and losses. A lot of research has been devoted to how people choose among risky choices, with a focus on either/or situations: a loss or a gain. But Alex B. Markle of HKUST and George Wu argue this may not be a realistic approach.

"Most important real-world decisions are mixed gambles, involving some possibility of gain and some possibility of loss," they say.

"Previous research has made a fundamental assumption that the valuation of gains and losses is separable. This would imply that a mixed gamble is valued by summing the valuations of the gain and loss portions of that gamble. However, we demonstrate a systematic violation of the double-matching axiom that is necessary for gain-loss separability."

Through several dozen tests involving hundreds of participants, they show that in a mixed-gamble situation, people do not necessarily choose the option with the best probability odds.

In one test, for example, participants were offered a choice between two outcomes, H and L. H had a 0.50 chance of a $4,200 gain and an equal chance of a $3,000 loss. L had a 0.75 chance of a $3,000 gain and a 0.25 chance of a $4,500 loss.

Although L in fact had a much greater probability of a gain and a much smaller probability of a loss, 52 per cent of participants chose H.

When people were presented the gain and loss probabilities separately, though, they chose L over H by a wide margin. This pattern of choosing H in mixed-gamble tests and L in single-option tests was repeated in 28 out of 34 tests. So why would participants not choose L both times?

"When individuals are completely insensitive to probability in facing a problem like this, H will appear to dominate L because the best outcome, a gain of $4,200, is higher than the best outcome in L ($3,000). And the worst outcome in H is $3,000, which is better than the worst outcome in L of $4,500," the authors say.

The authors also conducted more complex tests offering mixed gamble, sure thing gain or loss and gain or loss gamble choices, that further support the idea that individuals are less sensitive to probabilities in mixed gambles.

They suggest two reasons may be underlying the results. One is an "affective", or emotional, explanation. "To the extent that losses are inherently affect-rich, there may be a 'spillover' to gains in which mixed gambles evoke an affective rather than a calculative mindset. Such a mindset would lead to less sensitivity to intermediate probability differences for mixed gambles relative to single-domain gambles," they say.

Another explanation is cognitive. Gains and losses are processed in different parts of the brain. Hence, asking people to choose between the two is cognitively like asking them to compare apples and oranges.

The authors say more research could improve understanding of the forces at work in what they described as the understudied choice domain of mixed gambles.