How do people make decisions in situations where the outcome is uncertain? For many years, economists and academics used the idea of expected value – a rational or mathematical calculation of the probability and value of different outcomes. This was later refined into the concept of expected utility, which took more account of the decision-maker’s own circumstances.

In recent decades, decision theory has been advanced still further with concepts such as prospect theory, developed by Daniel Kahneman and Amos Tversky. Prospect theory teaches us that, faced with risky alternatives, rather than consider the final outcome, people make a decision based on the perceived value of potential losses and gains. However, the way they perceive those values is not always rational.

The classic example is the choice between the certainty of receiving $1000 and the chance of winning $2500 on the flip of a coin. Many people will opt for the guaranteed $1000, even though the expected utility of the gamble is higher (2500 x 0.5 probability = 1250).

If we vary the values of the alternatives in this scenario, we can arrive at a point where the two options are regarded as equal, and the decision maker is indifferent – for example, they may feel that a guaranteed $300 is pretty much the same as the chance to win $1000 in a 50-50 lottery. We call this point of balance the ‘certainty equivalent’ of a risk.

So much for decisions taken and resolved in the present. But what if the lottery will not take place, and the prize not be awarded, until a year has passed? Does that affect the way people make their decision? Some researchers have found that more people opt for the gamble when the risky outcome is further away in the future. This has important implications for everyday life. For example, one reason why people are unwilling to reduce their use of fossil fuels may be that they are happy to gamble on the risk of environmental catastrophe happening many years from now.

We wanted to look at this phenomenon in more detail, to discover the impact of different timeframes on people’s choices when faced with risk. To do this, we recruited 52 undergraduate students in economics from Bogazici University in Turkey and asked them to take a computer-based interview.

During the interview, subjects were asked to make choices between the certainty of one amount and the chance of winning another, larger amount. The chances were not always 50/50 – some had odds of 5/1 or 6/1. We represented these ‘lotteries’ as several cheques placed in tombolas (urns) – one made out with the value of the prize, and the others made out with a value of zero. We closed in on each subject’s certainty equivalent by asking them which one of two lotteries they preferred to the guaranteed cash – one with a higher expected utility, and one with a lower. After a while, we arrived at a point where they were indifferent over whether to take the certain cash or play the lottery, which indicated that the certainty equivalent had been reached.

We added the dimension of time by asking our subjects to give their preferences for three different specific times when the lottery would be drawn and the prize awarded: right now, six months in the future and twelve months in the future. We also asked them to respond based on the lottery being resolved at some uncertain time over the next twelve months.

Subjects were told that there were no right or wrong answers – we were just interested in learning their true preferences. This simple approach allowed us to examine people’s attitudes towards risk based on different probabilities and delays.

We also wanted to separate out our subjects’ assessment of probability (for example, the chance of winning a lottery) from utility (the value to them if they won). To do this, we used a two-stage method. First, we asked them to make several choices between certain amounts and lotteries that all offered the same chance of winning. This elicited their views on utility alone, since the probability was always the same. Then, we inferred their views on probability from the certainty equivalent they assigned to a single lottery.

We found that people would tolerate much more risk when the risky payments were to take place in the future. When they did not know the timing of the outcome, they opted for certainty equivalents equal or less than those given for the six-month delay. This implies that they feel ‘ambiguity aversion’ – the well-known phenomenon that people prefer known risks to unknown risks. However, our most interesting finding was that time only affects subjective evaluation of probability, not utility. In other words, while people are more optimistic about risk when the risky events will occur in the future, they still regard the possible outcomes of those events as being pretty much the same.

Why should this be? One possible explanation is ‘affect-based reasoning’, where emotional or sensual factors influence the way people make decisions. When a potential positive outcome could happen soon, people want it more intensely. They feel the potential joy of winning – and the potential disappointment of losing – much more keenly. As a result, they are less inclined to take risks, and more inclined to grab the prize before it gets away.

When the outcome is delayed by six months or a year, people’s emotions are less intense, and they act in a more calculating way. In other words, they are more prepared to accept risks that are ‘worth taking’ from a purely mathematical point of view.

As far as we know, our study is the first one to disentangle the effect of time on the evaluation of probability and outcomes at the level of individual decision-makers.

### Further Reading:

"Risk Preferences at Different Time Periods: An Experimental Investigation", published in Management Science.