To dissociate different components of risk, in terms of dispersion (variance) and asymmetry of outcomes (skewness), we designed a novel decision-making task that controlled the distribution of outcomes, and ensured that variance and skewness of a set of lotteries were manipulated independently by design. Hence, as variance and skewness of gambles were orthogonal factors, we could test whether neural activity evoked by variance could be distinguished from that evoked by skewness. Participants were required to choose between taking a ‘sure’ (fixed) amount of money or electing to ‘gamble’ (choosing to play a lottery with a number of potential outcomes). Gambles were represented as pie-charts, where variance and skewness of outcomes varied over a range, with expected value kept constant. We predicted distinct preferences for both variance and skewness (possibly with different preferences for positive versus negative skewness).

We represented gambles on-screen as pie-charts. The pie chart was divided into different segments showing possible outcomes from the lottery. The numbers written in each segment showed the monetary value of each outcome in pence (sterling) and the angle subtended by each segment indicated the probability of each outcome occurring. A positively skewed gamble (left) has a small chance of a better than average outcome (the tail of the distribution is to the right). Conversely, a negatively skewed gamble (right) has a small chance of a worse than average outcome (the tail is to the left). Both example gambles have identical variance and expected value. B. The task consisted of trials, grouped into experimental blocks of ten. For each trial, a pie chart was shown and after 5.5 s, a cue to respond appeared on screen (for 2 s). Subjects indicated by a button press while the cue was on-screen if they wanted to gamble on the lottery, or alternatively select a fixed, sure amount of money. To commence a block, the sure amount was written on the screen (3 levels—90p, 120p, 150p). At the end of each block, one trial from the block was randomly selected and played out for real. If subjects had elected to gamble, we resolved the lottery by an on-screen graphic of a red ball spinning around the outside of the pie which stopped at a randomly selected position. 180 trials were presented in total (60 stimuli at each of 3 sure levels).

For further information, please see the linked article:: Deconstructing risk: Separable encoding of variance and skewness in the brain