On the probabilistic risk attitude

Luo, Xuan (2019) On the probabilistic risk attitude. Doctoral thesis, University of London: London Business School.

Abstract

In this thesis, I theoretically analyze the influence of probabilistic risk attitude, which is the risk attitude caused by the non-linear assessment of probability information. Based on rank- dependent theory, the differences made by probabilistic risk attitude are investigated in three cases: group decision making, the determination of reasonable doubt of a jury, and the introduction of the Random Incentive Lottery mechanism to Multiple Price List experiments. In the case of group decision making, I build a theoretical model based on rankdependent theory to show that a decision maker with non-neutral probabilistic risk attitude may shift her choice in a group's decision. If she is probabilistic risk averse, there will be a consensus shift, i.e., a shift towards what other group members choose; if she is probabilistic risk seeking, there will be a disagreement shift, i.e., a shift away from what other group members choose. I study the conditions for both types of choice shift, and distinguish a strong choice shift (i.e., a shift from one option to another) from a weak choice shift (i.e., a shift from indifference to either option). I show that the risky shift and cautious shift in Eliaz et al. (2006) is a special case of the weak choice shift, and that the strong choice shift is not implied by the weak choice shift. In the case of the determination of the reasonable doubt of a jury, I show how reasonable doubt will be influenced by the agent's preference (i.e., the disutility of convicting an innocent and the disutility of acquitting a guilty), probabilistic risk attitude, the group decision rule and other jurors' choices. The impact of the group decision rule and other jurors' choices indicates that reasonable doubt cannot be assumed to be exogenous, though such an assumption is commonly made in most theoretical studies of jury decision making. Further, by analyzing the Nash Equilibria of a simple jury decision game, I demonstrate that the unanimity rule will lead to group polarization even in the absence of an information cascade, when every juror's information is truthfully revealed.