The spread betting context points to more general conditions of heuristic issue substitution and reference point shifting. They are expected when two different gam- bles, one complex and the other more intuitive, can be associated with the same scalar random variable but with different thresholds. The subjective probability of the intu- itive gamble is then substituted for that of the complex gamble although the latter is the proper rhetorical issue. In investing, for example, the variable might be the return of a company’s stock over a given time period; the policy gamble being whether the actual return exceeds the fixed return of a zero-risk asset such as a bond. However, group discussion may focus on the simpler, intuitive gamble concerning whether the stock’s price will rise or fall; the thresholds for the policy and intuitive gambles are the fixed and zero returns respectively. 

## Rhetorically-Proximate Majority Formation 

On its own, RIA does not explain group polarization. It must be combined with a mechanism for reaching a consensus position. Simply taking the policy corresponding to the mean rhetorical issue position, x (¯ ρ ), would yield depolarization as shown in Figure 1. The consensus process in our rhetorically-proximate majority model incor- porates majority influence. In Figure 1, the pair that is rhetorically more proximate, ( F$_{2}$, F$_{3}$ ), forms a majority at a policy intermediate between them, a position to which the outlier F$_{1}$ then concurs, leading to a policy more extreme than the mean x$_{2}$ . Assuming that the members of the rhetorically-proximate pair have equal influence in the deliberations, the intermediate policy should be the average of their policy positions, ¯ x$_{23}$ ≡ ( x$_{2}$ + x$_{3}$ ) / 2. Thus, the introduction of the rhetorical issue serves to facilitate, via RIA, agreement between the more extreme members who then average their policies, which are explicitly quantitative unlike the rhetorical issue itself. While 

