content_image/304496.jpg content_image/304497.jpg content_image/304498.jpg
the RPM and ASC simulations and, likewise, we supplement Equation S8 with a normative-based rounding scheme. p$_{max}$ is varied to minimize the total χ $^{2}$, which yields p$_{max}$ = 0 . 64. The results are plotted in Figure S3. The one-parameter χ 2 goodness-of-fit test for the intuitive confidence aggregation model yields Q = 0 . 005 for χ 2 = 27 . 0. 

## Abelson Model with Wager-Based Extremist-Tilting 

We first show that the Abelson model is a continuous-time version of the DeGroot model. The DeGroot model evolves the opinion x$_{i}$ over discrete times t$_{k}$ as 

<img src='content_image/304496.jpg'>

where b$_{ij}$ are the row-stochastic network weights, ∑ N j $_{=1}$b$_{ij}$ = 1. Formulated as a difference equation and using the identity x$_{i}$ = ∑ N j $_{=1}$b$_{ij}$ x$_{i}$ , this becomes 

Under continuous time, this yields the Abelson model: 

<img src='content_image/304497.jpg'>

<img src='content_image/304498.jpg'>

The policy is the wager so we let x$_{i}$ ( t ) = w$_{i}$ ( t ). In the wager-based extremist- tilting scheme, confidence increases with the initial wager w 0 i ≡ w$_{i}$ (0) (now denoted explicitly rather than just as w$_{i}$ given the time dependence in the Abelson model). Rather than using a confidence parameter directly, however, we use the susceptibility to influence, η , in accordance with social influence network theory. Each member has 

