them outsized influence (Kerr 1992). Extremist-tilting is the prevalent approach to extremism within the opinion network modeling literature (Deffuant et al. 2002; Xie et al. 2011; Waagen et al. 2015). Extremist-tilting has been specifically advanced within social influence network theory (Friedkin 2015; Friedkin and Johnsen 2011). Social influence network theory assumes a linear dynamic process whereby an indi- vidual’s opinion is updated as a weighted average of those of others and their own. It is implemented via the Friedkin-Johnsen model, which contains another prominent model, the DeGroot model (DeGroot 1974), as a special case. 

## Rhetorically-Induced Asymmetry 

We consider deliberations over a quantitative policy such as wagers, investments, interest rates, or military operation sizes. A mathematically idealized caricature of the deliberative process would then have group members stating only their numeri- cal policy values and then updating their own positions in response, perhaps in an iterative fashion. More prosaically, group members exchange persuasive messages in- volving facts and reasoning relevant to the policy question. If discussion is dominated by a single dimension of the policy question, the relative spacing of group member positions along this dimension need not be the same as along the policy itself. Such distortion may reduce the distance within some subgroups relative to others, thereby affecting the composition of the majority that emerges during deliberations. The distinction between policy and the rhetoric (in its general sense encompassing sub- stantive, not merely stylistic, persuasive speech) by which it is discussed can therefore be consequential to the outcome of deliberations. 

Accordingly, a different conceptualization of the deliberative process than the idealized direct exchange of policy positions involves members exchanging messages 

