content_image/326537.jpg
for one’s believed likely winner. Otherwise, this model is the same as the previous Abelson model. We denote the initial subjective probability of a favorite game victory by ρ 0 i ≡ ρ ( w 0 $_{i}$) where ρ ( w ) is given by Equation 6. The susceptibility to influence is then  

<img src='content_image/326537.jpg'>

The top (bottom) equation applies when the underdog (favorite) is thought more likely to win. The minimum susceptibility, η$_{min}$ , is reached when ρ 0 i = 0 , 1 while η$_{max}$ is reached when one believes the game is a tossup, ρ 0 i = 0 . 5. 

We simulate Equation S11 with network weights as given by Equations S13 and S14. We set σ = 12 . 8 in ρ ( w ) as in the main text. The simulation is conducted as for the previous Abelson model but, in addition to η$_{min}$ , p$_{max}$ is also a free parameter. Minimizing the total χ 2 yields values of p$_{max}$ = 0 . 85 and η$_{min}$ = 0. The simulation results are shown in Figure S4. The chain gives a good fit to the data but the complete network fit is poor. The total χ 2 = 16 . 4 which yields Q = 0 . 09 under a two-parameter goodness of fit test. 

