Table 1.
Table of the partial derivatives for different objective functions.
We have used μ to refer to the mean of the opinions.
Fig 1.
Path network with edges untouched by the initial shadow banning policy for different objectives.
The node colors indicate the opinion (lower are blue, higher are red). The direction of the edges indicates the flow of information on the network. The objectives are (top left) no shadow banning, (top right) maximize mean, (bottom left) minimize variance, and (bottom right) maximize variance.
Fig 2.
Opinion distributions and mean shadow ban strength versus time under shadow banning control policies for different objective functions on a path network.
For the opinions, the purple region is the 25th to 75th quantiles, and the pink region is the 5th to 95th quantiles. The objectives are (top left) no shadow banning, (top right) maximize mean, (bottom left) minimize variance, and (bottom right) maximize variance.
Fig 3.
Stochastic block model network with edges untouched by the shadow banning policy for different objectives.
The node colors indicate the opinion (lower are blue, higher are red). The direction of the edges indicates the flow of information on the network. The objectives are (top left) no shadow banning, (top right) maximize mean, (bottom left) minimize variance, and (bottom right) maximize variance. For the no shadow banning policy, the node colors correspond to opinions at time t = 0. For the other objectives, the node colors correspond to opinions at time t = 10.
Fig 4.
Opinion distributions and mean shadow ban strength versus time under shadow banning control policies for different objectives on a stochastic block model network.
For the opinions, the purple region is the 25th to 75th quantiles, and the pink region is the 5th to 95th quantiles. The objectives are (top left) no shadow banning, (top right) maximize mean, (bottom left) minimize variance, and (bottom right) maximize variance.
Table 2.
Basic information about the Twitter datasets.
M is millions and K is thousands.
Fig 5.
Bar plots of terminal objective values with (blue) no shadow banning versus (orange) shadow banning for the U.S. election and Gilets Jaunes datasets, with objectives being (left) maximize mean, (middle) minimize variance, and (right) maximize variance. For the variance objectives, the terminal variances are reported. The objective improvements by shadow banning compared to no shadow banning are (by U.S. election and Gilets Jaunes) 9% and 12% for maximizing mean, 7% and 23% for minimizing variance, and 40% and 60% for maximizing variance.
Fig 6.
Opinion distributions and mean shadow ban strength versus time under shadow banning control policies for different objectives on the 2016 U.S. presidential election Twitter network.
For the opinions, the purple region is the 25th to 75th quantiles, and the pink region is the 5th to 95th quantiles. The objectives are (top left) no shadow banning, (top right) maximize mean, (bottom left) minimize variance, and (bottom right) maximize variance.
Fig 7.
Initial and final opinion densities under shadow banning control policies for different objectives on the 2016 U.S. presidential election Twitter network.
The objectives are (top left) no shadow banning, (top right) maximize mean, (bottom left) minimize variance, and (bottom right) maximize variance.
Fig 8.
Opinion distributions and mean shadow ban strength versus time under shadow banning control policies for different objectives on the Gilets Jaunes Twitter network.
For the opinions, the purple region is the 25th to 75th quantiles, and the pink region is the 5th to 95th quantiles. The objectives are (top left) no shadow banning, (top right) maximize mean, (bottom left) minimize variance, and (bottom right) maximize variance.
Fig 9.
Initial and final opinion densities under shadow banning control policies for different objectives on the Gilets Jaunes Twitter network.
The objectives are (top left) no shadow banning, (top right) maximize mean, (bottom left) minimize variance, and (bottom right) maximize variance.
Fig 10.
Bar plots of shadow ban rates by partisan group at t = 0 for the (left) U.S. election and (right) Gilets Jaunes datasets.
The shadow banning objective is to maximize the opinion mean. For the U.S. election, this means to shift the mean towards Republicans. For Gilets Jaunes this means to shift the opinions towards pro-Gilets Jaunes. Shadow ban rate here is calculated by the fraction of number of accounts, or vertices, that have at least one out-degree edge that is shadow banned. Error bars indicate the 95% confidence interval of the mean estimate.
Fig 11.
The terminal objective values as a function of snetwork for the (left) U.S. election and (right) Gilets Jaunes datasets.
sedge = 1. The y-axis shows the relative magnitude of the objective value compared to that of no shadow banning.
Fig 12.
Terminal objective values for the U.S. election dataset as a function of snetwork and sedge.
The objectives are (top) maximize mean, (middle) minimize variance, and (bottom) maximize variance. Values in the cells are the magnitude relative to no shadow banning in percent.
Fig 13.
Terminal objective values for the Gilets Jaunes dataset as a function of snetwork and sedge.
The objectives are (top) maximize mean, (middle) minimize variance, and (bottom) maximize variance. Values in the cells are the magnitude relative to no shadow banning in percent.
Fig 14.
Terminal objective values for the U.S. election dataset as a function of ϵ and ω.
The objectives are (top) maximize mean, (middle) minimize variance, and (bottom) maximize variance. Values in the cells are the magnitude relative to no shadow banning in percent.
Fig 15.
Terminal objective values for the Gilets Jaunes dataset as a function of ϵ and ω.
The objectives are (top) maximize mean, (middle) minimize variance, and (bottom) maximize variance. Values in the cells are the magnitude relative to no shadow banning in percent.