Optimal social media content moderation and platform immunities

Abstract

This article presents a model of the lawmakers’ choice between implementing a new content moderation regime that provides for platform liability for user-generated content versus continuing platform immunity for the same. The model demonstrates that lawmakers prefer platform immunity, even if incivility is increasing, if the costs of implementing a platform liability regime are greater than the costs of enforcing status quo law. In addition, inasmuch as implementation of a platform liability regime is coupled with new speech restrictions that are unconstitutional or prohibitively costly, lawmakers prefer immunity, but platforms are free to set strong content moderation policies consistent with existing law.

Appendix

Proof of Proposition 1

Lawmakers are faced with $-\psi _{1}\left| y\right| -r_{1}{\bar{h}}-w_{1}{\bar{k}}+\delta V\left( y-{\bar{k}}\right) >-r_{0}{\bar{h}}-w_{0}{\bar{k}}+\delta V\left( y-{\bar{k}}\right)$. Consider platform penalties o. Recall that platforms set optimal non-compliance so that $h_{p}=\frac{y-\alpha _{p}}{o_{\lambda }+d_{\lambda }}+ \frac{d_{\lambda }y}{o_{\lambda }+d_{\lambda }}$. Increases (decreases) in o decrease (increase) $h_{p}$ for $\lambda =0,1$. It follows that ${\bar{h}}$, given by $\int h_{p}f\left( \alpha \right) d\alpha$, decreases (increases) as well, for $\lambda =0,1$. However, $r_{1}>r_{0}$. Thus, for any o, platform enforcement costs under liability are greater than platform enforcement costs under immunity. As a result, lawmakers prefer liability (immunity) when o is increasing (decreasing) holding other factors constant.

Lawmakers are faced with $-\psi _{1}\left| y\right| -r_{1}{\bar{h}}-w_{1}{\bar{k}}+\delta V\left( y-{\bar{k}}\right) >-r_{0}{\bar{h}}-w_{0}{\bar{k}}+\delta V\left( y-{\bar{k}}\right)$. Consider user penalties s. Recall that users set optimal incivility so that $k_{i}=\frac{y-\sigma _{i}}{1+s_{\lambda }+b_{\lambda }}+ \frac{b_{\lambda }y}{1+s_{\lambda }+b_{\lambda }}-\frac{1}{2 \left( 1+s_{\lambda }+b_{\lambda }\right) }\beta W_{\omega }$. Decreases (increases) in s increase (decrease) $k_{i}$ for $\lambda =0,1$. It follows that ${\bar{k}}$, given by ${\bar{k}}=\int k_{i}f\left( \sigma \right) d\sigma$, increases (decreases) as well, for $\lambda =0,1$. However, $w_{1}<w_{0}$. Thus, for any s, user enforcement costs under liability are less than user enforcement costs under immunity. As a result, lawmakers prefer liability (immunity) when s is decreasing (increasing) holding other factors constant. $\square$

Proof of Proposition 2

When moving from immunity to liability, lawmakers incur costs $\psi _{1}\left| y\right| +r_{1}{\bar{h}}+w_{1}{\bar{k}}$. Consider first, the radicalness of the change to the speech screening policy. Enactment costs $\psi$ are directly proportional to the status quo, normalized to be 0. Smaller distances from the status quo $y-0$ result in smaller $\psi$.

Consider second, the distances between the new policy location and the platforms’ and users’ ideal policy locations, $y-\alpha _{p}$ and $y-\sigma _{i}$, respectively. Recall that platforms set optimal non-compliance so that $h_{p}=\frac{y-\alpha _{p}}{o_{\lambda }+d_{\lambda }}+\frac{d_{\lambda }y}{o_{\lambda }+d_{\lambda }}$ and that users set optimal incivility so that $k_{i}=\frac{y-\sigma _{i}}{1+s_{\lambda }+b_{\lambda }}+\frac{b_{\lambda }y}{1+s_{\lambda }+b_{\lambda }}-\frac{1}{2\left( 1+s_{\lambda }+b_{\lambda }\right) }\beta W_{\omega }$. Decreases in $y-\alpha _{p}$ and $y-\sigma _{i}$ reduce $h_{p}$ and $k_{i}$, respectively. It follows that ${\bar{h}}$ and ${\bar{k}}$ decrease, and that lawmakers incur fewer enforcement costs r and w. $\square$

Proof of Proposition 3

Given a constitutionally fixed speech screening policy, lawmakers cannot change y. Enactment costs $\psi _{1}\left| y\right|$, given by $y-0$, equal 0. Lawmakers, therefore, are faced with $r_{1}{\bar{h}}+w_{1}{\bar{k}}>r_{0}{\bar{h}}+w_{0}{\bar{k}}$, where $r_{1}>r_{0}$ and $w_{1}<w_{0}$, and prefer immunity when $\left( r_{0}-r_{1}\right) {\bar{h}}>\left( w_{0}-w_{1}\right) {\bar{k}}$ for any level of aggregate incivility ${\bar{k}}$. $\square$