Bayesian estimation of severity in police use of force

In research reported in the journal Law and Human Behavior, Brad Celestin and I used Bayesian methods to measure perceived severities of police actions. For each of about two dozen actions, we had lay people rate the action's moral acceptability, appropriateness, punishability, and physical forcefulness. We regressed the ratings on the actions, simultaneously estimating latent scale values of the action severities. 

Below is a stylized graph to show the idea. The vertical axis shows the ratings, and the horizontal axis shows the underlying (latent) severity of the actions. In this graph, six actions are placed at arbitrary positions on the horizontal axis.

Below I've superimposed the regression equation. It's just linear regression, but the values of the predictors are estimated, not given.

Below is a stylized representation of the latent scale values that best fit the ratings:

Bayesian methods were especially useful for this because we obtained a complete posterior distribution on all the scale values. Bayesian methods were also very useful because the ratings were effectively censored by many respondents who pushed the response slider all the way to the top or bottom, so all we could discern from the response was that it was at least that high or low; censored dependent-variable data are handled very nicely in Bayesian analyses.

Here's the abstract from the article:

In modern societies, citizens cede the legitimate use of violence to law enforcement agents who act on their behalf. However, little is known about the extent to which lay evaluations of forceful actions align with or diverge from official use-of-force policies and heuristics that officers use to choose appropriate levels of responsive force. Moreover, it is impossible to accurately compare official policies and lay intuitions without first measuring the perceived severity of a set of representative actions. To map these psychometric scale values precisely, we presented participants with minimal vignettes describing officer and civilian actions that span the entire range of force options (from polite dialogue to lethal force), and asked them to rate physical magnitude and moral appropriateness. We used Bayesian methods to model the ratings as functions of simultaneously estimated scale values of the actions. Results indicated that the perceived severity of actions across all physical but non-lethal categories clustered tightly together, while actions at the extreme levels were relatively spread out. Moreover, less normative officer actions were perceived as especially morally severe. Broadly, our findings reveal divergence between lay perceptions of force severity and official law enforcement policies, and they imply that the groundwork for disagreement about the legitimacy of police and civilian actions may be partially rooted in the differential way that action severity is perceived by law enforcement relative to civilian observers.

A preprint of the article is here, and the published article is here. Full citation:

Celestin, B. D., & Kruschke, J. K. (2019). Lay evaluations of police and civilian use of force: Action severity scales. Law and Human Behavior, 43(3), 290-305.