@@ -63,7 +63,7 @@ Furthermore, since $\unobservable$ is unobserved we can assume its variance to b
% (Any deviation from this can be achieved by adjusting intercepts and coefficients in the following).
In the setting we consider (Section~\ref{sec:}), a negative decision $T=0$ leads to successful outcome $Y=1$.
In the setting we consider (Section~\ref{sec:setting}), a negative decision $T=0$ leads to successful outcome $Y=1$.
%
When $T=1$, the probability of success is given by a logistic regression model over the features $\obsFeatures$ and $\unobservable$:
\begin{eqnarray}
...
...
@@ -82,7 +82,8 @@ We model the decisions in the data similarly according to a logistic regression
) \label{eq:judgemodel}
\end{equation}%
%
Note that we are making the simplifying assumption that coefficients $\gamma_\obsFeatures,\gamma_\unobservable$ are the same for all $\human_\judgeValue$, but decision makers are allowed to differ in intercept $\alpha_\judgeValue$.
Although we model the decision makers here probabilistically, we do not imply that their decision are necessarily probabilistic (or include a random component). The probabilistic model arises from the unknown specific details of reasoning employed by each decision maker $\human_\judgeValue$.
Note also that we are making the simplifying assumption that coefficients $\gamma_\obsFeatures,\gamma_\unobservable$ are the same for all $\human_\judgeValue$, but decision makers are allowed to differ in intercept $\alpha_\judgeValue$.
%
Parameter $\alpha_{\judgeValue}$ controls the leniency of a decision maker $\human_\judgeValue\in\humanset$.
@@ -22,7 +22,7 @@ Mc-Candless et al. perform Bayesian sensitivity analysis while taking into accou
The importance in-detail causal modeling and evaluating counterfactual outcomes, as observed also here, is particularly prominent in recent work on fairness of automatic decision making~\cite{DBLP:conf/icml/NabiMS19,DBLP:conf/icml/Kusner0LS19,coston2020counterfactual,madras2019fairness,corbett2017algorithmic,DBLP:journals/jmlr/BottouPCCCPRSS13,DBLP:conf/icml/NabiMS19,DBLP:conf/icml/JohanssonSS16}.
%To properly assess decision procedures for their performance and fairness we need to understand the causal relations
Finally, more applied work can be found for example in~\cite{murder,tolan2019why,kleinberg2018human,chouldechova2017fair,rennan2009evaluating}.
Finally, more applied work can be found for example in~\cite{murder,tolan2019why,kleinberg2018human,chouldechova2017fair,brennan2009evaluating}.
