@@ -24,10 +24,14 @@ Each experiment is described in terms of
We employed the following decision makers in our experiments:
\begin{itemize}
\item\textbf{Random}: given leniency $r$ they release each subject with probability $r$.
\item\textbf{Batch}: Following Lakkaraju, this decision maker sorts its subjects according to a logistic regression model $y \sim x$ or $y\sim x+z$ and releases $r$ portion of the subjects.
\item\textbf{Independent}: Each subject is released with respect to a cumulative distribution function based on the logistic regression model. \acomment{EXPLAIN BETTER.}
\item\textbf{Probabilistic}: Each subject is released with probability based on the logistic regression model.
\item\textbf{Random}: With observed leniency $r$, a random judge releases portion $r$ randomly.
%they release each subject with probability $r$.
\item\textbf{Batch}: Following Lakkaraju, this decision maker sorts its subjects according to a logistic regression model
$y$ given features
%$y \sim x$ or $y\sim x+z$
and releases $r$ portion of the subjects.
\item\textbf{Independent}: Each subject is released with respect to a cumulative distribution function based on the logistic regression model. \acomment{EXPLAIN BETTER. MAKE DETERMINISTIC?}
\item\textbf{Probabilistic}: Each subject is released with probability based on the logistic regression model, where the leniency is inputted through $\alpha_j$.
\end{itemize}
Decision makers in the data (\human) have access to \unobservable. Evaluated decision makers do not have access to \unobservable. All parameters of the models are for evaluated decision makers are learned from the training data set.
\caption{This is only one judge. Leniency 0.5. What porportion of the subjects do a crime if released? 150 out 300 have $T=1$? What is the proportion of Y? 56 $Y=0, T=1$, 94 have $T=1,Y=1$. How many had $Y=0$ for the subjects (before censoring with decision)? 157.}
