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\section{Conclusions and Future work}

In this paper we considered the task of evaluating (automated) decision makers, which is vitally needed in replacing human decisions with automated ones.
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The challenge is that the evaluation often needs to be based on data where present decisions imply selective labeling and missing data, biasing any standard statistical data analysis results.  
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We showed that with proper causal modeling, automated decision makers can be evaluated even based on such selectively labeled data.
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Contrary to previous work, our proposed approach allows for more accurate evaluations, with less variation, also in settings that evaluation was not possible before.
In future work, we will examine further generalizing our setting and modeling assumption: more intricate differences in decision maker's behaviour could be modeled, e.g., via hierarchical Bayesian modeling. 
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Since our approach predicts outcomes based on decisions made by educated decision makers, it is still unclear how much this benefits the estimation the statistical models the automatic decision makers are ultimately based on~\cite{dearteaga2018learning}.
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We believe such approaches will allow for better evaluations in new application fields, ensuring the accuracy and fairness of automatic decision making procedures that can be then adopted in the society.



%\begin{itemize}
%\item Conclusions 
%\item Future work / Impact
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