@@ -14,7 +14,7 @@ We consider data recorded from a decision making process with the following char
%
Each case is decided by one decision maker and we use $\judge$ as an index to the decision maker the case is assigned.
%
For each such assignment, a decision maker $\human_\judgeValue$ considers a case described by a set of features \allFeatures and makes a binary decision $\decision\in\{0, 1\}$, nominally referred to as {\it positive} ($\decision=1$) or {\it negative} ($\decision=0$).
For each such assignment, a decision maker $\human_\judgeValue$(where $\judgeValue$ is a particular value for $\judge$) considers a case described by a set of features \allFeatures and makes a binary decision $\decision\in\{0, 1\}$, nominally referred to as {\it positive} ($\decision=1$) or {\it negative} ($\decision=0$).
%
Intuitively, in our bail-or-jail example of Section~\ref{sec:introduction}, $\human_\judgeValue$ corresponds to the human judge deciding whether to grant bail ($\decision=1$) or not ($\decision=0$).
%
...
...
@@ -41,7 +41,7 @@ Otherwise, if the decision of the judge was to keep the defendant in jail ($\dec
For each case a record $(\judgeValue, \obsFeaturesValue, \decisionValue, \outcomeValue)$ is produced that contains only observations on a subset $\obsFeatures\subseteq\allFeatures$ of the features of the case, the decision $\decision$ of the judge and the outcome $\outcome$ -- but leaves no trace for a subset $\unobservable=\allFeatures\setminus\obsFeatures$ of the features.
%
Intuitively, in our example, $\obsFeatures$ corresponds to publicly recorded information about the bail-or-jail case decided by the judge (e.g., the gender and age of the defendant) and $\unobservable$ corresponds to features that are observed by the judge but do not appear on record (e.g., whether the defendant appeared anxious in court).
Intuitively, in our example, $\obsFeatures$ corresponds to publicly recorded information about the bail-or-jail case decided by the judge (e.g., the harshness of the possible crime) and $\unobservable$ corresponds to features that are observed by the judge but do not appear on record (e.g., exact verbal response of the defendant in court).
%
The set of records $\dataset=\{(\judgeValue, \obsFeaturesValue, \decisionValue, \outcomeValue)\}$%produced by decision maker \human
