Well, thinking about it, responsibility is Boolean: either you've acted to bring about a certain consequence (consciously or not) or you strictly aren't.

\$\mathrm{Resp}(P,o) = \begin{cases} \texttt{true} & \text{If } P \text{ is a set of people, } o \text{ is a set of outcomes,} \\\\ & \text{and the set of people } P \text{ caused the outcomes } o.\\\\ \texttt{false} & \text{Otherwise.} \end{cases} \$

or diagrammatically,

\$\begin{matrix} \mathrm{People} & \overset{\text{Caused}}\rightarrow & \mathrm{Outcomes}\quad\quad \\\\ !_\mathrm{People}\downarrow & & \downarrow \mathrm{Resp} \\\\ \quad\quad\ \ \mathbf{1} & \underset{\texttt{true}}\rightarrow & \mathbf{Bool}\quad\quad\quad \end{matrix} \$

However, we could speak of various *degrees* of responsibility. For instance, keeping all other things equal, it seems reasonable to say people who aren't aware of what they are doing should have less than or an equal amount of responsibility as a person fully aware of what they are doing, but never strictly more responsible.

I believe that could be modeled using the preorder given by the product of the two preorders.