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\section{Liquid Democracy} 
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Recall the doctrinal paradox, which famously shows that consistent individual judgment sets sometimes leads to an inconsistent collective outcome:  \begin{center}  \begin{table}   \begin{tabular}{ l | c c c c }  & p & q & p \rightarrow q & \\  
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majority & 1 & 0 & 1 &   \end{tabular}   \end{table}  \end{center}  In the more general setting of liquid democracy, inconsistent individual judgment sets may lead to consistent collective outcomes, for instance. This raises new research questions: what are the conditions for a collective outcome to be consistent? What are the criteria for rational delegation?  As an example, consider the following modification of the above case of discursive dilemma: assume that agent $c$ votes himself on $p$ but delegates to agent $b$ his vote on $q$ and on $p\rightarrow q$. We obtain the following situation:   \begin{center}  \begin{table}   \begin{tabular}{ l | c c c c }  & p & q & p \rightarrow q & \\   \hline  a & 1 & 0 & 0 & \\   b & 0 & 0 & 1 & \\   c & 1 & \red{0} & 1 & \\   \hline  majority & 1 & 0 & 1 &   \end{tabular}   \end{table}  \end{center}  \section{Liquid Democracy as a limit case of DeGroot influence matrices}