deletions | additions       diff --git a/section_An_application_to_liquid__.tex b/section_An_application_to_liquid__.tex  index 8184833..0775d6a 100644  --- a/section_An_application_to_liquid__.tex  +++ b/section_An_application_to_liquid__.tex 
...
\section{An application to liquid democracy}   The natural interpretation of BDPs is in terms of processes of opinion formation (cf. \cite{Grossi_2014}) where agents' opinions are dictated by a personal `guru'.\footnote{Under a convergence assumption, they could be thought of concrete instantiations of profile-transformation functions (from the set of all opinion profiles to the set of all opinion profiles) as studied in \cite{List_2010}.} While this is obviously too constrained a model, it fits well with the sort of opinion formation process underpinning the aggregation method known as liquid democracy. \subsection{Liquid democracy}  Liquid democracy\footnote{Liquid democracy The natural interpretation of BDPs  isbased on the software known as Liquid Feedback (\url{liquidfeedback.org}). Campaigns (e.g., Make Your Laws, \url{www.makeyourlaws.org}, US) and even parties with representatives that sat  in national parliaments (e.g., Piratenpartei, Germany) terms of processes of opinion formation (cf. \cite{Grossi_2014}) where agents' opinions  are using and advocating dictated by a personal `guru'.\footnote{Under a convergence assumption, they could be thought of concrete instantiations of profile-transformation functions (from  the software.} is an aggregation method consider set of all opinion profiles  tostand between direct and representative democracy. At its heart is  the so-called method set  of ``proxy voting" \cite{Miller_1969,Tullock_1992}.   For each issue submitted to vote all opinion profiles) as studied  in \cite{List_2010}.} While this is obviously too constrained  a multiple referendum, each agent can either cast his own vote, or he can delegate model,  it to another agent---a ``proxy"---and that agent can delegate in turn to yet another agent and so far.\footnote{The on. In fits well with  the end only exception is possibly \cite{Boldi_2011}} sort of opinion formation process underpinning  the agents that decided not to delegate their votes cast their ballots, for instance under majority rule. aggregation method known as liquid democracy.  \subsection{Liquid Some analyses of liquid Liquid democracy\footnote{Liquid  democracy is based on the software known  as from a BDP} Liquid Feedback (\url{liquidfeedback.org}). Campaigns (e.g., Make Your Laws, \url{www.makeyourlaws.org}, US) and even parties with representatives that sat in national parliaments (e.g., Piratenpartei, Germany) are using and advocating the software.} is an aggregation method consider to stand between direct and representative democracy. At its heart is the best so-called method of our knowledge, no model has been proposed ``proxy voting" \cite{Miller_1969,Tullock_1992}. For each issue submitted to vote, each agent can either cast his own vote, or he can delegate it to another agent---a ``proxy"---and that agent can delegate in turn to yet another agent and so far.\footnote{The on. In the end only exception is possibly \cite{Boldi_2011}} the agents that decided not to delegate their votes cast their ballots, for instance under majority rule.  Analyses of liquid democracy from a social choice-theoretic perspective have been put forth in \cite{Alger_2006} and \cite{Green_Armytage_2014}, and from an algorithmic perspective in \cite{Boldi_2011}. However, the system remains rather underinvestigated.   \subsection{Cycles} \subsection{BDPs and proxy voting cycles}  Massive information loss (all votes in the cycles, and those upstream are lost) --> but not all cycles are necessarily disrupting the aggregation.