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\begin{document}

\title[Participatory Budgeting]{Participatory Budgeting}
\subtitle{Algorithms and Complexity}
\author{Tobias Eidelpes}

\begin{frame}
	\maketitle
\end{frame}

\begin{frame}
	\frametitle{Table of Contents}
	\tableofcontents
\end{frame}

\section{Introduction}

\begin{frame}
	\frametitle{What is Participatory Budgeting?}
	\begin{quote}
		Participatory Budgeting (PB) is a democratic process in which
		community members decide how to spend part of a public budget.
	\end{quote}
\end{frame}

\begin{frame}
	\frametitle{How does it work?}
	\begin{itemize}
		\item Designing the Process
		\item Collecting Ideas
		\item Developing Proposals
		\item Voting
		\item Funding Winners
	\end{itemize}
\end{frame}

\begin{frame}
	\frametitle{Benefits of Participatory Budgeting}
	\begin{itemize}
		\item More efficient spending
		\item Diverse participants
		\item Higher voter satisfaction
		\item Democratic and citizenship learning
		\item Institutional and political change
	\end{itemize}
\end{frame}

\section{Computational Aspects}

\begin{frame}
	\frametitle{Computational Aspects of PB}
	\begin{itemize}
		\item Discrete or continuous projects?
		\item How do we adequately capture voter's preferences?
		\item How do we model these preferences?
		\item How do we aggregate votes?
	\end{itemize}
\end{frame}

\begin{frame}
	\frametitle{Decision Space}
	\begin{figure}
		\centering
		\includegraphics[width=\textwidth]{taxonomy.png}
	\end{figure}
\end{frame}

\begin{frame}
	\frametitle{Bounded Divisible PB}
	\begin{itemize}
		\item Projects are divisible
		\item A cap for each project is defined
		\item Fractional funding
	\end{itemize}
	\begin{block}{Bounded Divisible PB}
		Each project has a cap $q_p = 1$ and $x_p = [0,1]$ denotes the
		fraction of project $p\in P$ that is completed. The set of
		feasible budget allocations under a budget $B = 1$ is therefore defined as
		\[ \{ \vec{x} : \sum_{p\in P}{x_p}\leq 1 \}. \]
	\end{block}
	\begin{exampleblock}{Example}
		A project that seeks to donate a bounded amount of money to a
		charity.
	\end{exampleblock}
\end{frame}

\begin{frame}
	\frametitle{Unbounded Divisible PB}
	\begin{itemize}
		\item Projects are divisible
		\item No caps for projects
		\item Generalizable to \emph{Portioning}
		\item In practice still bounded by total budget
	\end{itemize}
	\begin{block}{Unbounded Divisible PB}
		
	\end{block}
\end{frame}

\section{Preference Elicitation}

\section{Preference Modeling}

\section{Vote Aggregation}

\begin{frame}
	\frametitle{Algorithm Axioms}
	\begin{itemize}
		\item Pareto Optimality
		\item Monotonicity
		\item Truthfulness
		\item Fairness
	\end{itemize}
\end{frame}

\section{Algorithms}

\section{Comparison}

\section{Practicality}

\end{document}