Add outline and taxonomy of PB

talk/talk.tex

@@ -1,11 +1,20 @@
 \documentclass{beamer}
 
+\usetheme{Boadilla}
+\usecolortheme{dolphin}
+
+\usepackage{graphicx}
+
 \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
@@ -15,31 +24,98 @@
 
 \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 \pause
-		\item Collecting Ideas \pause
-		\item Developing Proposals \pause
-		\item Voting \pause
+		\item Designing the Process
+		\item Collecting Ideas
+		\item Developing Proposals
+		\item Voting
 		\item Funding Winners
 	\end{itemize}
 \end{frame}
 
 \begin{frame}
-	\frametitle{Differences to traditional Election}
+	\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{Properties of Algorithms}
+\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 \pause
-		\item Monotonicity \pause
-		\item Truthfulness \pause
+		\item Pareto Optimality
+		\item Monotonicity
+		\item Truthfulness
 		\item Fairness
 	\end{itemize}
 \end{frame}