Add conclusion

paper/termpaper.tex

@@ -436,6 +436,36 @@ cannot be bettered without making someone worse off while improving another
 voter and that results cannot only mirror one person's preferences,
 respectively.
 
+\section{Conclusion}
+\label{sec:conclusion}
+
+We have looked at different possibilities for conducting the voting and winner
+selection process for participatory budgeting. A budgeting scenario in the
+mathematical sense has been described and methods for modeling voter
+satisfaction are discussed. A deeper view on approval-based budgeting models has
+been given where the voters are assumed to have dichotomous preferences. The
+complexity of the different rules has been evaluated and contrasted to each
+other. We have seen that aggregation methods cannot only be compared in terms of
+complexity but also by using axioms that formulate desirable outcomes.
+
+Future research might focus on not only incorporating monetary cost and
+satisfaction into aggregating winning projects but also other factors such as
+environmental costs, practicability of participatory budgeting methods as well
+as scalability of these methods to a very high amount of projects and voters.
+Interesting further questions are posed by the possibility to combine projects
+that are indivisible with projects that are divisible under one aggregation
+rule, leading to a host of \emph{hybrid models}. Because a lot of the methods
+that have been theorized by researchers have not yet been implemented in
+practice, research on feasibility could lead to a better understanding of what
+works and what does not. Another area of research could focus on allowing
+projects to be related to each other and reflecting those inter-relations in the
+outcome while still maintaining a grip on the explosion of possible solutions.
+Exploring more axioms and rule configurations is important for achieving a
+complete picture of the possibilities within the field of computational social
+choice. As a final point, research into user interface design during the voting
+phase might uncover previously unknown impacts of ballot design on the resulting
+selection of winning projects.
+
 \printbibliography
 
 \end{document}