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\begin{document}

\title{Randomised Social Choice}
\author{Manuel Eberl}
\maketitle

\begin{abstract}
This work contains a formalisation of basic Randomised Social Choice, including Stochastic Dominance
and Social Decision Schemes (SDSs) along with some of their most important properties 
(Anonymity, Neutrality, \textit{SD}-Efficiency, \textit{SD}-Strategy-Proofness) and two particular SDSs -- Random Dictatorship 
and Random Serial Dictatorship (with proofs of the properties that they satisfy). Many important properties of these 
concepts are also proven -- such as the two equivalent characterisations of Stochastic Dominance and the fact that 
SD-efficiency of a lottery only depends on the support.

The entry also provides convenient commands to define Preference Profiles, prove their well-formedness, and 
automatically derive restrictions that sufficiently nice SDSs need to satisfy on the defined profiles. (cf. \cite{smt})

Currently, the formalisation focuses on weak preferences and Stochastic Dominance (\textit{SD}), but it should be easy to extend it 
to other domains -- such as strict preferences -- or other lottery extensions -- such as Bilinear Dominance or Pairwise Comparison.
\end{abstract}

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