Dictatorship, liberalism and the Pareto rule: Possible and impossible
The current economic crisis has shaken belief in the capacity of neoliberal 'free market' policies. Numerous supports of state intervention have arisen, and the interest for social choice theory has revived. In this paper we consider three standard properties for aggregating individual into social preferences: dictatorship, liberalism and the Pareto rule, and their formal negations. The context of the pure first-order classical logic makes it possible to show how some combinations of the above mentioned conditions, under the hypothesis of unrestricted domain, form simple and reasonable examples of possible or impossible social choice systems. Due to their simplicity, these examples, including the famous 'liberal paradox', could have a particular didactic value.