Sequential voting rules and multiple elections paradoxes

Multiple election paradoxes arise when voting separately on each issue from a set of related issues results in an obviously undesirable outcome. Several authors have argued that a sufficient condition for avoiding multiple election paradoxes is the assumption that voters have separable preferences. We show that this extremely demanding restriction can be relaxed into the much more reasonable one: there exists a linear order <b>x</b><sub>1</sub> > … > <b>x</b><sub><i>p</i></sub> on the set of issues such that for each voter, every issue <b>x</b><sub><i>i</i></sub> is preferentially independent of <b>x</b><sub><i>i+1</i></sub>, …, <b>x</b><sub><i>p</i></sub> given <b>x</b><sub>1</sub>, …, <b>x</b><sub><i>i</i>-1</sub>. This leads us to define a family of sequential voting rules, defined as the sequential composition of local voting rules. These rules relate to the setting of conditional preference networks (CP-nets) recently developed in the Artificial Intelligence literature. We study in detail how these sequential rules inherit, or do not inherit, the properties of their local components. We focus on the case of multiple referenda, corresponding to multiple elections with binary issues.

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