Sequential composition of voting rules in multi-issue domains

摘要

In many real-world group decision making problems, the set of alternatives is a Cartesian product of finite value domains for each of a given set of variables (or issues). Dealing with such domains leads to the following well-known dilemma: either ask the voters to vote separately on each issue, which may lead to the so-called multiple election paradoxes as soon as voters' preferences are not separable; or allow voters to express their full preferences on the set of all combinations of values, which is practically impossible as soon as the number of issues and/or the size of the domains are more than a few units. We try to reconciliate both views and find a middle way, by relaxing the extremely demanding separability restriction into this much more reasonable one: there exists a linear order x(1) > ... > x(p) on the set of issues such that for each voter, every issue xi is preferentially independent of x(i+1,) ... , x(p) given x(1), ... , x(i-1). 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. Lastly, we study in detail how these sequential rules inherit, or do not inherit, the properties of their local components.