Characterizing Neutral Aggregation on Restricted Domains
نویسنده
چکیده
Sen [6] proved that by confining voters to value restricted (acyclic) domains voting paradoxes (intransitive relations) can be avoided in aggregation by majority. We generalize this result to any neutral monotone aggregation. In addition, we show that acyclicity is neither necessary nor sufficient for transitivity for neutral non-monotone aggregation: we construct a cyclic transitive domain and introduce strong acyclicity as a sufficient condition for transitivity. We also show that strong acyclicity is necessary if repeated transitivity is sought. Finally, we present a cyclic domain repeatedly transitively aggregatable by a non neutral function.
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