Social choice trade-off results for conditions on triples of alternatives

• Some trade-offs implicit in the framework of Arrow’s Impossibility Theorem are uncovered.
• We provide a measure of the extent to which transitivity must be sacrificed to get a significant reduction in dictatorial power.
• We provide a measure of the extent to which the domain must be restricted to get a significant reduction in dictatorial power.

We quantify the trade-off between the scope of dictatorial power and (1) the extent to which social orderings are transitive and (2) the extent to which the domain has the free triple property.