Self-selective social choice functions

It is not uncommon that a society facing a choice problem has also to choose the choice rule itself. In such situations, when information about voters' preferences is complete, the voters' preferences on alternatives induce voters' preferences over the set of available voting rules. Such a setting immediately gives rise to a natural question concerning consistency between these two levels of choice. If a choice rule employed to resolve the society's original choice problem does not choose itself, when it is also used for choosing the choice rule, then this phenomenon can be regarded as inconsistency of this choice rule as it rejects itself according to its own rationale. Koray (2000) proved that the only neutral, unanimous universally self-selective social choice functions are the dictatorial ones. Here we introduce to our society a constitution, which rules out inefficient social choice rules. When inefficient social choice rules become unavailable for comparison, the property of self-selectivity becomes more interesting and we show that some non-trivial self-selective social choice functions do exist. Under certain assumptions on the constitution we describe all of them. JEL Classification: D71 ⋆ Correspondence to: A.Slinko ⋆⋆ This project was initiated in 1999 during a visit of Arkadii Slinko to Bo˘ gaziçi University of Istanbul. A support from T ¨ UB ˙ ITAK NATO PC-B Programme for that visit is gratefully acknowledged. Both authors are grateful to Murat Sertel for helpful discussions and encouragement.