Programming social choice in logic: some basic experimental results when profiles are restricted

Social choice theory argues mathematical models and their logical consequences for group decision making based on individuals’ preference orderings axiomatically. The most basic results have been proved in this field are two impossibility results for group decision making. Arrow’s general (im)possibility theorem for preference aggregation procedures, i.e., there is no nondictatorial social welfare functions (SWFs), and the Gibbard-Satterthwaite theorem for the strategy-proof social choice functions (SCFs), i.e., any voting procedure which cannot be manipulated by any individual’s false report on his/her own preference ordering should be dictatorial. The above two classical results are proved for unrestricted domain, i.e., any combinations of individual orderings can never be prohibited. This paper shows that, there are 18 non-dictatorial SWFs and 196 strategy-proof non-imposed SCFs by eliminating a double cyclical 6 profiles, each of these profiles are considered to be minimal and sufficient to prove the Arrow-type dictatorship for every two-individual and three alternatives. While these profiles are used in the Arrow’s original proof, we may have a thorough experimentation eliminating subsets of a set of special 12 profiles which is sufficient to deduce a dictatorship. The automated proof, instead of pure mathematical proof, unveils fairly comprehensive pattern rules for SWFs in parallel with