Decision–making on public facility location by using social choice rules with a deliberative suggestion

To decide a public facility location by considering both voters' preferences and a deliberative suggestion from the government (all of them are assumed to be complete preorders over a fixed finite location set), we propose a democratic–deliberative preference update system (DD system). The DD system updates the voters' preferences according to the government's preference as follows: if any two locations are indifferent for a voter, the updated preference of the voter is equivalent to that of the government, and if any two locations are ordered strictly by the voter, the updated preference is equal to the original one. We provide a simple axiomatic characterisation of the DD system and show that the system updates the voters' preferences in linear time. We then compare the set of winners by using (I) only the voters' preferences, (II) only the government's preference, and (III) the democratic–deliberative updated preferences based on the following five scoring rules: (adjusted) plurality, (adjusted) anti-plurality, and Borda rules. We run the simulation 10,000 times for each pair of the numbers of locations and voters and estimate the relationship between the set of winners, the numbers of locations and voters, and the voting rules. We find that the Borda rule has better performance than the others in our simulation and regression analyses.