Incorporating Reality into Social Choice
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When voting on a proposal one in fact chooses between two alternatives: (i) A new hypothetical social state depicted by the proposal and (ii) the status quo (henceforth: Reality); a Yes vote favors a transition to the proposed hypothetical state, while a No vote favors Reality. Social Choice theory generalizes voting on one proposal to ranking multiple proposed alternatives; we remorse that during this generalization, Reality was neglected. Here we propose to rectify this state of affairs by incorporating Reality into Social Choice. We do so by recognizing Reality as an ever present, always relevant, evolving social state, which is distinguished from hypothetical social states, and explore the ramifications of this recognition. We argue that incorporating Reality into Social Choice is natural, even essential, and show that doing so necessitates revisiting its foundation, as Arrow's theorem and the Condorcet voting paradox do not carry over. We explore the plethora of research directions opened by taking Reality into consideration: New models of Reality-aware Social Choice (we present three, from the most abstract to more concrete, with their associated axioms); new Reality-aware voting rules (we present voting rules that are simple to communicate and to implement); new concepts (we present democratic action plans, an extension of democratic decisions); and new game-theoretic questions related to strategic voting (we discuss one Reality-based game). Arrow's theorem was taken to show that democracy, conceived as government by the will of the people, is an incoherent illusion. As Reality-aware Social Choice renders Arrow's theorem vacuous and resolves the Condorcet voting paradox, it may clear this intellectual blemish on democracy; pave the way for a broad application of ranked voting according to the Condorcet criterion; and, more generally, may help restore trust in democracy.
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