Social choice is the theory about collective decision towards social welfare starting from individual opinions, preferences, interests or welfare. The field of Computational Social Welfare is somewhat recent and it is gaining impact in the Artificial Intelligence Community. Classical literature makes the assumption of single-peaked preferences, i.e. there exist a order in the preferences and there is a global maximum in this order. Recently, some theoretical results were published about Two-stage Approval Voting Systems (TAVs), Multi-winner Selection Rules (MWSR) and Incomplete (IPs) and Circular Preferences (CPs) that I claim leads to research about Preferences Graphs and Preferences Multi-dimensional Functions in Polynomial time.
The purpose of this paper is, firstly, to introduce Social Choice Optimization as a generalization of Approval Voting where there is a maximization stage and a minimization stage implementing thus a Minimax, a well-known Artificial Intelligence decision making rule to minimize hindering towards a (Social) Goal; secondly, to introduce, following my Open Standardization and Open Integration Theory (in refinement process) put in practice in my dissertation, the Open Standardization of Social Inclusion, as a global social goal of Social Choice Optimization; and thirdly to introduce and define the Coherent Social Inclusion problem, provide its solutions characterization and three algorithms to find them.