Prof. Leonidas Sakalauskas,
Vytautas Magnus University, Lithuania
FROM THE TRAGEDY OF THE COMMONS AND IMPOSSIBILITY THEOREMS TO CONSENSUS
In order to understand the phenomena of today’s social behavior, the following abstract approach is considered. Assume a set (group, community, network, etc.) of agents (individuals, persons, network nodes, etc.) is monitored and analyzed concerning the use of some resource. This model is often considered the “tragedy of the commons” (G. Hardin, 1968). The resources on which decisions are made may be economic and environmental, and, more recently, the use of shared resources in digital space is becoming increasingly relevant (G.M. Greco and L. Floridi, 2004). The central concept becomes “consensus,” an agreement between agents regarding the group solution or decision. In distributed data systems, say, in blockchain, the consensus is the agreement of a group of participants regarding the meaning of some state and data consistency. The role of impossibility theorems, including Arrow and Fisher-Lynch-Paterson theorems, formulated and explored with the application of non-classic logic models and reflexive game theory in constructing consensus algorithms, is discussed (V. Gisin, 2023). This approach helps us explain certain paradoxes of “group thinking.” The methodology of mathematical-computer modeling of social behavior phenomena, using structural equation modeling, game theory, and multi-agent modeling methods, is also reviewed.
