Achieving a decision in antagonistic multi agent networks: frustration determines commitment strength

A signed network perspective on the government formation process in parliamentary democracies

“…Interpreted in the context of a government formation process, this relationship states that the duration of the govern- www.nature.com/scientificreports/ ment negotiation talks (a proxy of π 1 ) is directly proportional to the frustration of the parliamentary network, see "Methods". When the frustration increases, the model predicts that the bifurcation threshold increases as well (see 31 and also Supplementary Fig. 4), meaning that a higher commitment will be required from the agents in order to escape a state of no decision and to reach a collective nontrivial equilibrium point.…”

“…Such models represent a decision as the trespassing of a bifurcation threshold, and the corresponding bifurcation parameter has the interpretation of "social commitment" of the agents, i.e., intensity of the interactions among the agents. In presence of signed graphs, it is known that the bifurcation threshold can be pushed to higher values of the bifurcation parameter, and in particular that its value is proportional to the frustration encoded in the signed network 31 . If we consider as decision a confidence vote on a candidate cabinet, and as "social commitment" the intensity of the government negotiation talks (quantified as duration of the bargaining phase), then in a multiagent dynamics perspective the positive correlation we find between frustration and duration of the government negotiation phase is an expected and reasonable property: more "disordered" parliaments require longer negotiations to form a government.…”

“…The high correlation between frustration and government negotiation days admits an interpretation in terms of dynamical models of collective decision-making, see "Methods" and "Supplementary Information". These models, used for instance in 30,31 , are inspired by the behavior of animal groups 28,29,35 and in our case associate a state variable to each MP, variable that represents the decision in a confidence vote. In order for a government to win a confidence vote, an attractor corresponding to a majority of positive decisions must be present.…”

“…. The latter is called in the signed graph literature the algebraic conflict 24 , and it is well-known to be closely related to the frustration 24,31,36 , see Supplementary Table 2 for an analysis on our data. Similarly, the signature of the corresponding eigenvector overlaps substantially with the signature of the ground state spin configuration S best , see Supplementary Table 2.…”

Modeling the Disorder of Closed System by Multi-Agent Based Simulation

“…They conclude that in the resulting n -strategy evolutionary games the analytical methods and numerical simulations indicate continuous order-disorder phase transitions when increasing the noise level if n does not exceed a threshold value. In Reference [ 29 ] authors have investigated how the frustration of a social network influences the appearance of nonzero equilibria as a function of a scalar parameter playing the role of social effort. In Reference [ 30 ] authors used the Lefebvre’s “algebra of conscience” to describe decision-making strategies of agents simulating people with different brain dominance.…”