Opinion formation model for markets with a social temperature and fear

Ideal Agent System with Triplet States: Model Parameter Identification of Agent-Field Interaction

On the capital market, price movements of stock corporations can be observed independent of overall market developments as a result of company-specific news, which suggests the occurrence of a sudden risk event. In recent years, numerous concepts from statistical physics have been transferred to econometrics to model these effects and other issues, e.g., in socioeconomics. Like other studies, we extend the approaches based on the "buy" and "sell" positions of agents (investors' stance) with a third "hold" position. We develop the corresponding theory within the framework of the microcanonical and canonical ensembles for an ideal agent system and apply it to a capital market example. We thereby design a procedure to estimate the required model parameters from time series on the capital market. The aim is the appropriate modeling and the one-step-ahead assessment of the effect of a sudden risk event. From a one-step-ahead performance comparison with selected benchmark approaches, we infer that the model is well-specified and the model parameters are well determined.

How the Brain Becomes the Mind: Can Thermodynamics Explain the Emergence and Nature of Emotions?

The neural systems' electric activities are fundamental for the phenomenology of consciousness. Sensory perception triggers an information/energy exchange with the environment, but the brain's recurrent activations maintain a resting state with constant parameters. Therefore, perception forms a closed thermodynamic cycle. In physics, the Carnot engine is an ideal thermodynamic cycle that converts heat from a hot reservoir into work, or inversely, requires work to transfer heat from a low- to a high-temperature reservoir (the reversed Carnot cycle). We analyze the high entropy brain by the endothermic reversed Carnot cycle. Its irreversible activations provide temporal directionality for future orientation. A flexible transfer between neural states inspires openness and creativity. In contrast, the low entropy resting state parallels reversible activations, which impose past focus via repetitive thinking, remorse, and regret. The exothermic Carnot cycle degrades mental energy. Therefore, the brain's energy/information balance formulates motivation, sensed as position or negative emotions. Our work provides an analytical perspective of positive and negative emotions and spontaneous behavior from the free energy principle. Furthermore, electrical activities, thoughts, and beliefs lend themselves to a temporal organization, an orthogonal condition to physical systems. Here, we suggest that an experimental validation of the thermodynamic origin of emotions might inspire better treatment options for mental diseases.

Repulsion in controversial debate drives public opinion into fifty-fifty stalemate

Opinion formation is a process with strong implications for public policy. In controversial debates with large consequences, the public opinion is often trapped in a fifty-fifty stalemate, jeopardizing broadly accepted political decisions. Emergent effects from millions of private discussions make it hard to understand or influence this kind of opinion dynamics. Here we demonstrate that repulsion from opinions favors fifty-fifty stalemates. We study a voter model where agents can have two opinions or an undecided state in between, and where we allow for repulsion of opinions and for doubt: in pairwise discussions, undecided agents can be not only convinced, but also repelled from the opinion expressed by another agent, and decided agents may return to the undecided state. As a result, we observe that, if an agent is repelled instead of being convinced in at least one out of four interactions, as in controversial debates, the frequencies of both opinions equalize. This voter model attractor reproduces the phenomenology of repeated Brexit poll data well and provides a mechanism solely based on local interactions between agents that may explain stalemate polarization in controversial opinion formation.

Role of voting intention in public opinion polarization

We introduce and study a simple model for the dynamics of voting intention in a population of agents that have to choose between two candidates. The level of indecision of a given agent is modeled by its propensity to vote for one of the two alternatives, represented by a variable p∈[0,1]. When an agent i interacts with another agent j with propensity p_{j}, then i either increases its propensity p_{i} by h with probability P_{ij}=ωp_{i}+(1-ω)p_{j}, or decreases p_{i} by h with probability 1-P_{ij}, where h is a fixed step. We assume that the interactions form a complete graph, where each agent can interact with any other agent. We analyze the system by a rate equation approach and contrast the results with Monte Carlo simulations. We find that the dynamics of propensities depends on the weight ω that an agent assigns to its own propensity. When all the weight is assigned to the interacting partner (ω=0), agents' propensities are quickly driven to one of the extreme values p=0 or p=1, until an extremist absorbing consensus is achieved. However, for ω>0 the system first reaches a quasistationary state of symmetric polarization where the distribution of propensities has the shape of an inverted Gaussian with a minimum at the center p=1/2 and two maxima at the extreme values p=0,1, until the symmetry is broken and the system is driven to an extremist consensus. A linear stability analysis shows that the lifetime of the polarized state, estimated by the mean consensus time τ, diverges as τ∼(1-ω)^{-2}lnN when ω approaches 1, where N is the system size. Finally, a continuous approximation allows us to derive a transport equation whose convection term is compatible with a drift of particles from the center toward the extremes.

Cumulative Dynamics of Independent Information Spreading Behaviour: A Physical Perspective

The popularization of information spreading in online social networks facilitates daily communication among people. Although much work has been done to study the effect of interactions among people on spreading, there is less work that considers the pattern of spreading behaviour when people independently make their decisions. By comparing microblogging, an important medium for information spreading, with the disordered spin glass system, we find that there exist interesting corresponding relationships between them. And the effect of aging can be observed in both systems. Based on the analogy with the Trap Model of spin glasses, we derive a model with a unified power-function form for the growth of independent spreading activities. Our model takes several key factors into consideration, including memory effect, the dynamics of human interest, and the fact that older messages are more difficult to discover. We validate our model by a real-world microblogging data set. Our work indicates that, other than various features, some invariable rules should be considered during spreading prediction. This work also contributes a useful methodology for studying human dynamics.

Dynamics of influence on hierarchical structures

Dichotomous spin dynamics on a pyramidal hierarchical structure (the Bethe lattice) are studied. The system embodies a number of classes, where a class comprises nodes that are equidistant from the root (head node). Weighted links exist between nodes from the same and different classes. The spin (hereafter state) of the head node is fixed. We solve for the dynamics of the system for different boundary conditions. We find necessary conditions so that the classes eventually repudiate or acquiesce in the state imposed by the head node. The results indicate that to reach unanimity across the hierarchy, it suffices that the bottommost class adopts the same state as the head node. Then the rest of the hierarchy will inevitably comply. This also sheds light on the importance of mass media as a means of synchronization between the topmost and bottommost classes. Surprisingly, in the case of discord between the head node and the bottommost classes, the average state over all nodes inclines towards that of the bottommost class regardless of the link weights and intraclass configurations. Hence the role of the bottommost class is signified.