Adaptive Probability Theory: Human Biases as an Adaptation

Humans make mistakes in our decision-making and probability judgments. While the heuristics used for decision-making have been explained as adaptations that are both efficient and fast, the reasons why people deal with probabilities using the reported biases have not been clear. We will see that some of these biases can be understood as heuristics developed to explain a complex world when little information is available. That is, they approximate Bayesian inferences for situations more complex than the ones in laboratory experiments and in this sense might have appeared as an adaptation to those situations. When ideas as uncertainty and limited sample sizes are included in the problem, the correct probabilities are changed to values close to the observed behavior. These ideas will be used to explain the observed weight functions, the violations of coalescing and stochastic dominance reported in the literature

Discrete Opinion models as a limit case of the CODA model

Opinion Dynamics models can be, for most of them, divided between discrete and continuous. They are used in different circumstances and the relationship between them is not clear. Here we will explore the relationship between a model where choices are discrete but opinions are a continuous function (the Continuous Opinions and Discrete Actions, CODA, model) and traditional discrete models. I will show that, when CODA is altered to include reasoning about the influence one agent can have on its own neighbors, agreement and disagreement no longer have the same importance. The limit when an agent considers itself to be more and more influential will be studied and we will see that one recovers discrete dynamics, like those of the Voter model in that limitComment: 10 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:0811.011

Trust in the CODA model: Opinion Dynamics and the reliability of other agents

A model for the joint evolution of opinions and how much the agents trust each other is presented. The model is built using the framework of the Continuous Opinions and Discrete Actions (CODA) model. Instead of a fixed probability that the other agents will decide in the favor of the best choice, each agent considers that other agents might be one one of two types: trustworthy or useless. Trustworthy agents are considered more likely to be right than wrong, while the opposite holds for useless ones. Together with the opinion about the discussed issue, each agent also updates that probability for each one of the other agents it interacts withe probability each one it interacts with is of one type or the other. The dynamics of opinions and the evolution of the trust between the agents are studied. Clear evidences of the existence of two phases, one where strong polarization is observed and the other where a clear division is permanent and reinforced are observed. The transition seems signs of being a first-order transition, with a location dependent on both the parameters of the model and the initial conditions. This happens despite the fact that the trust network evolves much slower than the opinion on the central issue.Comment: 15 pages, 14 figure

Continuous Opinions and Discrete Actions in Opinion Dynamics Problems

A model where agents show discrete behavior regarding their actions, but have continuous opinions that are updated by interacting with other agents is presented. This new updating rule is applied to both the voter and Sznajd models for interaction between neighbors and its consequences are discussed. The appearance of extremists is naturally observed and it seems to be a characteristic of this model.Comment: 10 pages, 4 figures, minor changes for improved clarit