A framework for consensus modelling is introduced using Kleene's three valued logic as a means to express vagueness in agents' beliefs. Explicitly borderline cases are inherent to propositions involving vague concepts where sentences of a propositional language may be absolutely true, absolutely false or borderline. By exploiting these intermediate truth values, we can allow agents to adopt a more vague interpretation of underlying concepts in order to weaken their beliefs and reduce the levels of inconsistency, so as to achieve consensus. We consider a consensus combination operation which results in agents adopting the borderline truth value as a shared viewpoint if they are in direct conflict. Simulation experiments are presented which show that applying this operator to agents chosen at random (subject to a consistency threshold) from a population, with initially diverse opinions, results in convergence to a smaller set of more precise shared beliefs. Furthermore, if the choice of agents for combination is dependent on the payoff of their beliefs, this acting as a proxy for performance or usefulness, then the system converges to beliefs which, on average, have higher payoff.
As an alternative to DeGroot's model, the Bounded Confidence (BC) model introduced in @cite_0 provides agents with a confidence measure. An agent quantifies their level of confidence in their own opinions and are then able to limit their interactions to those agents who possess similar beliefs if they are highly confident (small bounds), or extend the range of possible interactions if the agents possess low confidence (large bounds). In this model agents do not a priori assign weights to the beliefs of others, but instead determine such weightings based on similarity and on their own confidence levels. This is similar in essence to the inconsistency threshold that we introduce in section , but applied on an individual basis.
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Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines such as physics, mathematics, computer science, social psychology and philosophy. In these models agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to each other. Usually, the models are analyzed with agent-based simulations in a Monte Carlo style, but they can also be reformulated on the agent's density in the opinion space in a master equation style. The contribution of this survey is fourfold. First, it will present the agent-based and density-based modeling frameworks including the cases of multidimensional opinions and heterogeneous bounds o... Online users tend to select claims that adhere to their system of beliefs and to ignore dissenting information. Confirmation bias, indeed, plays a pivotal role in viral phenomena. Furthermore, the wide availability of content on the web fosters the aggregation of likeminded people where debates tend to enforce group polarization. Such a configuration might alter the public debate and thus the formation of the public opinion. In this paper we provide a mathematical model to study online social debates and the related polarization dynamics. We assume the basic updating rule of the Bounded Confidence Model (BCM) and we develop two variations a) the Rewire with Bounded Confidence Model (RBCM), in which discordant links are broken until convergence is reached; and b) the Unbounded Confidence Model, under which the interaction among discordant pairs of users is allowed even with a negative feedback, either with the rewiring step (RUCM) or without it (UCM). From numerical simulations we find that the new models (UCM and RUCM), unlike the BCM, are able to explain the coexistence of two stable final opinions, often observed in reality. Lastly, we present a mean field approximation of the newly introduced models. Abstract Several competing human behavior models have been proposed to model boundedly rational adversaries in repeated Stackelberg Security Games (SSG). However, these existing models fail to address three main issues which are detrimental to defender performance. First, while they attempt to learn adversary behavior models from adversaries' past actions (“attacks on targets”), they fail to take into account adversaries' future adaptation based on successes or failures of these past actions. Second, existing algorithms fail to learn a reliable model of the adversary unless there exists sufficient data collected by exposing enough of the attack surface – a situation that often arises in initial rounds of the repeated SSG. Third, current leading models have failed to include probability weighting functions, even though it is well known that human beings' weighting of probability is typically nonlinear. To address these limitations of existing models, this article provides three main contributions. Our first contribution is a new human behavior model, SHARP, which mitigates these three limitations as follows: (i) SHARP reasons based on success or failure of the adversary's past actions on exposed portions of the attack surface to model adversary adaptivity; (ii) SHARP reasons about similarity between exposed and unexposed areas of the attack surface, and also incorporates a discounting parameter to mitigate adversary's lack of exposure to enough of the attack surface; and (iii) SHARP integrates a non-linear probability weighting function to capture the adversary's true weighting of probability. Our second contribution is a first “repeated measures study” – at least in the context of SSGs – of competing human behavior models. This study, where each experiment lasted a period of multiple weeks with individual sets of human subjects on the Amazon Mechanical Turk platform, illustrates the strengths and weaknesses of different models and shows the advantages of SHARP. Our third major contribution is to demonstrate SHARP's superiority by conducting real-world human subjects experiments at the Bukit Barisan Seletan National Park in Indonesia against wildlife security experts. In open settings, the participants are autonomous and there is no central authority to ensure the felicity of their interactions. When agents interact in such settings, each relies upon being able to model the trustworthiness of the agents with whom it interacts. Fundamentally, such models must consider the past behavior of the other parties in order to predict their future behavior. Further, it is sensible for the agents to share information via referrals to trustworthy agents. Much progress has recently been made on probabilistic trust models including those that support the aggregation of information from multiple sources. However, current models do not support trust updates, leaving updates to be handled in an ad hoc manner. This paper proposes a trust representation that combines probabilities and certainty (defined as a function of a probability-certainty density function). Further, it offers a trust update mechanism to estimate the trustworthiness of referrers. This paper describes a testbed that goes beyond existing testbeds to enable the evaluation of a composite probability-certainty model. It then evaluates the proposed trust model showing that the trust model can (a) estimate trustworthiness of damping and capricious agents correctly, (b) update trust values of referrers accurately, and (c) resolve the conflicts in referral networks by certainty discounting.