Negative updating applied to the best-of-n problem with noisy qualities

The ability to perform well in the presence of noise is an important consideration when evaluating the effectiveness of a collective decision-making framework. Any system deployed for real-world applications will have to perform well in complex and uncertain environments, and a component of this is the limited reliability and accuracy of evidence sources. In particular, in swarm robotics there is an emphasis on small and inexpensive robots which are often equipped with low-cost sensors more prone to suffer from noisy readings. This paper presents an exploratory investigation into the robustness of a negative updating approach to the best-of-n problem which utilises negative feedback from direct pairwise comparison of options and opinion pooling. A site selection task is conducted with a small-scale swarm of five e-puck robots choosing between $$n=7$$ n = 7 options in a semi-virtual environment with varying levels of sensor noise. Simulation experiments are then used to investigate the scalability of the approach. We now vary the swarm size and observe the behaviour as the number of options n increases for different error levels with different pooling regimes. Preliminary results suggest that the approach is robust to noise in the form of noisy sensor readings for even small populations by supporting self-correction within the population.

Joint desirability foundations of social choice and opinion pooling

We develop joint foundations for the fields of social choice and opinion pooling using coherent sets of desirable gambles, a general uncertainty model that allows to encompass both complete and incomplete preferences. This leads on the one hand to a new perspective of traditional results of social choice (in particular Arrow’s theorem as well as sufficient conditions for the existence of an oligarchy and democracy) and on the other hand to using the same framework to analyse opinion pooling. In particular, we argue that weak Pareto (unanimity) should be given the status of a rationality requirement and use this to discuss the aggregation of experts’ opinions based on probability and (state-independent) utility, showing some inherent limitation of this framework, with implications for statistics. The connection between our results and earlier work in the literature is also discussed.

An Interpretation of Weights in Linear Opinion Pooling

This paper explores the fact that linear opinion pooling can be represented as a Bayesian update on the opinions of others. It uses this fact to propose a new interpretation of the pooling weights. Relative to certain modelling assumptions the weights can be equated with the so-called truth-conduciveness known from the context of Condorcet's jury theorem. This suggests a novel way to elicit the weights.

Combining Opinion Pooling and Evidential Updating for Multi-Agent Consensus

The evidence available to a multi-agent system can take at least two distinct forms. There can be direct evidence from the environment resulting, for example, from sensor measurements or from running tests or experiments. In addition, agents also gain evidence from other individuals in the population with whom they are interacting. We, therefore, envisage an agent's beliefs as a probability distribution over a set of hypotheses of interest, which are updated either on the basis of direct evidence using Bayesian updating, or by taking account of the probabilities of other agents using opinion pooling. This paper investigates the relationship between these two processes in a multi-agent setting. We consider a possible Bayesian interpretation of probability pooling and then explore properties for pooling operators governing the extent to which direct evidence is diluted, preserved or amplified by the pooling process. We then use simulation experiments to show that pooling operators can provide a mechanism by which a limited amount of direct evidence can be efficiently propagated through a population of agents so that an appropriate consensus is reached. In particular, we explore the convergence properties of a parameterised family of operators with a range of evidence propagation strengths.

Probabilistic Opinion Pooling

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This chapter is a review of several proposed solutions to this problem, focusing on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). Axiomatic characterizations of each class of pooling functions are presented (most characterizations are classic results, but one is new), with the argument that linear pooling can be justified “procedurally” but not “epistemically”, while the other two pooling methods can be justified “epistemically”. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. In conclusion a number of other pooling methods are mentioned.