A market scoring rule (MSR) - a popular tool for designing algorithmic prediction markets - is an incentive-compatible mechanism for the aggregation of probabilistic beliefs from myopic risk-neutral agents. In this paper, we add to a growing body of research aimed at understanding the precise manner in which the price process induced by a MSR incorporates private information from agents who deviate from the assumption of risk-neutrality. We first establish that, for a myopic trading agent with a risk-averse utility function, a MSR satisfying mild regularity conditions elicits the agent's risk-neutral probability conditional on the latest market state rather than her true subjective probability. Hence, we show that a MSR under these conditions effectively behaves like a more traditional method of belief aggregation, namely an opinion pool, for agents' true probabilities.

We develop a theory of intelligent agency grounded in probabilistic modeling for neural models. Agents are represented as outcome distributions with epistemic utility given by log score, and compositions are defined through weighted logarithmic pooling that strictly improves every member's welfare. We prove that strict unanimity is impossible under linear pooling or in binary outcome spaces, but possible with three or more outcomes. Our framework admits recursive structure via cloning invariance, continuity, and openness, while tilt-based analysis rules out trivial duplication. Finally, we formalize an agentic alignment phenomenon in LLMs using our theory: eliciting a benevolent persona ("Luigi'") induces an antagonistic counterpart ("Waluigi"), while a manifest-then-suppress Waluigi strategy yields strictly larger first-order misalignment reduction than pure Luigi reinforcement alone. These results clarify how developing a principled mathematical framework for how subagents can coalesce into coherent higher-level entities provides novel implications for alignment in agentic AI systems.

The specification of prior distributions is fundamental in Bayesian inference, yet it remains a significant bottleneck. The prior elicitation process is often a manual, subjective, and unscalable task. We propose a novel framework which leverages Large Language Models (LLMs) to automate and scale this process. We introduce \texttt{LLMPrior}, a principled operator that translates rich, unstructured contexts such as natural language descriptions, data or figures into valid, tractable probability distributions. We formalize this operator by architecturally coupling an LLM with an explicit, tractable generative model, such as a Gaussian Mixture Model (forming a LLM based Mixture Density Network), ensuring the resulting prior satisfies essential mathematical properties. We further extend this framework to multi-agent systems where Logarithmic Opinion Pooling is employed to aggregate prior distributions induced by decentralized knowledge. We present the federated prior aggregation algorithm, \texttt{Fed-LLMPrior}, for aggregating distributed, context-dependent priors in a manner robust to agent heterogeneity. This work provides the foundation for a new class of tools that can potentially lower the barrier to entry for sophisticated Bayesian modeling.

Summary of the paper: The paper aims to address the question of how to combine beliefs to a central judgement in the case that the beliefs held by agents have an information asymmetry in each agents perspective on the future outcomes of particular stochastic events. In particular the paper particularly focuses on the concept of Hanson 2003 known as the prediction market based on a logarithmic market scoring rule. The market scoring rule framework is sometimes also known as a market studied in the context of cost function based market makers. The motivation provided for the MSR setting involves financial markets in which market makers or dedicated specialists are provided incentives, typically in the form of rebates to take trades on both sides of the book ie. the place limit and market orders in such a way that they create liquidity in the market to facilitate buying and selling of an asset. In this context it is argued that a MSR effectively acts as a cost function-based market maker always willing to take the other side of a trade with any willing buyer or seller, and re-adjusting its quoted price after every transaction.

A market scoring rule (MSR) – a popular tool for designing algorithmic prediction markets – is an incentive-compatible mechanism for the aggregation of probabilistic beliefs from myopic risk-neutral agents. In this paper, we add to a growing body of research aimed at understanding the precise manner in which the price process induced by a MSR incorporates private information from agents who deviate from the assumption of risk-neutrality. We first establish that, for a myopic trading agent with a risk-averse utility function, a MSR satisfying mild regularity conditions elicits the agent's risk-neutral probability conditional on the latest market state rather than her true subjective probability. Hence, we show that a MSR under these conditions effectively behaves like a more traditional method of belief aggregation, namely an opinion pool, for agents' true probabilities. We also point out the interpretation of a market maker under these conditions as a Bayesian learner even when agent beliefs are static.

The rapid development of collaborative robotics has provided a new possibility of helping the elderly who has difficulties in daily life, allowing robots to operate according to specific intentions. However, efficient human-robot cooperation requires natural, accurate and reliable intention recognition in shared environments. The current paramount challenge for this is reducing the uncertainty of multimodal fused intention to be recognized and reasoning adaptively a more reliable result despite current interactive condition. In this work we propose a novel learning-based multimodal fusion framework Batch Multimodal Confidence Learning for Opinion Pool (BMCLOP). Our approach combines Bayesian multimodal fusion method and batch confidence learning algorithm to improve accuracy, uncertainty reduction and success rate given the interactive condition. In particular, the generic and practical multimodal intention recognition framework can be easily extended further. Our desired assistive scenarios consider three modalities gestures, speech and gaze, all of which produce categorical distributions over all the finite intentions. The proposed method is validated with a six-DoF robot through extensive experiments and exhibits high performance compared to baselines.

A market scoring rule (MSR) - a popular tool for designing algorithmic prediction markets - is an incentive-compatible mechanism for the aggregation of probabilistic beliefs from myopic risk-neutral agents. In this paper, we add to a growing body of research aimed at understanding the precise manner in which the price process induced by a MSR incorporates private information from agents who deviate from the assumption of risk-neutrality. We first establish that, for a myopic trading agent with a risk-averse utility function, a MSR satisfying mild regularity conditions elicits the agent's risk-neutral probability conditional on the latest market state rather than her true subjective probability. Hence, we show that a MSR under these conditions effectively behaves like a more traditional method of belief aggregation, namely an opinion pool, for agents' true probabilities.

Cyber threat attribution can play an important role in increasing resilience against digital threats. Recent research focuses on automating the threat attribution process and on integrating it with other efforts, such as threat hunting. To support increasing automation of the cyber threat attribution process, this paper proposes a modular architecture as an alternative to current monolithic automated approaches. The modular architecture can utilize opinion pools to combine the output of concrete attributors. The proposed solution increases the tractability of the threat attribution problem and offers increased usability and interpretability, as opposed to monolithic alternatives. In addition, a Pairing Aggregator is proposed as an aggregation method that forms pairs of attributors based on distinct features to produce intermediary results before finally producing a single Probability Mass Function (PMF) as output. The Pairing Aggregator sequentially applies both the logarithmic opinion pool and the linear opinion pool. An experimental validation suggests that the modular approach does not result in decreased performance and can even enhance precision and recall compared to monolithic alternatives. The results also suggest that the Pairing Aggregator can improve precision over the linear and logarithmic opinion pools. Furthermore, the improved k-accuracy in the experiment suggests that forensic experts can leverage the resulting PMF during their manual attribution processes to enhance their efficiency.

To construct flexible nonlinear predictive distributions, the paper introduces a family of softplus function based regression models that convolve, stack, or combine both operations by convolving countably infinite stacked gamma distributions, whose scales depend on the covariates. Generalizing logistic regression that uses a single hyperplane to partition the covariate space into two halves, softplus regressions employ multiple hyperplanes to construct a confined space, related to a single convex polytope defined by the intersection of multiple half-spaces or a union of multiple convex polytopes, to separate one class from the other. The gamma process is introduced to support the convolution of countably infinite (stacked) covariate-dependent gamma distributions. For Bayesian inference, Gibbs sampling derived via novel data augmentation and marginalization techniques is used to deconvolve and/or demix the highly complex nonlinear predictive distribution. Example results demonstrate that softplus regressions provide flexible nonlinear decision boundaries, achieving classification accuracies comparable to that of kernel support vector machine while requiring significant less computation for out-of-sample prediction.

A market scoring rule (MSR) – a popular tool for designing algorithmic prediction markets – is an incentive-compatible mechanism for the aggregation of probabilistic beliefs from myopic risk-neutral agents. In this paper, we add to a growing body of research aimed at understanding the precise manner in which the price process induced by a MSR incorporates private information from agents who deviate from the assumption of risk-neutrality. We first establish that, for a myopic trading agent with a risk-averse utility function, a MSR satisfying mild regularity conditions elicits the agent’s risk-neutral probability conditional on the latest market state rather than her true subjective probability. Hence, we show that a MSR under these conditions effectively behaves like a more traditional method of belief aggregation, namely an opinion pool, for agents’ true probabilities. In particular, the logarithmic market scoring rule acts as a logarithmic pool for constant absolute risk aversion utility agents, and as a linear pool for an atypical budget-constrained agent utility with decreasing absolute risk aversion. We also point out the interpretation of a market maker under these conditions as a Bayesian learner even when agent beliefs are static.