We show that the answer to this question depends on the properties of underlying preference distributions.

We consider the classical problem of finding the minimum feedback arc set on tournaments (MFAST). The problem is NP-hard in general and we study it for important classes of tournaments that arise naturally in the problem of learning to rank from pairwise comparisons. Specifically, we consider tournaments classes that arise out of parametric preference matrices that can lead to cyclic preference relations. We investigate their structural properties via forbidden sub tournament configurations. Towards this, we introduce \emph{Tournament Dimension} - a combinatorial parameter that characterizes the size of a forbidden configuration for rank $r$ tournament classes i.e., classes that arise out pairwise preference matrices which lead to rank $r$ skew-symmetric matrices under a suitable link function.

This paper proposes an Interactive Inference Behavior Tree (IIBT) framework that integrates behavior trees (BTs) with active inference under the free energy principle for distributed multi-robot decision-making. The proposed IIBT node extends conventional BTs with probabilistic reasoning, enabling online joint planning and execution across multiple robots. It remains fully compatible with standard BT architectures, allowing seamless integration into existing multi-robot control systems. Within this framework, multi-robot cooperation is formulated as a free-energy minimization process, where each robot dynamically updates its preference matrix based on perceptual inputs and peer intentions, thereby achieving adaptive coordination in partially observable and dynamic environments. The proposed approach is validated through both simulation and real-world experiments, including a multi-robot maze navigation and a collaborative manipulation task, compared against traditional BTs(https://youtu.be/KX_oT3IDTf4). Experimental results demonstrate that the IIBT framework reduces BT node complexity by over 70%, while maintaining robust, interpretable, and adaptive cooperative behavior under environmental uncertainty.

Interactive preference elicitation (IPE) aims to substantially reduce human effort while acquiring human preferences in wide personalization systems. Dueling bandit (DB) algorithms enable optimal decision-making in IPE building on pairwise comparisons. However, they remain inefficient when human feedback is sparse. Existing methods address sparsity by heavily relying on parametric reward models, whose rigid assumptions are vulnerable to misspecification. In contrast, we explore an alternative perspective based on feedback augmentation, and introduce critical improvements to the model-free DB framework. Specifically, we introduce augmented confidence bounds to integrate augmented human feedback under generalized concentration properties, and analyze the multi-factored performance trade-off via regret analysis. Our prototype algorithm achieves competitive performance across several IPE benchmarks, including recommendation, multi-objective optimization, and response optimization for large language models, demonstrating the potential of our approach for provably efficient IPE in broader applications.

Pairwise comparison methods, such as Fuzzy Preference Relations and Saaty's Multiplicative Preference Relations, are widely used to model expert judgments in multi-criteria decision-making. However, their application is limited by the high cognitive load required to complete $m(m-1)/2$ comparisons, the risk of inconsistency, and the computational complexity of deriving consistent value scales. This paper proposes the Tournament Tree Method (TTM), a novel elicitation and evaluation framework that overcomes these limitations. The TTM requires only $m-1$ pairwise comparisons to obtain a complete, reciprocal, and consistent comparison matrix. The method consists of three phases: (i) elicitation of expert judgments using a reduced set of targeted comparisons, (ii) construction of the consistent pairwise comparison matrix, and (iii) derivation of a global value scale from the resulting matrix. The proposed approach ensures consistency by design, minimizes cognitive effort, and reduces the dimensionality of preference modeling from $m(m-1)/2$ to $m$ parameters. Furthermore, it is compatible with the classical Deck of Cards method, and thus it can handle interval and ratio scales. We have also developed a web-based tool that demonstrates its practical applicability in real decision-making scenarios.

We consider the classical problem of finding the minimum feedback arc set on tournaments (MFAST).

We show that the answer to this question depends on the properties of underlying preference distributions.