Large-scale group decision making, or LSGDM, is the formal discipline behind many high-stakes choices that involve twenty or more experts with different backgrounds, risk tolerances, and information. In emergencies, the stakes are extreme: hesitation or misjudgment can cost lives, yet forcing rapid agreement risks steamrolling minority opinions that may contain crucial insights. The traditional remedy is the consensus reaching process, an iterative loop in which experts whose views stray too far from the group are asked to adjust them until a preset consensus threshold is met. The trouble, the authors argue, is that the feedback parameters governing how strongly experts are pushed to compromise have historically been fixed by hand, based on experience. Too large a step and expert preferences get bulldozed; too small a step and the discussion drags on for rounds that an unfolding disaster cannot spare.

The core innovation is to model the entire consensus process as a Markov decision process and let a Deep Deterministic Policy Gradient, or DDPG, agent learn the feedback strategy. In this formulation, the state at each round captures the group’s evolving condition: the vector of opinion deviations between each expert cluster and the group center, the current group consensus level, the historical effect of previous feedback adjustments, and the trend in how quickly opinions are changing. Because these variables contain the essential statistics of the consensus environment, the next state depends only on the current state and the action taken, satisfying the Markov property that makes reinforcement learning well-posed. The action is deceptively simple: a single continuous value between zero and one, the feedback parameter that determines how far identified experts should move their opinions toward the group position.

What makes the problem genuinely hard is the reward. The authors designed a bi-objective, piecewise reward function that pays the agent for improving group consensus, penalizes it for each additional discussion round, and rewards it for preserving what they call the opinion retention degree, a measure of how much of each expert’s original judgment survives the adjustment. The result is an agent that learns to walk a narrow line: converge quickly, but not by erasing the diversity of expert judgment that makes large-group decisions robust in the first place. Sensitivity analysis over reward weight configurations confirmed the trade-off is real and tunable. A consensus-heavy weighting cut the rounds to agreement to 5.2 but dropped preference preservation to 0.6498, while a preference-oriented configuration raised preservation to 0.7235 at the cost of more rounds. The default weights of 0.5, 0.3, and 0.2 struck the best balance.

Before the learning agent ever sees a decision problem, the raw expert input must be made computable. Experts express preferences using hesitant fuzzy linguistic term sets, which allow a decision maker to offer several linguistic evaluations at once, for instance rating an alternative as both good and very good when uncertain. Conventional score functions for these sets can misjudge cases where a multi-element set and a single-element set yield identical scores. The team introduced a hesitation degree into the score function, quantifying how much uncertainty an expert’s linguistic expression carries, so that more hesitant judgments are weighted accordingly. In the case study, this refinement changed the final ranking of the middle alternatives, evidence that the hesitation information embedded in expert language genuinely matters to the outcome rather than being mathematical decoration.

Clustering twenty or more experts into manageable subgroups poses its own trap. Grouping by preference similarity alone ignores the trust relationships that determine who actually influences whom; grouping by trust alone can lump together mutually trusting experts who hold wildly divergent views. The method fuses both signals into a comprehensive relationship matrix, blending preference similarity and normalized trust values with a balance coefficient, then applies K-Means clustering with the number of clusters chosen by the silhouette coefficient. Sensitivity tests across coefficient values from 0.0 to 1.0 showed that equal weighting produced the best clustering, the fewest consensus rounds, and the highest final consensus level, while relying on either signal alone degraded performance significantly. Expert and cluster weights are then computed from network topology, in-degree and out-degree in the trust graph, and credibility, using a Hamacher t-norm to fuse scale and credibility weights.

The real-world test replayed the emergency decision scenario sparked by the 2023 rainstorm, in which 33 people died in Beijing and more than one million people across the region were evacuated. Twenty simulated experts evaluated four emergency alternatives, spanning headcounts and medical treatment, safe transfer of trapped residents, infrastructure repair, and water rescue with secondary disaster management, across four attributes including personnel search and rescue, resource allocation, public opinion management, and timeliness. The initial group consensus level came out at 0.8599, below the emergency threshold of 0.9. The DDPG agent then generated a sequence of feedback parameters, starting conservatively at 0.2195 and escalating round by round to 0.5946, reaching the threshold in six iterations with a final consensus level of 0.9043.

Notably, the attribute weights were not set by the experts themselves. The team crawled more than 50,000 Weibo posts about the rainstorm and applied the TF-IDF algorithm to extract keyword frequencies, matching terms like search and rescue, relief supplies, and rumor control to the decision attributes. Personnel search and rescue emerged as the heaviest weighted attribute at 0.3051, followed by public opinion management at 0.2542. This grounds the final ranking of alternatives in the aggregate concern of the affected public, an unusual touch of democratic signal in a mathematical procedure. The comprehensive scores ranked the fourth alternative, focused on water rescue and secondary disaster control, as optimal, and the refined score function preserved that top ranking while reshuffling the middle options compared with the original function.

Head-to-head comparisons against three benchmark paradigms, a fixed-parameter feedback method, a random small-step adjustment method without reinforcement learning, and a traditional linearly increasing consensus approach, showed the DDPG method reaching consensus in 6.2 rounds for 50 experts versus 8.4, 12.4, and 10.5 respectively, with the gap widening as groups grew to 200 experts. The random method did preserve slightly more of the experts’ original preferences, but needed roughly twice as many rounds, a cost the authors argue is unacceptable when disaster conditions are changing by the hour. Simulated experiments with 20 to 200 experts, and with uniform, normal, and multimodal preference distributions, all reached the 0.9 threshold within eight rounds, with preference preservation rates between 0.65 and 0.73, suggesting the approach generalizes beyond the showcase case.

The authors are candid about the model’s central assumption: that experts adjust their opinions gradually according to the feedback intensity the agent prescribes. Real experts accept, reject, negotiate, or partially adopt suggestions, and the team flags modeling those behaviors as the next frontier of human-machine collaborative decision making. Even so, the study marks a meaningful shift in how consensus might be engineered, from static rules tuned by intuition to a learned policy that reads the live state of a debating group and modulates its pressure in real time. If such agents mature, the quiet work of reconciling expert disagreement in the next flood, wildfire, or pandemic could begin not in a tense conference room, but inside a neural network that has already rehearsed thousands of arguments.

Subject of Research: Reinforcement learning-based adaptive feedback consensus for large-scale group emergency decision making

Article Title: Machine-assisted adaptive feedback consensus method for large-scale group decision making based on reinforcement learning

Article References: Yu, H., Xu, X., & Zhang, W. (2026). Machine-assisted adaptive feedback consensus method for large-scale group decision making based on reinforcement learning. Frontiers in Big Data, 9, Article 1921037. https://doi.org/10.3389/fdata.2026.1921037

Image Credits: AI Generated

DOI: 10.3389/fdata.2026.1921037

Keywords: reinforcement learning, DDPG, large-scale group decision making, consensus reaching, hesitant fuzzy linguistic term sets, emergency decision making, Markov decision process, social network analysis, K-Means clustering, TF-IDF, human-machine collaboration, disaster response

The framework operates within a Pythagorean fuzzy multi-scale information system, a setting designed for situations in which different decision makers grade their assessments at different levels of granularity. One expert might rate a transportation option simply as poor, fair, or excellent, while another provides a finely tuned linguistic scale with seven or nine gradations. The researchers first deploy a recursive scale-expansion mechanism that converts these heterogeneous Pythagorean fuzzy evaluations into representations at different levels of granularity. Pythagorean fuzzy sets extend ordinary fuzzy logic by assigning each element both a membership degree and a non-membership degree whose squares must sum to no more than one, giving evaluators more room to express hesitation. The recursive mechanism ensures that opinions expressed at coarse scales can be consistently compared and merged with those expressed at fine scales without discarding information in the process.

What distinguishes the new framework from earlier consensus models is its refusal to treat decision makers as identical rational agents. Decades of behavioral economics research, most famously the work of Daniel Kahneman and Amos Tversky, have shown that real people distort probabilities, fear losses more than they value equivalent gains, and weigh unlikely events in systematically biased ways. The team captures this heterogeneity through a hybrid behavioral model that combines cumulative prospect theory with rank-dependent utility. Cumulative prospect theory describes how individuals evaluate gains and losses relative to a reference point, weighting outcomes by a distorted probability function, while rank-dependent utility transforms cumulative probabilities in a rank-ordered fashion. Merging the two yields five psychological parameters for each decision maker: sensitivity to gains, sensitivity to losses, a loss-aversion coefficient, and two curvature parameters describing probability distortion in the gain and loss domains.

Estimating these parameters is far from trivial, and the paper devotes a detailed appendix to the problem. The authors designed a structured questionnaire of nineteen binary choices, each pitting a sure outcome against a probabilistic lottery, following the standard elicitation paradigm in behavioral decision theory. Participants switch preferences at points that reveal their certainty equivalents for various lotteries, and those switching points allow the researchers to back out each parameter. Gain sensitivity, for example, is estimated from the ratio of the probability weighting at even odds to the logarithm of the normalized certainty equivalent, while the loss-aversion coefficient follows from the indifference gain and loss identified in a mixed gamble. Probability-weighting curvatures are fitted by least squares across probability levels ranging from one percent to eighty percent. The team notes that this choice-based approach reduces the cognitive burden on respondents and improves the reliability of the resulting estimates compared with direct questioning.

Once every decision maker carries a psychological profile vector, the framework clusters participants hierarchically according to the similarity of their estimated parameters. This step recognizes that a risk-seeking optimist and a loss-averse pessimist will interpret the same fuzzy evaluation in profoundly different ways, and that consensus mechanics should account for those differences rather than averaging them away. The clustering partitions the large group into subgroups of psychologically like-minded members, each of which can then be managed with its own consensus strategy. Within each subgroup, social network analysis takes over: by mapping who trusts, consults, or influences whom, the method computes degree-centrality weights that identify the most connected and persuasive individuals. Feedback and opinion adjustment are targeted at those influential members, amplifying the effect of each intervention without forcing every participant to revise their views repeatedly.

The second layer of the framework coordinates the subgroups themselves, and this is where machine learning enters the picture. A regularized graph attention network learns adaptive weights for the different clusters, attending more strongly to subgroups whose current positions matter most for closing the consensus gap. Graph attention networks compute weights dynamically from the structure and content of the network rather than fixing them in advance, which makes them well suited to the shifting landscape of a consensus process as opinions evolve across iterations. Crucially, the authors add a regularization term that penalizes excessive weight concentration, preventing the model from pouring all its attention into one dominant cluster and neglecting the tail of smaller groups whose agreement is still needed. The result is an inter-group negotiation that adapts its weighting scheme as the discussion progresses while remaining numerically stable.

To demonstrate the machinery in action, the researchers applied the framework to a real-world class of problem: selecting a low-carbon urban transportation scheme. Such decisions are ideal testbeds because they involve large panels of stakeholders, from traffic engineers to environmental planners, who naturally differ in both the precision of their assessments and their tolerance for risk about future costs and emissions. When the authors benchmarked their method against five representative group decision-making approaches, the double-layer framework reached the prescribed consensus threshold in fewer inter-group iterations and with lower total adjustment cost, meaning that experts had to modify their opinions less aggressively to reach collective agreement. The method also preserved more of the original evaluation information, an important consideration since forcing coarse or over-smoothed judgments erodes the very expertise that large panels are convened to harvest.

The team went beyond a single demonstration, subjecting the framework to both ablation studies and sensitivity analyses. In the ablation experiments, removing or disabling individual components—such as the behavioral clustering, the social-network-based influence weighting, or the regularization of the attention network—degraded performance, confirming that each element contributes measurably to the overall result. The sensitivity analyses varied key parameters across plausible ranges and found that the outcomes remained stable, suggesting that the method is not a fragile artifact of carefully tuned settings but a robust procedure that practitioners could realistically deploy. That robustness matters, because consensus models that only work under idealized conditions rarely survive contact with the noisy, deadline-driven environments of municipal planning and corporate strategy.

The implications extend well beyond transportation policy. Any setting in which many stakeholders with vague, multi-granularity information and divergent risk attitudes must converge—health technology assessment, disaster response planning, infrastructure investment, environmental regulation—could benefit from a consensus mechanism that respects both the uncertainty of the data and the psychology of the people. By uniting Pythagorean fuzzy mathematics, behavioral economics, social network analysis, and graph neural networks in a single coherent architecture, the Shanxi University team has sketched a template for what next-generation group decision support might look like: models that do not pretend humans are perfectly rational, information is perfectly comparable, or influence is perfectly flat, but instead build those imperfections into the mathematics of agreement itself. The work was supported by the Humanities and Social Sciences Research Project of the Ministry of Education of China, and the article is available open access.

Subject of Research: Group decision-making with multi-scale fuzzy information and behavioral preferences

Article Title: A double-layer consensus framework for group decision-making with multi-scale fuzzy information and behavioral preferences

Article References: Chai, M., Fan, J., Lu, J., Wu, M., Cheng, R., & Chen, R. (2026). A double-layer consensus framework for group decision-making with multi-scale fuzzy information and behavioral preferences. Complex & Intelligent Systems. https://doi.org/10.1007/s40747-026-02492-0

Image Credits: AI Generated

DOI: 10.1007/s40747-026-02492-0

Keywords: group decision-making, Pythagorean fuzzy sets, consensus framework, cumulative prospect theory, rank-dependent utility, social network analysis, graph attention network, behavioral preferences, multi-scale information system, loss aversion, machine learning, low-carbon transportation