Socially-aware Multi-Agent Systems （MASs） rely on leadership structures to enhance collaborative decision-making efficiency， but are vulnerable to privacy leakage risks caused by the analysis of state trajectories in Markov Decision Processes （MDPs）， exposing critical nodes to targeted attacks. To address these challenges， a Virtual Leader Minimal Dependency Privacy protection strategy （VLMDs-Privacy） was proposed， which achieved secure and efficient collaborative decision-making in MAS through the following methods： 1） A State Transition Adaptive Differential Privacy mechanism （STADP） was designed to establish a dynamic mapping between state-transition probabilities and privacy budgets， protecting MDP state trajectories from reverse inference attacks； 2） A Virtual Leader Minimal Dependency strategy （VLMDs） was developed to reduce reliance on virtual leaders while achieving globally optimal decision-making， thereby significantly improving resistance to single-point failures； 3） A privacy-efficiency dual-regulation mechanism was constructed to dynamically allocate privacy budgets based on agent behavior credibility， achieving an adaptive trade-off between social awareness and privacy protection. Experimental results showed that under a strong privacy constraint （ \epsilon = 0.1）， VLMDs-Privacy achieved an average arrival success rate of 94.2% in navigation and dynamic maintenance scenarios， outperforming the conventional leader-based differential privacy scheme VLDPs-Privacy （27.9%） by 66.3 percentage points， with only a 3.3% drop compared to non-private settings. These findings validate the robustness of VLMDs-Privacy in maintaining system collaboration capability and privacy preservation efficiency under strong privacy constraints， providing theoretical and technical support for collaborative decision-making in privacy-sensitive MAS deployed in open environments.