复杂网络视角下基于非二元偏好的投票理论与方法

Based on the research achievements of complex networks and group decision-making, this project will use graph theory, game theory,order theory, probability and statistics, and topology etc. tools in order to build a complex-voting theory and method system, considering the uncertainty factors (including the recessive and dominant) in large voting problems and preference without binariness. The main contents of the project as follows: ① Based on mass group-voting problems using the order theory and complex network theory to build structure model and analyze the network structure, reveal the multidimensional nature of the network structure and explore the determining rules and determining methods for the key element, network center and the minimum decision subgroup.② Based on non-binary preference voting question, the research will focus on the mechanism of voters' preference clarity and measure method of voters' priori and posteriori multidimensional voting power.③To construct the voting and decision rules which can portray the preferences and voting power of group members, the aggregation method for group decision making and evolutionary mechanism of group view based on voting power are studied.④To evaluate the decision-making capacity of decision systems,the robustness of the complex group-decision network is researched from three perspectives, the voting results, network structure and voting rule.⑤The application research will be given, and its main task is researching how to implement complex voting decision. The project intends to use the election of grassroots cadres that voting power not entirely obvious, personnel relations complicated and multi-voters as a case, summarize and improve decision-making method and theory to solve practical problems. Results of this project will not only increase the fusion with the traditional group decision theory, but also promote the development of decision science.

以复杂网络和群体决策的研究成果为基础,在非二元选择环境下考虑大群体投票问题中的不确定性因素,运用图论、博弈论、序理论、概率统计和拓扑学等工具,构建复杂投票理论与方法体系。主要内容:①借助序理论与复杂网络理论构建复杂网络系统的结构模型,揭示网络结构的多维性质，探索关键元、网络中心及最小决定子群的确定规则及确定方法；②基于非二元偏好投票问题,投票者偏好明晰化的机理及投票者的先验与后验多维表决权的测度方法；③构建能刻画群体成员偏好和表决权的投票与决策规则,研究基于表决权的群决策结果形成机制与集结方法；④从投票结果、网络结构及投票规则三个视角评价决策系统决策能力的鲁棒性；⑤应用研究:研究实施复杂投票决策的步骤,拟以多投票者及其表决权不完全明显、人员关系复杂的基层干部选举为案例,总结和提升投票决策解决实际问题的理论和方法。本项成果将增进与传统群决策理论的融合，以推进决策科学的发展。

以复杂网络和群体决策的研究成果为基础,在非二元选择环境下考虑大群体投票问题中的不确定性因素,运用图论、博弈论、序理论、概率统计和拓扑学等工具,构建复杂投票理论与方法体系。主要内容:①借助序理论与复杂网络理论构建复杂网络系统的结构模型, 在不同类型结构网络上进行投票决策模型的演化模拟，将不同投票规则在复杂网络上进行模拟；②基于非二元偏好投票问题,在网络视角下研究投票者偏好明晰化的机理及影响因素、投票者的先验与后验多维表决权、权威度的测度方法，考虑社会学习行为对决策权力的影响，并进行对比仿真研究；③构建了能刻画群体成员偏好和表决权的投票与决策规则,研究基于表决权的群决策共识机制与集结方法；针对传统投票问题假设投票者各自独立投票，表明投票者之间不存在协商或信任传递的研究现状，事实上投票者之间的信任网络存在且观点时常交互，结合先验与后验信息及渗流理论，构建了基于条件随机场的投票概率估计模型，提出一种基于信任传递网络的信任度测量算法,并基于此,利用投票者在观点演化后的收敛值预测出投票者的最终选票，进而模拟群体决策结果的演化过程及影响因素和鲁棒性；④从投票结果、网络结构及投票规则三个视角评价决策系统决策能力的鲁棒性，给出有效性判定条件，在社会网络视角的投票框架下，构建了全局最优候选人作为投票规则的评价标准，该标准能够更准确地衡量Condorcet规则与多数赞成规则所选获胜者偏离投票群体真实意愿的程度；⑤揭示了网络结构的多维性质，基于渗流理论及投票网络的信任度传递机制探索关键元（影响力最大点）、网络中心及最小决定子群的确定规则及确定方法，通过应用实例总结和提升投票决策解决实际问题的理论和方法，本项成果将增进与传统群决策理论的融合，以推进决策科学的发展。