In a 2017 paper, later presented at the Web and Internet Economics conference, titled ``Sequential Deliberation for Social Choice", the authors propose a mechanism in which a series of agents, are tasked to negotiate over a set of decisions S. Building on assumptions of Nash Bargaining and assuming the decision space follows the median graph, the authors constructed a robust algorithm which approximates the decision which minimizes the social cost to the entire population. In this paper, we give a brief overview of the background theory which this paper builds upon from foundational work from Nash, and social choice results which hold true in Condorcet mechanisms. Following this analysis, we consider the stability of the results in the paper with different deviations from Nash equilibrium. These deviations could be pessimal, in the context of unequal bargaining power (say in a labor market) or constructive, as in the context of opinion dynamics. Our analysis is observatory, in the context of simulations, and we hope to formalize the results of these simulations to get an understanding of more general properties in spaces beyond our simulation.

翻译：2017年发表并后续在Web与互联网经济学会议上展示的论文《社会选择的序贯协商》中，作者提出了一种机制：一系列主体被委托就决策集S进行协商。基于纳什讨价还价假设，并假设决策空间遵循中位数图，作者构建了一种鲁棒算法，该算法能够逼近使全体社会成本最小化的决策。本文首先简要概述该论文所依托的纳什基础工作及孔多塞机制中成立的社会选择结果。在此基础上，我们考察了论文结果在偏离纳什均衡情形下的稳定性——这些偏离可能具有消极性（如劳动市场中讨价还价能力不对等的情况），也可能具有建设性（如意见动态中的情形）。我们的分析基于仿真观察，并期望通过形式化这些仿真结果，以理解超出仿真范围的更一般空间中的属性。