发表机构
Management Science and Engineering, Stanford University（斯坦福大学管理科学与工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出锚定序贯审议机制，在序贯谈判中引入现状锚定，证明收敛与稳定性的权衡，并给出平稳失真界，表明强锚定虽减慢混合但降低社会成本。
AI 中文摘要
序贯审议是一种集体决策机制：在每一轮中，均匀随机选择的一对参与者被要求修订集体结果，该结果随后成为下一轮的参考点。Fain等人~\ncite{fain2017sequential}的现有理论将当前结果仅视为谈判中的分歧替代方案。然而，现有的草案、政策或提案可能带有社会影响力，并将参与者的表达立场锚定在现状上。我们在一个一维决策空间上引入了锚定序贯审议。在每一轮中，具有理想点$U$和$V$的两名参与者以锚定强度$\lambda$将其立场向先前结果$O_{t-1}$移动，然后使用$O_{t-1}$作为分歧替代方案进行纳什谈判。更新简化为$O_t=(1-\lambda)\mathsf{Median}\{U,V,O_{t-1}\}+\lambda O_{t-1}$。我们建立了收敛性与稳定性之间的权衡。对于每个总体分布和$\lambda<1$，该过程具有唯一的平稳分布。单调耦合产生至多$\frac{1+\lambda}{2}$且至少$\lambda$的$1$-Wasserstein收缩因子；因此，更强的锚定会减慢混合速度。另一方面，平稳社会成本随$\lambda$弱递减，尽管最坏情况失真仍为$\frac{1+\sqrt{2}}{2}$。我们还确定了一个唯一的\emph{审议不动点}，其中预期的未锚定运动为零，并证明随着$\lambda \to 1$，平稳分布集中在其周围。对于均匀总体，平稳失真介于$1+\frac{1-\lambda}{9+7\lambda}$和$1+\frac{1-\lambda}{6(1+\lambda)}$之间，且随着$\lambda\to1$，两个界限都趋近于$1$。针对均匀和Beta总体的模拟表明，更强的锚定会减慢混合速度，使平稳分布更集中，并在这些实例中降低平稳失真。
英文摘要
Sequential deliberation is a mechanism for collective decision making: at each round, a uniformly randomly selected pair is asked to revise a collective outcome, which then becomes the input for the next round. Existing theory by Fain et al.~\cite{fain2017sequential} treats the current outcome solely as the disagreement alternative in bargaining. Yet the existing outcome might also carry social influence and anchor participants' positions toward the status quo. In this paper, we introduce \emph{anchored sequential deliberation}. At each round, two participants with bliss points $U$ and $V$ shift their positions toward the previous outcome $O_{t-1}$ with anchoring strength $0\leq λ<1$. They then bargain using $O_{t-1}$ as the disagreement alternative. For the sake of analysis, we assume that the decision space is one-dimensional, the anchoring effect is linear, and participants use Nash bargaining. The update simplifies to $O_t=(1-λ)Med\{U,V,O_{t-1}\}+λO_{t-1}$. Our analysis reveals a trade-off. Through a coupling of two outcomes, we find that the process contracts in $1$-Wasserstein distance with a factor of at most $\frac{1+λ}{2}$, which implies that stronger anchoring slows mixing. On the other hand, stationary distortion weakly decreases with $λ$, although the worst-case distortion remains $\frac{1+\sqrt{2}}{2}$ for every feasible $λ$. We also identify a unique \emph{deliberative fixed point}, at which the expected movement is zero, and prove that the stationary distribution concentrates around it as $λ$ increases. For symmetric populations, we further provide a tighter bound on the stationary variance around this fixed point. For the uniform distribution, we establish upper and lower bounds on stationary distortion, both of which approach $1$ as $λ$ increases.
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