Anchoring influences how groups reach decisions over time
Anchored Sequential Deliberation
Computer Science and Game TheoryMultiagent Systems
Summary
This paper looks at how groups make decisions when two people talk and update the group’s choice step by step. The authors study what happens if people are influenced or anchored by the previous decision outcome when negotiating. They find that stronger anchoring slows how fast opinions change but tends to keep decisions closer to the best overall choice. Their math shows how this balance works and predicts stable decisions around certain points. Simulations confirm that anchoring shapes both the speed and quality of group decisions.
What this means in practice
- •For group decision facilitators: Design decision processes that balance influence of past proposals with fresh input to achieve stable group outcomes.
- •For online platform designers: Build negotiation tools that tune anchoring strength to control how fast consensus forms and how close it is to optimal.
A theory result. No direct application yet.
Authors
Sijing Tu, Ashish Goel
Abstract
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 reference point for the next round. Existing theory by Fain et al.~\cite{fain2017sequential} treats the current outcome solely as the disagreement alternative in bargaining. Yet an existing draft, policy, or proposal might carry social influence and anchor participants' expressed positions toward the status quo. We introduce anchored sequential deliberation on a one-dimensional decision space. In each round, two participants with bliss points $U$ and $V$ shift their positions toward the previous outcome $O_{t-1}$ with anchoring strength $λ$, then Nash-bargain using $O_{t-1}$ as the disagreement alternative. The update simplifies to $O_t=(1-λ)\mathsf{Median}\{U,V,O_{t-1}\}+λO_{t-1}$. We establish a convergence--stability trade-off. For every population distribution and $λ<1$, the process has a unique stationary distribution. A monotone coupling yields a $1$-Wasserstein contraction factor of at most $\frac{1+λ}{2}$ and at least $λ$; thus, stronger anchoring slows mixing. On the other hand, stationary social cost weakly decreases with $λ$, although the worst-case distortion remains $\frac{1+\sqrt{2}}{2}$. We also identify a unique \emph{deliberative fixed point}, where the expected unanchored movement is zero, and prove that the stationary distribution concentrates around it as $λ\to 1$. For the uniform population, stationary distortion lies between $1+\frac{1-λ}{9+7λ}$ and $1+\frac{1-λ}{6(1+λ)}$, with both bounds approaching $1$ as $λ\to1$. Simulations for uniform and Beta populations show that stronger anchoring slows mixing, concentrates the stationary distribution, and lowers stationary distortion in these instances.