We study a majority based preference diffusion model in which the members of a social network update their preferences based on those of their connections. Consider an undirected graph where each node has a strict linear order over a set of $\alpha$ alternatives. At each round, a node randomly selects two adjacent alternatives and updates their relative order with the majority view of its neighbors. We bound the convergence time of the process in terms of the number of nodes/edges and $\alpha$. Furthermore, we study the minimum cost to ensure that a desired alternative will ``win'' the process, where occupying each position in a preference order of a node has a cost. We prove tight bounds on the minimum cost for general graphs and graphs with strong expansion properties. Furthermore, we investigate a more light-weight process where each node chooses one of its neighbors uniformly at random and copies its order fully with some fixed probability and remains unchanged otherwise. We characterize the convergence properties of this process, namely convergence time and stable states, using Martingale and reversible Markov chain analysis. Finally, we present the outcomes of our experiments conducted on different synthetic random graph models and graph data from online social platforms. These experiments not only support our theoretical findings, but also shed some light on some other fundamental problems, such as designing powerful countermeasures.

翻译：我们研究了一种基于多数偏好的偏好扩散模型，在该模型中，社交网络成员根据其连接者的偏好更新自身偏好。考虑一个无向图，其中每个节点对 $\alpha$ 个备选方案具有严格线性序。在每个轮次中，一个节点随机选择两个相邻备选方案，并根据其邻居的多数观点更新它们的相对顺序。我们根据节点数/边数和 $\alpha$ 来界定该过程的收敛时间。此外，我们研究了确保某个期望备选方案在过程中“获胜”的最小代价，其中占据节点偏好顺序中的每个位置都有代价。我们针对一般图和具有强扩展性质的图，给出了最小代价的紧界。进一步地，我们研究了一个更轻量级的过程：每个节点均匀随机选择其一个邻居，并以某个固定概率完全复制该邻居的偏好顺序，否则保持不变。我们使用鞅和可逆马尔可夫链分析，刻画了该过程的收敛性质，包括收敛时间和稳定状态。最后，我们展示了在不同合成随机图模型和在线社交平台图数据上进行的实验结果。这些实验不仅支持了我们的理论发现，还揭示了其他基本问题，例如设计有效的对抗措施。