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 $α$ 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 $α$. 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.