We consider opinion diffusion on social graphs where agents hold opinions and where social pressure leads them to conform to the opinion manifested by the majority of their neighbors. Within this setting, we look for dynamics that allows us to maximize the diffusion of a target opinion given the initial opinions of all agents. In particular, we focus on the setting where more than two opinions are available to the agents, and we show that the properties of this setting are entirely different from those characterizing the setting where agents hold binary opinions only. Indeed, while it is well-known that greedy dynamics are always optimal ones in the binary case, this is no longer true in our more general setting and—rather surprisingly—even if just three opinions are available. Moreover, while it is possible to decide in polynomial time if a dynamics leading to consensus exists when agents have two available opinions, the problem becomes computationally intractable with three opinions, regardless of the fraction of agents that have the target opinion as their initial opinion.

我们考虑社会图上的观点扩散，在这些图中代理人持有观点，社会压力促使他们遵循大多数邻居所表达的观点。在这种情况下，我们寻找动态因素，使我们能够根据所有代理的初始意见最大化目标意见的传播。特别是，我们关注于代理可以使用两个以上观点的设置，并且我们证明了此设置的属性与那些仅代表代理持有二元观点的设置的特征完全不同。的确，虽然众所周知，贪婪动力学在二元情况下始终是最优的，但在我们更一般的情况下（甚至令人惊讶的是，即使只有三种观点也是如此），情况不再如此。而且，