The Effect of Iterativity on Adversarial Opinion Forming

Understanding how opinions are formed is as important as ever, as the spread of misinformation becomes more prevalent every day. Assume there is some new innovation being either good or bad that is introduced to a group of people who want to form their (binary) opinion about it. Following a key insight by Rogers [22], the opining forming process can be modelled as follows. At first, a small set of so-called early adopters, or experts, forms their opinion about the newly introduced innovation. Afterwards, they disseminate their opinion to all other non-experts in the network. When looking at that network from the outside an observer wants to infer the quality of the new innovation by observing the opinion of all individuals, but without taking the actual structure of the network into consideration (maybe by doing a poll). One popular method to achieve this is using the wisdom of the crowd. In this case that corresponds to a simple majority rule, that is, the observer takes the majority of opinions as an estimate. Wisdom of the crowd has been shown to have a plethora of useful applications in decision making, see e.g.