In light of the recent popularity of online social networking websites and the increasing number of users consuming political content on these websites, the study of opinion formation in online settings is more relevant than ever before. Crucial to this study is social influence, a fundamental sociological concept that serves as the micro-mechanism to theories about cohesion, social distinction, and political polarization. On the one hand, there is a very rich theoretical literature studying the collective outcomes of social influence in networks. On the other hand, existing models are based on many competing assumptions about influence and empirical research testing these competing assumptions remains scarce. In particular, attempts to find negative influence, the tendency to increase opinion differences to disliked sources of influence, have so far remained fruitless, often criticized for being based on problematic sampling approached and inadequate experimental design.

We introduce a general theoretical model of social influence that is able to capture the most prominent assumptions about social influence. Next, we conduct a power analysis in order to inform the design a laboratory experiment able to test these competing assumptions against each other. In particular, we derive conclusions about a study’s necessary sample size, and prior opinion distribution.

Various mechanisms have been proposed that could explain observed opinion shifts, both at the individual and group level. These mechanisms largely fall into three categories: assimilation, distancing and alignment of opinions. There is, however, not yet an integrative framework that could explain when what type of influence is experienced. This is important since neither mechanism alone can explain the patterns of opinion polarization and convergence that we observe in society. When bridging the micro-macro gap in the opinion dynamics literature, a strong empirical basis for the behavioral rules that govern opinion change is required.

In order to test the three influence mechanisms we present a general theoretical framework that researchers can apply in experimental settings where fine grained data on pre and post stimulus opinion measurement are available. First, the broad landscape of social-influence theories is integrated into two hybrid formal models: a linear social influence and a so-called bounded confidence model. With these two models, we are able to distinguish between the experienced influence direction and strength, and the general persuasiveness of an argument, as a function of opinion discrepancy. Estimating the core parameters of the two models proves particularly challenging since survey measurement as well as behavioral measurement of opinions is usually truncated, resulting in odd-shaped multimodal distributions even for latent Gaussian distributed traits. Detailed power analyses with simulated datasets provide confidence in the estimation method and identify the most volatile model parameters.

Second, a general experimental setting is presented that could be applied in different contexts wherein -or subjects on which- opinion change is expected. Various conditions under which the influence function might differ are discussed. Lastly, an example of such a setting is presented in which we maximize opinion discrepancy in order to find out whether there is empirical evidence of negative influence.