Cross-correlation patterns in social opinion formation with sequential data

Recent research on large-scale internet data suggests existence of patterns in the collective behavior of billions of people even though each of them may pursue own activities. In this paper, we interpret online rating activity as a process of forming social opinion about individual items, where people sequentially choose a rating based on the current information set comprising all previous ratings and own preferences. We construct an opinion index from the sequence of ratings and we show that (1) movie-specific opinion converges much slower than an independent and identically distributed (i.i.d.) sequence of ratings, (2) rating sequence for individual movies shows lesser variation compared to an i.i.d. sequence of ratings, (3) the probability density function of the asymptotic opinions has more spread than that defined over opinion arising from i.i.d. sequence of ratings, (4) opinion sequences across movies are correlated with significantly higher and lower correlation compared to opinion constructed from i.i.d. sequence of ratings, creating a bimodal cross-correlation structure. By decomposing the temporal correlation structures from panel data of movie ratings, we show that the social effects are very prominent whereas group effects cannot be differentiated from those of surrogate data and individual effects are quite small. The former explains a large part of extreme positive or negative correlations between sequences of opinions. In general, this method can be applied to any rating data to extract social or group-specific effects in correlation structures. We conclude that in this particular case, social effects are important in opinion formation process.