We show that the Matthew effect, or Matthew mechanism, was present in the artificial cultural market Music Lab in one-fourth of the "worlds" when social influence between individuals was allowed, whereas this effect was not present in the "world" that disallowed social influence between individuals. We also sketch on a class of social network models, derived from social influence theory, that may generate the Matthew effect. Thus, we propose a theoretical framework that may explain why the most popular songs could be much more popular, and the least popular songs could be much less popular, than when disallowing social influence between individuals.