  The division of a social group into subgroups with opposing opinions, which
we refer to as opinion disparity, is a prevalent phenomenon in society. This
phenomenon has been modeled by including mechanisms such as opinion homophily,
bounded confidence interactions, and social reinforcement mechanisms. In this
paper we study a complementary mechanism for the formation of opinion disparity
based on higher-order interactions, i.e., simultaneous interactions between
multiple agents. We present an extension of the planted partition model for
uniform hypergraphs as a simple model of community structure and consider the
hypergraph SIS model on a hypergraph with two communities where the binary
ideology can spread via links (pairwise interactions) and triangles (three-way
interactions). We approximate this contagion process with a mean-field model
and find that for strong enough community structure, the two communities can
hold very different average opinions. We determine the regimes of structural
and infectious parameters for which this opinion disparity can exist and find
that the existence of these disparities is much more sensitive to the triangle
community structure than to the link community structure. We show that the
existence and type of opinion disparities are extremely sensitive to
differences in the sizes of the two communities.
