Social networks play an important role in analyzing the impact of individual-level interactions on societal or economic outcomes. We model interactive decision making for a community of individuals with different traits, represented by a social network with trait-attributed nodes. We develop a deterministic process generating a sequence of choices for each individual based on a trait-attributed social network, initial choices of individuals and a set of predetermined trait-dependent rules for making decisions. The object of interest is the sequence of cumulative sum of choices over all individuals, which we call the cumulative sequence and consider as an index of collective decisions. We observe that, in a time period, a cumulative sequence can be unpredictable or predictable showing a repeated pattern either escalating to an extreme or constantly oscillating. We consider that predictable cumulative sequences represent unstable collective decisions of communities either extremizing or internally conflicting, while unpredictable cumulative sequences show stable changes. We analyze the effects of network topology and trait distribution on the probability of cumulative sequences being predictable, escalating and oscillating by simulations. Our findings include that unstable collective decisions are more probable as network density increases, that centralized networks are more likely to have unstable collective decisions and that networks with excessively clustered or scattered conformists and rebels tend to produce unstable cumulative sequences. We discuss the potential of the model as a framework for studying individuals with different traits on a social network directly and indirectly interacting in decision making.