We consider the problem of multi-choice majority voting in a network of $n$ agents where each agent initially selects a choice from a set of $K$ possible choices. The agents try to infer the choice in majority merely by performing local interactions. Population protocols provide a framework for designing pairwise interactions between agents in order to perform tasks in a coordinated manner. In this paper, we propose ``Broadcasting Population Protocol" model as a counterpart model of conventional population protocols for the networks that each agent can send a message to all its neighbors simultaneously. We design two distributed algorithms for solving the multi-choice majority voting problem in the model of broadcasting population protocols. We prove the correctness of these algorithms and analyze their performance in terms of time and message complexities. Experiments show that the proposed algorithm improves both time and message complexities significantly with respect to previous algorithms proposed in conventional population protocols and they can be utilized in networks where messages can be transmitted to a subset of agents simultaneously such as wireless networks.