In this paper, we show that for elections in distributed systems the conversion from non-binary choices to binary choices does not always provide optimal results when the preferences of nodes are not identical. With this observation, we study the problem of conducting democratic elections in distributed systems in the form of social choice and social welfare functions with three or more candidates. We present some impossibility and possibility results for distributed democratic elections in presence of Byzantine behavior. We also discuss some existing election schemes, and present a new approach to counter the effects of Byzantine votes. We analyze the performance of these schemes through simulations to compare their efficacy in producing the most desirable social welfare rankings.