In Iterative Voting, voters first cast their ballots but may change their minds upon observing the ballots of others. Previous models have extended Iterative Voting to the incomplete information domain of social networks, where voters only observe the ballots of their friends. However, these models are based on computationally-intensive calculations of expected utilities. We propose a framework of bounded rationality for voters situated in social networks. Using this framework, we propose and test a number of heuristics that reduce the computation required for optimal strategic reasoning by several orders of magnitude compared to previous work, while retaining similar qualitative behaviors. These heuristics enable us to conduct simulations on how the size of the voting population affects strategic behavior. To illustrate the effectiveness of our approach, we apply our heuristics to explore the Micromega rule --- an observation in political science that large political parties favor small assemblies. We find that the size of electoral districts is a contributing factor to the Micromega rule in some networks. Fringe candidates retain more support in smaller districts, while larger parties dominate in larger districts.