  The outcome of an election depends not only on which candidate is more
popular, but also on how many of their voters actually turn out to vote. Here
we consider a simple model in which voters abstain from voting if they think
their vote would not matter. Specifically, they do not vote if they feel sure
their preferred candidate will win anyway (a condition we call complacency), or
if they feel sure their candidate will lose anyway (a condition we call
dejectedness). The voters reach these decisions based on a myopic assessment of
their local network, which they take as a proxy for the entire electorate:
voters know which candidate their neighbors prefer and they assume -- perhaps
incorrectly -- that those neighbors will turn out to vote, so they themselves
cast a vote if and only if it would produce a tie or a win for their preferred
candidate in their local neighborhood. We explore various network structures
and distributions of voter preferences and find that certain structures and
parameter regimes favor undemocratic outcomes where a minority faction wins,
especially when the locally preferred candidate is not representative of the
electorate as a whole.
