We study a model of opinion formation and analyze the link between network architecture and the “left-right spectrum” that frequently characterizes opinions and beliefs. We correct a key result of DeMarzo, Vayanos and Zwiebel (QJE, 2003) who claim that after some time, an agent’s position on a set of different issues will always be either “left” on all of those issues or “right” on all of those issues. We provide counterexamples to this claim and show that in the long-run an agent’s position can flip-flop between “left” on all issues and “right” on all issues indefinitely. However, we provide necessary and sufficient conditions for a stable left-right characterization of opinions to be possible in the long run. Roughly, a flip-flop will occur when agents give relatively little weight to the opinions of agents with similar political positions (including themselves). Following this intuition, we show that a simple sufficient condition is that agents become “stubborn” over time and give little weight to the opinions of others. Finally, we characterize classes of networks in which it is possible for agents to flip-flop between “left” and “right” indefinitely. We argue that qualitatively, these results are robust to alternative models of opinion formation.