On status quo bias and the existence of Condorcet cycles in binary voting situations

In most real-life binary voting situations, multiple challenger alternatives can potentially contest the status quo alternative, but only one of them can be listed on the ballot. Consequently, Condorcet cycles cannot be detected by analyzing voting data alone, even when they exist. This paper considers a standard theoretical framework where Condorcet cycles cannot exist, but demonstrates that this need not be the case when voters experience status quo bias. Necessary and sufficient conditions for the existence of Condorcet cycles are provided. Monte Carlo simulations predict the probability that Condorcet cycles exist in binary voting situations with status quo bias to roughly one percent under different assumptions and scenarios.