Status Quo Bias and Hidden Condorcet Cycles in Binary Referendums

In most real-life binary referendums, there are several alternatives that potentially can challenge the status quo alternative. Depending on which alternative that is selected, the voters are also differently likely to caste their vote on it. The fact that there are several potential challenger alternatives also means that there may exist Condorcet cycles that only can be identified by taking into account the alternatives that not are listed on the ballot. We analyse such "hidden" cycles in a simple theoretical framework where Condorcet cycles cannot exist, but may emerge when taking into account that voters often experience a reluctance to abandon the status quo alternative. Necessary and sufficient conditions for the existence of hidden Condorcet cycles are derived and a Monte Carlo simulation finds (in different scenarios) that the probability is roughly one percent.