# Single Peaked Preferences and Condorcet Cycles [closed]

How can you prove the theorem that Single peaked preferences imply that there are no Condorcet cycles

Here, the space of alternatives is 2-dimensional, and there is no natural way to define a linear order on $$\mathbb R^2$$. Voters' preferences are still single-peaked in the sense that each voter has only one bliss point. As a result, we cannot rule out cycling (non-existence of Condorcet winner) as is shown in the example.