It's not just the political spectrum. You need at least 2 spatial dimensions to demonstrate the possibility of non-transitive group preferences (i.e. the commun

It's not just the political spectrum. You need at least 2 spatial dimensions to demonstrate the possibility of non-transitive group preferences (i.e. the community prefers candidate A > B > C > A), which is one fundamental reason Arrow's impossibility theorem is true. If candidates are just on a number line, then the group's preferences would always be transitive and there would always be a Condorcet winner (or a tie).