Arrow's impossibility

Imagine we want any good voting method to obey these rules. If every single person prefers A over B, then A should finish above B. No one person should always get their way no matter what everyone else wants (no dictator). Whether A ranks above B should depend only on how people compare A and B. It should not flip just because someone changes their opinion about a third option C.

These feel like minimum requirements. Arrow's theorem shows that when there are three or more candidates, no ranked voting system can satisfy all three rules at the same time.

Any method you choose must break at least one. Some methods let a third candidate spoil the result between the other two. Some give one voter effective dictatorial power in certain situations. Some ignore unanimous preferences in edge cases. The theorem does not say democracy is impossible; it says every voting rule makes a compromise somewhere.