The "no dictator" property states that a single voter should not override the preferences of the majority. For example, if every voter (excluding the dictator)

The "no dictator" property states that a single voter should not override the preferences of the majority. For example, if every voter (excluding the dictator) prefers candidate A over candidate C, then the dictator should not be able to control the outcome so that candidate C is ranked higher than candidate A. If you follow the proof closely (it's very subtle) you can see that despite every candidate ranking A over candidate C, the actual preferential outcome will have candidate C ranked higher than candidate A (and this is entirely dependent on the dictator's choice). In other words, there's a counterexample where every single voter decides to rank A > C, and yet the dictator alters the outcome so that C > A. This is different from a swing voter that pushes one candidate over the top in a very close race.