It took me a while to find the statement of the theorem. For other readers like me, starting at page 5 might help.
It's about how it is impossible for democracies to simultaneously satisfy certain desirable traits.
It's about how it is impossible for democracies to simultaneously satisfy certain desirable traits.
The page member rfreytag indicates, https://mises.org/wire/arrows-impossibility-theorem-exposes-... , has a very good explanation.
Edit: I realize there could be another (suggestive) way to express it: at least in the (theoretically possible) cases where preferences show a cyclic pattern (when similar numbers of voters claim A>B>C, C>A>B, B>C>A), there is no """optimal""" way to determine a collective preference.
Edit: there is again another nice way to express it - member ajennings shows it at the end of his video (see nearby) with a simulation: if when all voters express preference for an option the outcome reflects that ("unanimity"), and we take a decision in the controversial scenarios, and we demand that the collective preference between two alternatives will be a function of the preferences individual voters claim about those two alternatives ("relevance"), then one ordered list of preferences will make the others uninfluent ("dictatorship").
This is the rational response to Arrow's theorem - not to cynically conclude all voting systems are "bad", or that "dictatorship" makes some sort of sense, but rather just to say that if there's a rock-paper-scissors situation among the top candidates, one of them should win.