Let’s prove, using colour coded diagrams to follow the argument visually, why group decisions, from democracy to take-away choice, are always flawed.

‘Flawed’ is a judgement. Arrow never said that any group decisions are ‘wrong’ or ‘bad,’ per se… only that they don’t necessarily reflect the aggregate underlying choices of the individuals involved. That’s the paradox.

(and, BTW, Arrows ‘group decisions’ involve three or more distinct choices, so pizza v. salad is irrelevant here… It would have to be pizza v salad v ice cream or something similar…)