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> The part of the impossibility proof that deals with dictators is subtle and neat. At first, I was convinced that the dictator was actually a "swing voter" who
by Wowfunhappy 2y ago
> The part of the impossibility proof that deals with dictators is subtle and neat. At first, I was convinced that the dictator was actually a "swing voter" whose power was entirely conditioned on the other voter's preferences, but that's not actually the case.
Based on the video, I am still convinced of this. Why is it not the case?
- dirtdobber 2y agoThe "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.