Comments by "Mikko Rantalainen" (@MikkoRantalainen) on "Why Democracy Is Mathematically Impossible" video.

I think that the rated voting system (approval voting) is simple to understand but it would result in strategic voting because if you have one good candidate X and one barely acceptable candidate Y, you don't want to select X+Y in the election because that would give too much power to Y. Many would rather just vote for X to avoid ending getting Y selected in case it would be the logically 2nd best option for many people but never the best option for anybody. If you actually wanted to have regression to mean though, this would be the way to go. I'd rather want a voting system that can switch to radically different candidate if majority of the people voted for him or her. It seems to me that the least bad option would be to use Condorcet voting system with Schulze ranking. The bad part of that system is that it's next to impossible to easily calculate by hand. In practice, we would need to use computers to calculate the initial result and hand calculation could be later used to confirm the result. However, you wouldn't need to trust random computer but every interested voter could take the whole list of votes (this would obviously need to be public) and run the program of their choice on a computer of their choice to verify the official voting results.
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I think the "pivotal voter" example is an artifial problem that doesn't happen in reality. It basically argues that if the voting results were otherwise perfectly tied, there must not be a new ballot that tips the balance one way or another because the voter with the new ballot could be declared as "dictator" because it broke the tie. If you want to avoid nearly arbitrary results for near perfect ties, just compute the pairwise ranking between the resulting ranking and if the winner doesn't win with at least 1% margin, organize a new round of voting. This would force another round of voting until enough people adjust their ballots so that at least 1% margin between the best and second best candidate can be found. The change of resulting in more than two rounds would be practically zero with real world humans as the voters as long as you make the results of previous round public.
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