I have seen a few too many voting-system presentations that all seem to have a few of the same common arguments, arguments that I believe are flawed.

Here I can isolate it to these statements. First, "The whole point of the election was to force the group to make a choice about an ice cream flavor." This is false. The election's point was to interpret the preference of the electorate. We then use that preference to come to a choice. In the cyclic cases, this is no failure of the voting system. This is an accurate portrayal that the group is not able or ready to come to a decision.

"In its inability to identify a clear winner, ranked voter has failed in its primary task." This is also not true. It was not its primary task, and didn't fail at all. It succeeded wildly in identifying a confusion in the electorate itself.

Of course any attempt to "break that tie" will be flawed and invalid.

For those who don't know, the video up to that point explored Condorcet Voting, and the Condorcet Winner criteria. The existence of a cycle is known as a Smith Set or Schwartz Set (subtly different, but very similar). Tiebreaking methods to elect single winners from Schwartz Sets are all flawed, but that does not mean the Condorcet Winner method is flawed.

Elimination Voting is more commonly known as Instant Runoff voting. In his example at 7:04, this is again a Schwartz Set. So it's improper to declare that one of the three flavors is a winner, because the electorate is inherently undecided. The gold coins scenario changes nothing; it is still a cycle, and the electorate is still undecided. So the tiebreaker chooses a different winner - it doesn't really matter, because it is already invalid to pick a winner in that scenario.

But the bigger problem with IRV (elimination voting) is that it will sometimes pick the wrong winner even when there ISN'T a cycle. This is awful.

Finally, the presenter glosses over his description of Arrow's Theorem. You can practically hear the parentheses when he says, "given certain assumptions". In truth, not all voting criteria are the same. All Arrow's Theorem does is say you can't simultaneously meet four criteria, that he chose, in all cases. It does not prove that those four criteria are required. One of those criteria, the "Independence of Irrelevant Alternatives" criteria, is particularly problematic - and if I recall correctly, it can only move an election from a Condorcet Winner to a Schwartz Set. It cannot itself select a new winner entirely. And in my view, that is not a problem, because if adding a new candidate creates a Schwartz Set, then it only means that the electorate was probably not given enough choice from the outset. Although, there is a counterpoint that says that if you give voters more and more choice, cycles will inevitably occur.

So really when we're talking about voting theory, the entire problem with the subject is that we are conflating two needs. The first need is to measure the public's preference for a choice. But the other need is for the public to come to a choice. Often times, the process of the voting system is what motivates the public to do so. But it is not always sufficient. And at the same time, the fact that the voting system is not sufficient for this, is not a failing of the voting system itself.

I find it instructive to mull two questions, because I find that these two questions drive a lot of opinions on who feels what voting systems are superior.

1) If a candidate would beat all other candidates in a multi-candidate single-winner election head-to-head, should that candidate be the winner?

2) If, in a two-candidate election, one candidate narrowly defeats the other, but the other candidate's supporters are clearly more passionate, should the first candidate still win?

(EDIT: Calmed some language)