The study of voting systems is a hobby of mine and I've encoding vote gathering algorithms implementing them before, so this gives me a bit of insight into the discussion at hand that I would like to share. The goal of any voting system is to reach a consensus, and while majority rule (regardless of the amount of the majority) is appropriate for most issues, it is not appropriate for all. Specifically, it fails to work in any situation where the group is being asked to reach a consensus on three or more choices.
Ironically the choice put forth in this thread is just such an instance. Stay at 50%+1, Go to 2/3rds, 3/4ths has been mentioned and 3/5ths is another commonly required ratio. Four choices. The best method for dealing with this situation is a ranked choice ballot and an instant run off vote. The ballot itself asks the voters to rank their choices, not just stamp a single one. The votes are counted using the expressed first choice on the ballot. If the measure doesn't pass then the option with the fewest supporters is disqualified. The ballots for that option are recounted and the 2nd choice is added to the counts. If the measure still doesn't pass this process is repeated, recursively until there are only two candidate, in which case the one with the majority wins. This method doesn't work directly with methods requiring a plurality other than a simple majority, but it isn't meant to be applied in the same situations. I'm putting this forward because I worry the group might paint themselves into a corner by requiring all issues require a super majority, because that's going to fall apart when there are three or more possibilities. The methods can be combined, using ranked choice to determine which option will be put up against the status quo, then a super majority vote to determine if that option will be chosen over the status quo.
