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Good work on choosing approval voting!

Single-vote (first past the post) methods are terrible methods of translating voter will into meaningful results. They discourage most people from voting and most candidates from running, and produce divisive results (see american presidential elections). If most people dislike a particular candidate, it can still win, because the vote against it may be split between the other options, since people can only express their first preference, and nothing else.

Preferential (ranked) voting systems can be ok, but it gets complicated when you decide how to count the preferences. If you use instant-runoff (eliminate the least popular candidate if there is no majority, then re-distribute the second-preferences from those votes. Repeat until someone has a majority) is divisive, because most people who didn't vote for whoever ends up winning, do not get their preferences counted at all. This is because their first-preference option doesn't get eliminated before a majority is reached by another candidate.

There are some decent preferential systems (e.g. borda count, kemeny-young), but they all suffer from arrow's impossibility theorem (which shows that they're all flawed in some key aspects).

Approval voting is simple to use, simple to count, and tends to produce consensus results.

This site doesn't appear to have a whole team of volunteers like SoylentNews (which I also like), so progress is slower, but I very much like and admire the effort. Consider me sold.