You're proposing plurality voting (plus a weird tie-breaker), which is the worst method on basically every criterion except for "simplicity" and "familiarity to Americans". It leads to really obvious vote-splitting, and people will vote strategically, because they know perfectly well what happens to honest votes in plurality voting. They will also simply propose fewer things.
If the computer is counting votes for you, simplicity shouldn't be the highest priority.
There's a reason people have put years and years of research into voting methods. The best method is unlikely to be the one you think of off the top of your head and post in an HN comment.
What I think is really weird is why would a system put much weight, if any at all, on someone's 4+ choice? We might be coming up with a result that received the most points, but are we actually coming up with a result that the most people will be happy with, or is it the least boring thing that people will put up with?
The thing to note about our particular situation is that we're really only a little interested in the #1 result. The app is primarily about helping groups prioritize things, for instance "What features do we need to build next".
Rating systems are a no go, because the whole point is to force people to choose and hence consider the tradeoffs (hence "ForceRank" :)
In this case, some of the voting system criteria such as "susceptibility to burying" play out a bit different than in a regular election. eg If everyone thing "Project C" is a great idea but Frank _hates_ Project C, we want to do what we can to highlight that fact, not just continue on our merry way with the majority vote.
The most common favorite is not the definition of democracy - it's just the method of choosing that is most common. It's sort of self-justifying; "it's what we've always done, so we should keep doing it". But, things change over time, and we have the ability to better understand large groups of preferences than we used to (when counting first choices was the only possible way to vote), which means a better ability to provide social utility and help a group of voters help themselves in the most useful way.
Anyway, ordinal method doesn't actually apply any "weight" to a 4+ choice. The concept of "weight" doesn't actually apply to a Condorcet method. All you're really communicating is that you prefer candidate #4 to candidate #5, and to candidate #6, etc. There's no extra proportional "power" or weight given to higher-ranked candidates, though, because you've already communicated that you prefer candidate #1 to all of them.
It really is the same thing as if someone gave you (n(n-1))/2 ballots of one candidate against one other, with you picking your favorite. It's just faster to communicate in ranked form. It also doesn't run afoul of "one-person, one-vote", because no voter has extra power compared to another voter.
Finally, yes - say that 49% prefer A, have B as a close second, and hate C. 49% prefer C, have B as a close second, and hate A. 2% prefer B and hate both A and C. B's definitely just the "least objectionable", but also should definitely win as the consensus choice, even though B only got 2% first-place votes.