I've seen the data (at least from the organizations that support approval voting), and it seems to deliver the most optimum results.

However, I have some concerns. The way I see the two voting systems is like this:

Advantages approval voting:

- much simpler

- eliminates spoiler effect

- may give third-party candidates better chances in most elections

- reduces negative campaigning, since the winner would have to be "approved" by like 70% of the country in typical elections.

Disadvantages AV:

- the winner may be someone who was #2 on 80% of the country's wishlist. So 51% of country won't love the candidate, as they may with RCV or two-round voting systems, but also the other 49% won't hate the candidate (perhaps only 20% will). So from that point of view, it would be "better". But it would be someone most are just content with.

- I believe even the organizations supporting it admit that it would lead to "centrist" leaders. Perhaps in most situations a centrist is preferable, but what if the country has gone in the wrong direction for 2 decades, and it needs a completely new direction? Would a centrist still be enough? Or would the approval voting system and people pick exactly the guy that is willing to go in a different direction this one time? I'm not sure what would happen in this scenario.

Advantages RCV:

- eliminates spoiler effect

- also reduces negative campaigning, because a candidate would need some of the opponent's voters, too, to rank them as #2 on their list.

- easier transition to multi-winner RCV system for state legislature and Congress - and this alone is much bigger than just using approval voting system. Proportional representation beats all single-winner voting systems, including approval voting

Disadvantages RCV:

- it may eliminate spoiler effect, but other than that, it won't do much else to help third-parties. The main two parties would likely still be elected for a long time, at least until population's thinking about at least one of the the two parties changes in a major way
- a bit more complicated to understand how votes are counted by the average person, and a higher number of "lost" votes (I believe 5% or so, compared to about 1% or less for AV).

I believe both could also be used strategically - as in rank #1 the person you think is more likely to win with RCV, or only vote for the person that's more likely to win with AV, instead of multiple people.

So I would qualify the two as: AV would be a great improvement over FPTP, while RCV would be a moderate, but still well worth it and welcome improve, for the fact that it would eliminate spoiler effect alone. However, if single-winner RCV makes it much more likely that multi-winner RCV (STV) is also adopted for state legislature and Congress, then I would definitely choose RCV over AV, because the ultimate goal should be to adopt proportional representation in the US.

I think proportional representation coupled with a limit of $200 of individual donations and a ban on any other political donations would greatly improve democracy in the US, and these are the main changes Americans should fight for, if they want all of the other issues (as Lessig often says) to be solved as well. First fix democracy and change the system to a better one, so that the people that actually represent you get to pass laws in your favor for whatever issue you (the People) want.