As I wrote in the comments above, I first was very sceptical about this change when Robert asked for it. In the meantime, however, my opinion changed a bit and I think the positive effects of the change most probably outweigh the negative ones.
Don't get me wrong, I still have the strong opionionopinion there are currently too many community members around here who don't behave nicely:
downvoting and closing question with minor issues or no apparent issues (at least not apparent to me, so maybe my fault?)
refuse to give constructive or specific feedback to askers which are willing to improve their question (last example here, where after a full week of silence Thomas Owens finally was gracious enough to write a kind of answer I had expected to get from one of the initial high-rep close-voters).
stay away from curating questions actively, though they have more than enough rep for being able to do so
stay away from any reflective discussion like this one about the groups self-moderating style
mark questions frequently as duplicates of older questions which are way-too-general (or simply unsuitable) for giving the asker a helpful answer
give me the impression the only moderation tools they know are the downvote and the close vote button.
My fear was that the influence of those community members would increase even more when they now get a chance to close reasonable questions with just three votes, and probably it has become now. And I still don't buy Robert HarveysHarvey's argument that quick closing will motivate more askers to improve their question, so 3 reopen votes will actually lead to more improved, reopened questions, balancing the formerly described, IMHO abusive behaviour.
On the other hand, I see that ourthis site isbeing still flooded with way more unsuitable questions than ones which might be salvaged, and these kind of posts now vanish a lot more quickly than before from the site. So there is probably some collateral damage I have to accept here. And the fact Thomas gets a little bit unburdened from cleaning up cumbersome stuff is definitely a positive one.
Of course, all what I wrote above is not based on any statistics, just my personal impression, so I am looking forward to see a statistical summary at the end of the experiment.