Such trust could be transparently tracked, even anonymous.
People pledge toward a floor price. Each is given a random fraction of a dollar price to set their buy price (ie $100.1032). Everyone can see that the buy price is filled on the exchange and can collectively say "1000 people pledge $1,000 toward keeping the bitcoin price above $100 for a total of $1,000,000 backing a $100 floor".
This would create confidence that the Bitcoin price will not crash below $100. But only as much confidence shown by those that have put in their bids. If someone pulls their bid, it is shown as less confidence, if people add to it it shows more confidence.
This would also be a way to do as many Austrians call for and peg the price floor to gold. But that would be more difficult as people would need software for their own bids to follow the gold price.
I think this could be achieved by some kind of insurance: Bitcoiners purchase an insurance to make sure the bitcoin price won't drop below certain level, when insurance company collected enough money, those money could build a huge wall on exchanges and immediately show the guaranteed price floor