I still wait to find out how.

Security.

Now we come to security. Assume that I am a very powerful adversary, capable of corrupting users extremely quickly whenever I want. Clearly, I would love to corrupt the members of the committee, but I have a problem: I do not know who they are.

This is so because committee members are selected by a secretly run, cryptographically fair, individual lottery. Thus, only they know who they are, up to the moment in which they propagate through the network both their winning tickets and their opinions about the block. Only at that time I might learn who the committee members are and, given my super powers, I can immediately corrupt the entire committee. But so what? Corrupting them at this time is too late. Whatever the committee members had to say, they have already said, and their winning tickets and up-or-down opinions about the block are virally propagating throughout the network. I have no more power to put their messages back in the bottle than a government has the power to put back in the bottle messages virally propagated by WikiLeaks.

In other words, the Algorand approach is secure because beforehand, an adversary does not know whom to corrupt, and by the time he does, corruption is useless.