# The Communication Complexity of Majority, What does Bob send to Alice? Can Bob just wait for Alice's input?

I'm following along the examples in https://people.csail.mit.edu/rrw/6.045-2020/note-cc.pdf and in specifically the following text:

What’s a good protocol for computing MAJORITY? The natural thing to do is to have Alice and Bob send the vote counts! Over multiple rounds, when it’s Alice’s turn, she sends bits of the integer $$N_x$$ which is the number of 1s in $$x$$, Bob computes $$N_y$$ which is the number of 1s in $$y$$, and Bob sends 1 to Alice if and only if $$N_x+N_y$$ is greater than $$n$$. (Note the total number of voters is $$2n$$.) If Alice sends $$N_x$$ encoded in binary, this takes $$O(\log n)$$ rounds. We therefore have:

If Alice is sending her total number of 1s over $$\approx \log n$$ bits to Bob ... what is Bob sending in back in return before the Alice is done with her input? I assumed or thought that in communication complexity, Alice and Bob are always taking turns back and forth right? Can Bob not send anything and just wait for Alice to send the $$\log n$$ bits?