Henderson is in charge of the initial information that gets fed into the super computer named Multivac. Henderson was in charge of collating intelligence that came from numerous other small computers. Henderson admits that as the war dragged on the intel that he received was next to meaningless. He began to notice that lower level officials were submitting information that they believed would make them look good.
"Do you know," said Henderson, "to what extent data concerning our production capacity, our resource potential, our trained man power everything of importance to the war effort, in fact-had become unreliable and untrustworthy during the last half of the war? Group leaders, both civilian and military, were intent on projecting their own improved image, so to speak, so they obscured the bad and magnified the good. Whatever the machines might do, the men who programmed them and interpreted the results had their own skins to think of and competitors to stab."
In other words, the war effort was publicly relying on the data of all of these computers, but it was human people that were choosing to input data that more favorably reflected upon themselves. Humans were deciding what the machines would say. Henderson figured it out early on, and began to sift through the clutter and give Multivac info that his intuition said was likely correct. It eventually got to the point where Henderson was just making stuff up for Multivac.
"Since the war is won, I'D tell you what I did. I corrected the data." "How?" asked Swift. "Intuition, I presume. I juggled them till they looked right. At first, I hardly dared, I changed a bit here and there to correct what were obvious impossibilities. When the sky didn't collapse about us, I got braver. Toward the end, I scarcely cared. I just wrote out the necessary data as it was needed. I even had the Multivac Annex prepare data for me according to a private programming pattern I had devised for the purpose."
Long story short, if the humans had given truthful data, Henderson would not have taken over with his intuition. Had he not done that, maybe Jablonski wouldn't have resorted to using his intuition. Had Jablonski not done that, maybe Swift wouldn't have flipped a coin. And had Swift not flipped a coin, maybe they would have lost the war.