The Romans, represented by Pontius Pilate, acted out of political expediency. Pilate saw that if he didn't give in, he would have a riot on his hands so he took the easy way out even though he knew Jesus to be innocent.
Matthew 27:24 When Pilate saw that he could prevail nothing, but that rather a tumult was made, he took water, and washed his hands before the multitude, saying, I am innocent of the blood of this just person: see ye to it.
Here is a link to some information that will be useful to you:
I hope you have found this helpful.