Jesus' death

yes i know a few weeks late... I was reading in John the other day about how the Pharisees, claimed they were not allowed to carry out a death penalty (John 18:31). as i was reading this it struck me(for the very first time) that this was contrary (their actions, not the Bible) to the incident where Jesus stops the Pharisees from stoning the adulterous woman (John 8:2-11). Why did they retreat to claiming that they were not allowed to execute Jesus themselves? The whole court case against him was the biggest farce in human history anyways. Why get so stuck on this, when so many other laws and regulations were broken? Why not just go ahead and stone him in some back alley... doubt a single Roman would every have noticed or cared. There is of course one obvious 'larger' answer; it happened so that the prophecies concerning Jesus death would be fulfilled (e.g. John 18:32, Zechariah 12:10, Psalms 22:16). but I'm more curious as to what was going through the Pharisees minds as they decided to not take matters into their own hands... (fear of the people?) I'm sure that if i could be bothered to look in a commentary or two i might find answers rather than semi-coherent postulations... if i do indeed look this up and find some answers, i might just let you know, unless this is answered in a satisfactory way by others who might comment. As this is unlikely (not the intellectual capabilities of the two people who might read this, but rather the possibility of anyone commenting), as is my own further study on the subject, this will probably remain an incomplete or rather unconcluded discussion. Not that this was really the hope of this post; it’s purpose was to ask the question rather than to find the answer (not, that this is a good thing, I’m just plain lazy, and I have Greek homework to do)