Iris Hineman: If the unintended consequences of a series of genetic mistakes and science gone haywire can be called 'invention', then yes, I invented Precrime. (00:57:50)
Dr. Iris Hineman: Sometimes, in order to see the light, you have to risk the dark.
Agatha: You can choose.
John Anderton: That's all, huh? Just walk right into Precrime, go in the Temple, somehow tap into these Precogs, and then download this Minority Report.
Dr. Iris Hineman: If you have one.
John Anderton: And then walk out.
Dr. Iris Hineman: Actually, I think you'll have to run out, but yes, that is what you have to do.
John Anderton: Mr. Marks, by mandate of the District of Columbia Precrime Division, I'm placing you under arrest for the future murder of Sarah Marks and Donald Dubin that was to take place today, April 22 at 0800 hours and four minutes.
Officer Fletcher: John, don't run.
John Anderton: You don't have to chase me.
John Anderton: Why should I trust you?
Dr. Iris Hineman: You shouldn't. You shouldn't trust anyone. Certainly not the Attorney General who just wants it all for himself, and not the young Federal agent, who wants your job. Not even the old man who just wants to hold on to what he created. Don't trust anyone. Just find the Minority Report.
Agatha: I'm sorry, John, but you're going to have to run again.
Agatha: Can you see?
John Anderton: They set me up.
Dr. Solomon: Now, you understand I can't just give you new irises. Because if I do, the retinal scans will read the scar tissue, alarms will go off, and large men with guns will appear.
John Anderton: I'm not being set up. I really am going to kill this man.
John Anderton: Don't you ever say his name.
John Anderton: I have to know. I have to find out what happened to my life.
Danny Witwer: He came to see you the other day right before he was tagged. What did you talk about?
Lamar Burgess: The Mets. John doesn't think they have a deep enough pitching roster this year, and I'm inclined to.
Danny Witwer: Why are you protecting him?
Agatha: Is it now?
John Anderton: He set me up. He set me up.
John Anderton: There hasn't been a murder in six years. The system, it is perfect.
Dr. Iris Hineman: Find the minority report.
John Anderton: How do I even know which one has it?
Dr. Iris Hineman: It's always in the more gifted of the three.
John Anderton: Which one is it?
Dr. Iris Hineman: The female.
Answer: Well, there isn't really a simple solution, but here goes. For a pre-vision to form, there have be two things present within the range of the precog ability (which appears to be limited to the Washington area - regardless of the stated plan to take the programme countrywide, there's never any indication that the precogs can sense beyond that range). Firstly, someone with the intent to kill. Secondly, there has to be a target for that intent within the range of the precogs. Anderton is present, and has the intent within him to kill the man who took his son, but has no target - the real kidnapper is presumably either dead or beyond the precog ability. Burgess, by bribing Crow to pretend to be that man, has provided a viable target for Anderton's intent within the range of the precog ability, thus triggering the prevision, and beginning the chain of events.
Tailkinker ★
The above answers the question, but there do appear to be some time travel issues with this plot point in the movie. Burgess set things up for Crow to fake being the kidnapper and thus triggering Jon's desire to kill that person, everything starts by the pre-cogs seeing the future. If the pre-cogs did not exist or did not have the vision, Jon would have never known that Leo Crow existed and would have continued on without having killed anyone. This is unique within the movie, as the other murders would have been commited regardless of whether or not the pre-cogs saw it. In this case, the ONLY reason this murder occurred is because the pre-cogs saw it.
oldbaldyone
Thinking about this a little more, it could be conceivable that Burgess had planned a different option for Jon finding Crow. We just never saw that on screen, because the precogs changed everything to an alternative future timeline once they saw the original murder. Originally, Jon could have been triggered by Burgess himself, stating that they got a lead on his son's murder and pointing him to Crow.
oldbaldyone
No I think Burgess set it up so that Anderton would find Crow because of the precogs, not have a different plan set up before or else it could be possible Burgess himself would be visible in the prevision. He manipulated the system perfectly, he has done it before after all. He knows exactly how the precogs work so he is able to set it up so that it's untraceable. Except, except for the fact there is always a choice. Only then did it go wrong for him. This proves both true for Anderton and Burgess in the end.
lionhead