Utilitarianism

A classic utilitarian thought experiment is as follows
let’s pretend, he said, and that some mad scientist has figured out a way to bring peace, prosperity, and general happiness to the whole world.

There was just one catch: this brave new world required the yearly sacrifice of one innocent person, chosen at random. Supposing this scheme were perfected: would it be moral to close with the offer and subscribe universal happiness at the cost of one innocent life per annum?

Note the addition of the "chosen at random" to older thought experiments. To many people this helps, but as the post on right reason indicates - most people reject it anyway. I wonder if this indicates that people are reading things into this.

Any ideas how else we can get to the very root of the objection to the model?
One of the main issues here is that I know most people are not radical deontologists (or radical utilitarian for that matter) so I expect to find all sorts of interesting reasons why people reject it on an intuitive level reasons that are worthy of being investigated.

Let us do a chose your own adventure here. At the end of each point offer you two choices

1) Now imagine that (as is surely the case) one of the benefits is preventing the murder of at least one person (aside from other benefits). What this does is demonstrates that there is at least one murderer in the first world. Still oppose it? Go to (2) support it? Go to (4)

2) Now imagine that you would not have to actually do the killing - you just accept the deal. Still oppose it? Go to (3) support it? Go to (4)

3) What if the state doesn’t do any killing either - it just provides the information to the general public that the death of
"Person X" will have all sorts of benefits (and where he lives and whatever else is required to ensure the end result) and waits for someone to kill him. Still oppose it? Go to (4) support it? Go to (5)

4) What if "whatever it takes to ensure he gets killed" is "failing to give him medical treatment" or failing to give him access to use the local public goods. Still oppose it? Go to (6) support it? Go to (5)

5) Your a bit of a utilitarian just this is being confused by some aspect of the question.
Either
a) Your intuitions result in you not entirely believing the person proposing the hypothesis OR
b) You have a strong desire to protect yourself from being culpable - for example culpable in the face of a god as a result you favor inaction over action.

6) What if you can guarantee it won’t be you? Still oppose it? Go to (8) support it? Go to (7)

7) You belief in a right to life - it just happens to be your own!

8) What if the person is not random it is a person you can choose (although you can’t have been about to kill them anyway)?
Still oppose it? Go to (9) support it? Go to (10)

9) Maybe you do fundamentally reject utilitarianism and support a right to life!

10) You seem to be concerned about the death of a sub group of most deserving people - potentially people you could protect - a sort of moral elite.