Edit: TL;DR I made equivalent problem. It is sufficient and necessary. Prove: p(H causes destruction | H is Alive) < p(H causes destruction | H is Dead)

I have exams so I don't have enough time to do the whole process, as it should be done. I wanted to donate my thoughts and hope for someone else to do the job.

If you remember, we are not supposed to give solutions at once, we should talk about problem first. This includes gathering fair knowledge about all the mechanisms mentioned.

I see some people listed available objects, which could be used in open combat. Which is exactly what we should do, given that the problem is how to fight them. The problem is, however, not how to win the fight.

Now, I have to admit i haven't thought about the whole problem (I am not facing 37 Deathe-Eaters, true, but I am facing 3 exams next week), I focused on two things: Harry's mind, and Voldy's mind. I will deduce if Harry will actually try to defend himself.

These are my thoughts:

• Voldy (V) wants to stop the prophesy. Prophesy says Harry will cause great destruction.
• Harry (H) cannot change V's utility function.
• V's utility function has high preference for this world not being destroyed.
• V tried to maximize this function. (He showed he is quite "rational" up until now)

This is part where I imagined myself being V.

"H will cause great destruction. There is greater probability of him causing destruction, than his death causing destruction. Therefore i have to kill him. I just resurrected Hermione, so, someone can resurrect H. I have to stop that, so i will destroy his remnants."

• H did the whole Unbreakable Vow thing => he is now practically the only human who has no options when it comes to destroying the world.

• H's utility function is practically the same as V's utility function now. (Both V and H prefer world over H)

• "There is a prophesy i will destroy the world. I don't want to cause destruction. Is probability ("i cause destruction" if "I am alive") greater than ("I cause destruction" if "I am dead")? Whatever probability is lower, i will do that. "* (He can't chose anymore, he sacrificed it

  H would not try to live if that would lead to greater probability of mass destruction. He would prefer himself dead over alive. (If he is rational he would do that, because his utility function is such.)

Now, let's see compare pA = p(H causes destruction | H is Alive) and pD = pp(H causes destruction | H is Dead)

Vow ensures that if there is even a minor risk of H's next step creating destruction, he would have to interrogate that risk, and avoid it if there really is such a possibility. With regard to this and H's cleverness, he could cause something destructive much easier while absent than while present. =>
pD>pA

Since I don't see EY killing Harry or being inconsistent, pD is probably indeed greater, whether or not my deduction has flaws.

On this deduction depends whether or not H will actually do something to defend himself. If he will defend himself, he might as well communicate all this to V and he will let him go, because V prefers no destruction over destruction.

Edit: formatting.