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Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 15, chapter 84 · 2012-04-12T20:12:13.610Z · score: 3 (5 votes) · LW · GW

I downvoted the previous post because it was a needlessly complicated, poorly justified plan. Crucially, there was little indication of why Voldemort would want to pretend to lose, when he was already winning the war. By contrast, your more recent post is a good analysis of the new insight into Voldemort's history and motivations provided by the latest chapter.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 14, chapter 82 · 2012-04-08T04:03:53.644Z · score: 6 (6 votes) · LW · GW

I'm not saying I think Narcissa is alive, but...

There’s no obvious reason not to return her after he thought Voldemort was gone

Except that Narcissa could then testify in front of the Wizengamot that Dumbledore kidnapped her.

or at least to let Lucius know what happened in case she’s alive and didn’t want to return

Dumbledore believes Voldemort will return. This would limit his ability to threaten Death Eaters in the next war.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 14, chapter 82 · 2012-04-06T02:48:33.359Z · score: 17 (21 votes) · LW · GW

I would much prefer to have them released all at once. I could read them and re-read them at my own pace. There would still be plenty to discuss. The cliff-hangers mean that I currently think about each update more than is productive. It would be nice if the disruptive effect they have on the rest of my life was more localized.

Mostly, though, I'm happy to read it whenever EY gets around to posting it.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-04-02T00:43:12.968Z · score: 3 (3 votes) · LW · GW

Sorry, apparently I'm illiterate.

Also, I guess "siblings getting killed" isn't much of a pattern. Given that people were getting killed in the war, and that people have siblings, you can count the people getting killed as siblings.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-04-01T16:29:21.337Z · score: 3 (3 votes) · LW · GW

It's also difficult to see why Voldemort would want to pretend to die at Godric's Hollow. He was winning the war. Why pretend to lose, throw away what he had built up to then, and try an entirely different approach to gaining power? I think the more obvious explanation for the burnt body is that whatever ritual magic protected Harry was very destructive to Voldemort. I think it is clear that some ritual magic is involved here; how else can we explain the danger of Harry's and Quirrell's magic interacting? And the violence of their magics' interaction in Azkaban makes it plausible that if Voldemort were to cast a killing curse directly at Harry, he might end up as a burnt corpse.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-04-01T16:22:25.949Z · score: 2 (2 votes) · LW · GW

Perhaps its not such a strange thing to say if you don't think Mr. Potter knows about the prophecy, and are trying to correct his insubordination. In the following chapters, Dumbledore doesn't act as though he has decided Harry is unsuitable as a hero. Rather than trying to replace him, Dumbledore begins to confide in him.

Does Nornagest's explanation of Dumbledore's relationship with story-book reasoning affect your previous analysis? If you agree that Dumbledore feigns a story-book persona, rather than taking story-book logic seriously, then doesn't it seem strange that he would hatch such a plot? Note that his manipulation of the last battle in December is consistent with having realistic view of the world. Yes, Dumbledore did manage to acheive a "story-book outcome," but he clearly didn't expect this to happen---he had a contingency plan.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-04-01T04:58:00.506Z · score: 1 (1 votes) · LW · GW

You are right, those are both possibilities. Though, one of them has been explicitly presented by the author, and endorsed by Harry. I don't think we have much reason to doubt the canonical interpretation.

"SO THAT'S HOW THE COMED-TEA WORKS! Of course! The spell doesn't force funny events to happen, it just makes you feel an impulse to drink right before funny things are going to happen anyway! I'm such a fool, I should have realized when I felt the impulse to drink the Comed-Tea before Dumbledore's second speech, didn't drink it, and then choked on my own saliva instead - drinking the Comed-Tea doesn't cause the comedy, the comedy causes you to drink the Comed-Tea! I saw the two events were correlated and assumed the Comed-Tea had to be the cause and the comedy had to be the effect because I thought temporal order restrained causation and causal graphs had to be acyclic BUT IT ALL MAKES SENSE ONCE YOU DRAW THE CAUSAL ARROWS GOING BACKWARDS IN TIME!"

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-04-01T00:33:34.765Z · score: 3 (3 votes) · LW · GW

Harry could still get a false negative. Remember, Harry will feel the impulse to offer a drink to Alice if and only if if Alice is about to be surprised. So not feeling an impulse to offer her a drink would indicate that either that Alice would not be surprised that Voldemort is alive, or that Harry will not actually end up telling her.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-03-31T22:13:55.313Z · score: 4 (4 votes) · LW · GW

If, for example, Harry wishes to test whether or not someone knows that Voldemort is alive, he could see if he has the Impulse to give that person a drink, all while thinking about saying that "The Dark Lord is still alive". If he gets the Impulse, they don't know. If he doesn't, then they already know/has been suspecting that he's been alive.

Unless he actually followed through with saying that Voldemort is still alive, this wouldn't be enough.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-03-31T16:06:12.284Z · score: 2 (2 votes) · LW · GW

In the aftermath of the prophecy, his manipulation of Snape and Lily netted him a defeated Dark Lord, a double agent and powerful ally, and a newly horcruxed hero. If the prophecy hadn't occurred, he'd instead have... a bouncing baby boy. It's hard to see what he hoped to accomplish by driving Snape and Lily apart if he didn't intend to prod Voldemort into attacking the Potters.

One possibility is that he didn't intentionally drive Snape and Lily apart. I don't think there's enough evidence of that to overcome the prior probability that Trelawney's prophecy was genuine. Note that Dumbledore himself seems to regard the prophecy as genuine---witness, for example, his apparently genuine interest in discovering the "power [Voldemort] knows not."

Here's another way of looking at it. Assume Dumbledore planned in advance to defeat Voldemort by (i) convincing Voldemort of a false prophecy that would lead him to attempt the murder of a baby, and (ii) somehow manipulating the baby's mother into either performing ritual magic herself, or causing Voldemort to perform ritual magic that would bring about Voldemort's death when he attempted to kill the baby. We might now ask, is there a simpler way that Dumbledore might have tried to enact (i) and (ii), other than the means you have suggested?

Note that a priori, assuming that Dumbledore is primarily concerned with defeating Voldemort, there is no reason for Dumbledore to deliver the false prophecy to Voldemort via an agent who is in love with the mother in question. He must then rely on the agent not understanding the prophecy in time. Furthermore, if the agent figures out the prophecy after relaying it to Voldemort, Dumbledore must then rely on Voldemort disregarding the agent's request to spare the mother. So going out of his way to push Snape and Lily apart, and then using Snape as a messenger, seems like a very unintuitive way for Dumbledore to execute this plot. Why not keep Snape and Lily together, see that they have a child, and then deliver the false prophecy to Voldemort via some other agent?

Now, personally, I do think it's a possibility that Snape and Lily were driven apart by Dumbledore, maybe even intentionally. But I don't think it was for this reason.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-31T15:32:43.986Z · score: 0 (0 votes) · LW · GW

You're right, I misremembered. Still, I think there is a lot to suggest that interacting directly with one's time-clones (as opposed to waiting with one's eyes closed while a clone drops off a message, for example), particularly in battle, is a bad idea. You would never observe a future-you doing something ineffective in combat---failing to dodge or block, or casting an ineffective spell, for example---since, after observing that mistake, you would be prepared for it in the future. So the only consistent possibilities involve losing or running away before you can go back in time, or winning right away.

But, since you know these are the only consistent possibilities, if you showed up to a battle intending to use a Time Turner and didn't see your time clones appear at the very beginning, you would deduce that you would not win, and therefore (if you could) you would run away. So, I expect that from Time's perspective, the most stable solution for people who intend to use Time Turners in battle is for them to not do battle at all.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-31T15:14:11.950Z · score: 0 (0 votes) · LW · GW

He has never interacted directly with himself in a way that involves seeing a copy of himself, or coordinating actions in real-time, as would be the case in a battle. Harry has so far always heeded Professor McGonnagal's advice, and looked the other way when his time clones are around. Though, as pedanterrific points out, I have overstated the severity of McGonnagal's warning.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-03-30T21:03:02.018Z · score: 1 (1 votes) · LW · GW

Seems unlikely that the original prophecy was caused by Dumbledore, at least by the method of the magical clock. As in canon, Trelawney seems to have made the prophecy during a job interview, presumably before she was regularly sleeping with the clock. I expect that if Dumbledore wanted her to make a false prophecy at a specific time, something like an Imperius folled by Obliviation would be more expedient. Furthermore, we have seen Trelawney spontaneously prophecy in the dining hall; this prophecy at least appeared unplanned by Dumbledore.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-29T13:34:45.436Z · score: 0 (0 votes) · LW · GW

Sure, though my impression is that people don't think graph isomorphism actually is in P. And integer factorization turned out to be a problem for Harry. But you're right, we can actually just simulate a nondeterministic Turing machine this way: every time you have a choice for which state to visit next, just listen as future you tells you which ones not to visit.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-29T03:06:05.664Z · score: 1 (1 votes) · LW · GW

Sorry, I'm really not following your pie argument. Harry would learn about the pies in the near future; since it is his style, he would think about throwing them to frighten the bullies. So, his observation of Harry+1 throwing the pies is not necessary for him to think to throw pies anyway.

What do you mean by "they don't recurse"? Surely the fact that this procedure results in fast graph isomorphism testing shows that it is not a particularly "stable" solution? Or, do fast integer factorization by writing down the first digit for the least factor greater than 1, listen as future you says "no, no, maybe," and change it to whatever, and then figure out the second digit, and so forth. The scenario you've outlined results in nearly instant integer factorization (or password guessing, or whatever), so it is probably illegal.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-03-29T02:33:57.766Z · score: 3 (5 votes) · LW · GW

I hope you write the ending you want, rather than playing games to see which ending we will earn.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-29T02:00:52.360Z · score: 0 (0 votes) · LW · GW

that doesn't follow. Where would Harry have gotten the pies if not from Harry+1?

He got them from the breakfast table. Where did he get the idea to get them? Well, he would have seen the pies later on anyway. Just like he would have learned about time turners later on in the day anyway, but a more stable scenario was obtained by learning about them earlier.

The recursion is non-iterative beyond the number of loops actually manifested, however.

I'm not quite sure how to parse this. If you would think about an idea at time T, but don't because future you tells you it won't work out, that means your whole thought process going forward has completely changed. But maybe the thing you start thinking about instead doesn't work out, so someone warns you about the idea at time T+epsilon. And so on. So if you are proposing that Time works by iterating through a number of scenarios until you get to something stable, the situation you've pointed to "requires recursion." (It's worth pointing out that Harry, when he gets his Time Turner, doesn't think this is a likely answer to how Time works.) But perhaps I am not understanding you correctly?

My main objection to the scenario you are proposing, though, is that you are gaining information as a result of some work, but that work is never performed. Try taking your scenario to its logical extreme. You sit in a room with one copy of future-you, and a large composite number N on a sheet of paper. On scrap work hidden from future-you, you write down an integer K. If you are not told that K does not divide N, you check. If it does, you keep track of the factor of N you have found. In any case, you then systematically select a new integer K' to check for divisibility. Once you have a complete factorization, you sit quietly, and at the end of the hour you go back in time. Then, you let past-you know the "keys" for all of the integers that weren't factors. Thus, you must have ended up only trying actual factors. So, you have a slightly more complicated version of Harry's factorization algorithm.

Edit to add: I guess this situation actually still is still an exponential time algorithm, since you still have to consider every possibly integer. But you could do, for example, graph isomorphism testing in polynomial time with a similar method: try constructing a map by first finding what vertex 1 should map to. Future you says "nope, nope, maybe," and on "maybe" you try to figure out where to put vertex 2, given that vertex 1 maps to whatever. If the graphs are not isomorphic, future you will say "no" to every choice for vertex 1, so you have your answer in polynomial time. Otherwise, you will construct the isomorphism in polynomial time.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-03-29T01:25:34.673Z · score: 9 (9 votes) · LW · GW

There is one offhand remark, vengeance, and a practical cold-heartedness favoring Bones. "Why not Bones?" is only a little better than no argument at all.

Also there is the fact (mentioned by someone else, sorry I forget who) that Narcissa's sister, Bellatrix, murdered Bones' brother. Edit: I am an idiot, you already mentioned this.

Bringing in Aberforth is a really interesting idea. Now that I think about it, even given the wizarding wars, it is remarkable that so many siblings have died or nearly died:

  • Albus/Aberforth

  • Bellatrix/Narcissa

  • Bones/her brother (who, exactly?)

  • Petunia/Lily

The last one is interesting with the role of survivor exchanged as well, since there is a hint that Petunia may have threatened suicide in order to convince Lily to brew the beauty potion.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-03-29T01:19:08.857Z · score: 7 (7 votes) · LW · GW

I think Lucius may have been playing very high speed chess when he picked the amount. The point isnt to have Harry in debt to him, the point is to afford ex-deatheaters loyal to Lucius the oppertunity to trade in a blood debt to Harry for a monetary one to him.

I don't think so. It's clear from his reaction that he did not want Harry to accept the trade:

It was clear that Lucius Malfoy had not been expecting that reply.

And later:

"I withdraw my offer!" shouted the Lord of Malfoy. "I will not accept the debt to House Potter in payment, not even for a hundred thousand Galleons! The girl's blood debt to House Malfoy stands!"

Indeed, it is a taboo tradeoff from Lucius perspective. He has traded justice for his son for money and the resolution of a political (though not moral) debt to Harry. He picked the amount because he thought there was no possibility that Harry would accept such a large amount.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-03-29T01:13:57.262Z · score: 10 (10 votes) · LW · GW

I don't get how a cunning Slytherin like him can discard such an advantage for pure vengeance over an "attempt" which didn't do any real harm.

On the contrary:

And Draco was getting angry again. "Dumbledore killed Mother, it's not enough to just say it's sad! I don't understand what you think you have to do, but the Malfoys have to take revenge!" Not avenging the deaths of family went beyond weakness, beyond dishonor, you might as well not exist.

Lucius never meant for Harry to accept the monetary bargain. This is clear from his reaction. He wanted his revenge, and Harry was interfering.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 13, chapter 81 · 2012-03-29T00:23:24.652Z · score: 10 (10 votes) · LW · GW

I completely agree. Recall also Draco's speech about muggles scratching in the dirt, and his reaction to Harry's estimate of the lunar program budget. It's not just wizards not paying attention to relative values of gold and silver in the muggle world---for the most part, the possibility that there could be a substantial amount of either in the muggle world doesn't occur to them. Now you might expect muggleborns to know better, even after making allowances for the fact that they enter the wizarding world at age 11. On the other hand, if a muggleborn is clever enough to see the potential for profit, they might also be clever enough to see what Harry apparently does not---that calling attention to the fact that the muggles are ripe for exploitation is a Bad Idea.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-28T19:21:50.502Z · score: 0 (0 votes) · LW · GW

I see. So I guess there is some benefit gained from this, but it is very minor. It seems to me that the simplest rule that explains why Harry's integer factorization is not okay, but, for example, the "silver on the tree" password from the end of TSPE is okay, is the following: if you would gain information at time T, and send information from time T to any time S < T, then it must be the case that you would have gained that same information even if you hadn't learned it at time S.

Now consider your "keying" scenario. We have clones 0-5, and at time 1 clone x goes back to time 0 and becomes clone x+1. When clones give a "time key," it will be a number between 0 and 6, identifying a clone/wall-clock pair. Now suppose at wall-clock time T clone 1 says: "the thought I had at time P doesn't work." Assume for simplicity that time P refers to clone 0 at a wall-clock time S > T (though it would work out the same anyway). Now at time S, when clone 0 has the thought, he has two choices. On the one hand, he can continue working out why it doesn't work, but in this case he gains only the minor benefit of knowing in advance that it will not work out. On the other hand, he can move on and not consider the thought, but at time T as clone 1 just repeat (without knowing why), the fact that it doesn't work. In that case, he gained information that he would not have learned had he not told himself. Or, in your terminology, recursion was required in order to reach a stable state.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-28T14:05:27.104Z · score: 0 (0 votes) · LW · GW

I'm not sure I understand what you mean by "keying." Could you elaborate, and explain how you end up with a scenario that is more stable from "Time's perspective" than, say, clone #5 just summarizing all the ideas at the beginning of the hour? The scenarios I can come up with seem to involve information magically appearing (which the universe doesn't seem to like, as in Harry's integer factorization algorithm), or fail to provide a benefit over just thinking on one's own for six hours.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-28T04:08:16.089Z · score: 0 (0 votes) · LW · GW

Good point, though I don't think this would ever be useful. In the unlikely scenario that Time-Traveling Tom has a problem amenable to a straightforward, parallelized algorithm which requires six Tom-hours while Tom needs the solution within two hours, he may as well just go back six hours, "thread" his thoughts, not bother with any communication.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-25T03:28:27.131Z · score: 0 (0 votes) · LW · GW

Dumbledore doesn't give a straight answer when Harry asks if more than one time turner can be used to get more than 30 hours.

There was another slight pause, during which Harry went on smiling. He was a little apprehensive, actually a lot apprehensive, but once it had become clear that Dumbledore was deliberately messing with him, something within him absolutely refused to sit and take it like a defenseless lump.

"I'm afraid Time doesn't like being stretched out too much," said Dumbledore after the slight pause, "and yet we ourselves seem to be a little too large for it, and so it's a constant struggle to fit our lives into Time."

On the other hand, we may infer that thirty hours is the limit from e.g. Amelia Bones' behavior in the Azkaban arc:

"I'll check if we have anything from six hours forward," said the voice of Madam Bones, "if so they wouldn't have told me, but I'll have them tell you. Do you have anything you want to tell me, Albus? Which of those two possibilities is it looking like?"

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-25T03:05:20.169Z · score: 2 (2 votes) · LW · GW

Consistency is important. We see this in full force in the Azkaban arc.

To get 6 of yourself, starting at noon, you wouldn't go back to 11, then "together" go back to 10. You have already created a paradox because the original 11 o'clock you was supposed to wait until noon and then go back in time. Instead, at 11, you would walk into a room with 5 other copies of you waiting, and then at noon, you and 4 of those copies would go back in time to 11.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-25T02:43:18.756Z · score: 1 (1 votes) · LW · GW

Some of them will magically disappear every hour until only one remains, but imagine the firepower!

They wouldn't disappear. They would, after a period, go back in time in order to become one of the other people in the battle.

Using a time turner to make clones in battle is a very, very dangerous idea. Harry has been warned, strenuously, by Professor McGonnagal that he should not directly interact with himself, and we have an anecdote about an auror/criminal pair that went insane because they abused time turners. I imagine that one of the more stable time loops would involve the original Dumbledore/Harry getting disabled before going back in time for the first time.

But yeah, the cloning objects thing is a reasonable use of a Time Turner.

Edit to add: If by collaborating on tricky problems, you are referring to e.g. academic problems, rather than problems of strength, this amounts to a rather absurd charade. If you use a Time Turner to put 6 copies of yourself in a room, and in an hour they succeed in answering the problem, that means that at the beginning of the hour, 5 of them already knew the answer.

Comment by eponymuse on Counterfactual Mugging · 2012-03-23T23:10:02.437Z · score: 1 (1 votes) · LW · GW

Ah. But under mild assumptions about how Omega's simulation works, I can expect that with some probability p bounded away from zero, I am in a simulation. So with probability at least p, there is another universe I care about, and I can increase utility there.

So, I guess I do pay $100, but only because my utility function values the utility of others. I remain unconvinced that paying is winning for someone with a different utility function.

Comment by eponymuse on Counterfactual Mugging · 2012-03-23T22:34:18.267Z · score: 0 (0 votes) · LW · GW

The only mechanisms I know of by which Omega can accurately predict me without introducing paradoxes is by running something like a simulation, as others have suggested. But I really, truly, only care about the universe I happen to know about, and for the life of me, I can't figure out why I should care about any other. So even if the universe I perceive really is just simulated so that Omega can figure out what I would do in this situation, I don't understand why I should care about "my" utility in some other universe. So, two box, keep my $100.

Edit: I should add that my not caring about other universes is conditional on my having no reason to believe they exist.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-23T20:47:34.233Z · score: 3 (3 votes) · LW · GW

I find it very unlikely that Bella is in contact with anyone except the healer. Why would Quirrell want her running around and discussing the escape with people? It's also unlikely that she remembers any part of the escape from Azkaban at all, including Harry's role. Remember that she was Obliviated.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-18T15:36:14.088Z · score: 4 (4 votes) · LW · GW

These are good observations. However, I think you are inferring plot points from what is merely literary technique. H&C using the same disguise is well explained by EY intending us to identify Hermione's manipulator with Zabini's. Similarly, the many attempts/Hermione's exhaustion are well explained if EY wants to make it clear what the nature of the attack is without spelling it out explicitly.

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-18T13:52:40.047Z · score: 5 (5 votes) · LW · GW

The inefficiency of H&C's attack against Hermione's mind is not evidence of a "simple mistake" on his/her part, but rather exceptional cleverness. Note that this attack has replaced something that would be detected (Legilimency) with something that cannot be (Obliviation). I myself take this as further evidence that H&C is Quirrell.

Were there other mistakes you had in mind?

Comment by eponymuse on Harry Potter and the Methods of Rationality discussion thread, part 11 · 2012-03-18T13:47:19.256Z · score: 2 (2 votes) · LW · GW

It seems unlikely that the good Defense Professor would have orchestrated a plan which is entirely dependent for it's success on Lucius failing to take advantage of the situation - unless putting Harry in Lucius's debt was his goal.

Assuming Quirrell is Voldemort, he presumably had years of access to Lucius' mind (if he regularly required Lucius to drop Occlumency barriers). At the very least, we can assume he has an excellent mental model of how Lucius behaves. The plot therefore doesn't seem like too great of risk for Quirrell, particularly when we consider that Lucius is about to discover Harry's progress in turning Draco. Quirrell can safely assume that Lucius will react in a way that will pull Draco and Harry apart when he discovers this, and will therefore be less inclined to trade Hermione for something of Harry's.