{EU(administer penicillin) = 0.9, EU(don’t administer penicillin) = 0.3}
Choose :
-> (Argmax A in Actions: Expected_Utility(A)) Pick an action whose “expected utility” is maximal.
{return: administer penicillin}
For every action, calculate the conditional probability of all the consequences that might follow, then add up the utilities of those consequences times their conditional probability. Then pick the best action.
This is a mathematically simple sketch of a decision system. It is not an efficient way to compute decisions in the real world.
What if, for example, you need a sequence of acts to carry out a plan? The formalism can easily represent this by letting each Action stand for a whole sequence. But this creates an exponentially large space, like the space of all sentences you can type in 100 letters. As a simple example, if one of the possible acts on the first turn is “Shoot my own foot off,” a human planner will decide this is a bad idea generally—eliminate all sequences beginning with this action. But we’ve flattened this structure out of our representation. We don’t have sequences of acts, just flat “actions.”
So, yes, there are a few minor complications. Obviously so, or we’d just run out and build a real AI this way. In that sense, it’s much the same as Bayesian probability theory itself.
But this is one of those times when it’s a surprisingly good idea to consider the absurdly simple version before adding in any high-falutin’ complications.
Consider the philosopher who asserts, “All of us are ultimately selfish; we care only about our own states of mind. The mother who claims to care about her son’s welfare, really wants to believe that her son is doing well—this belief is what makes the mother happy. She helps him for the sake of her own happiness, not his.” You say, “Well, suppose the mother sacrifices her life to push her son out of the path of an oncoming truck. That’s not going to make her happy, just dead.” The philosopher stammers for a few moments, then replies, “But she still did it because she valued that choice above others—because of the feeling of importance she attached to that decision.”
So you say,
TYPE ERROR: No constructor found for Expected_Utility -> Utility.
Allow me to explain that reply.
Even our simple formalism illustrates a sharp distinction between expected utility, which is something that actions have; and utility, which is something that outcomes have. Sure, you can map both utilities and expected utilities onto real numbers. But that’s like observing that you can map wind speed and temperature onto real numbers. It doesn’t make them the same thing.
The philosopher begins by arguing that all your Utilities must be over Outcomes consisting of your state of mind. If this were true, your intelligence would operate as an engine to steer the future into regions where you were happy. Future states would be distinguished only by your state of mind; you would be indifferent between any two futures in which you had the same state of mind.
And you would, indeed, be rather unlikely to sacrifice your own life to save another.
When we object that people sometimes do sacrifice their lives, the philosopher’s reply shifts to discussing Expected Utilities over Actions: “The feeling of importance she attached to that decision.” This is a drastic jump that should make us leap out of our chairs in indignation. Trying to convert an Expected_Utility into a Utility would cause an outright error in our programming language. But in English it all sounds the same.
The choices of our simple decision system are those with highest Expected_Utility, but this doesn’t say anything whatsoever about where it steers the future. It doesn’t say anything about the utilities the decider assigns, or which real-world outcomes are likely to happen as a result. It doesn’t say anything about the mind’s function as an engine.
The physical cause of a physical action is a cognitive state, in our ideal decider an Expected_Utility, and this expected utility is calculated by evaluating a utility function over imagined consequences. To save your son’s life, you must imagine the event of your son’s life being saved, and this imagination is not the event itself. It’s a quotation, like the difference between “snow” and snow. But that doesn’t mean that what’s inside the quote marks must itself be a cognitive state. If you choose the action that leads to the future that you represent with “my son is still alive,” then you have functioned as an engine to steer the future into a region where your son is still alive. Not an engine that steers the future into a region where you represent the sentence “my son is still alive.” To steer the future there, your utility function would have to return a high utility when fed ““my son is still alive””, the quotation of the quotation, your imagination of yourself imagining. Recipes make poor cake when you grind them up and toss them in the batter.
And that’s why it’s helpful to consider the simple decision systems first. Mix enough complications into the system, and formerly clear distinctions become harder to see.
So now let’s look at some complications. Clearly the Utility function (mapping Outcomes onto Utilities) is meant to formalize what I earlier referred to as “terminal values,” values not contingent upon their consequences. What about the case where saving your sister’s life leads to Earth’s destruction by a black hole? In our formalism, we’ve flattened out this possibility. Outcomes don’t lead to Outcomes, only Actions lead to Outcomes. Your sister recovering from pneumonia followed by the Earth being devoured by a black hole would be flattened into a single “possible outcome.”
And where are the “instrumental values” in this simple formalism? Actually, they’ve vanished entirely! You see, in this formalism, actions lead directly to outcomes with no intervening events. There’s no notion of throwing a rock that flies through the air and knocks an apple off a branch so that it falls to the ground. Throwing the rock is the Action, and it leads straight to the Outcome of the apple lying on the ground—according to the conditional probability function that turns an Action directly into a Probability distribution over Outcomes.
In order to actually compute the conditional probability function, and in order to separately consider the utility of a sister’s pneumonia and a black hole swallowing Earth, we would have to represent the network structure of causality—the way that events lead to other events.
And then the instrumental values would start coming back. If the causal network was sufficiently regular, you could find a state B that tended to lead to C regardless of how you achieved B. Then if you wanted to achieve C for some reason, you could plan efficiently by first working out a B that led to C, and then an A that led to B. This would be the phenomenon of “instrumental value”—B would have “instrumental value” because it led to C. The state C itself might be terminally valued—a term in the utility function over the total outcome. Or C might just be an instrumental value, a node that was not directly valued by the utility function.
Instrumental value, in this formalism, is purely an aid to the efficient computation of plans. It can and should be discarded wherever this kind of regularity does not exist.
Suppose, for example, that there’s some particular value of B that doesn’t lead to C. Would you choose an A which led to that B? Or never mind the abstract philosophy: If you wanted to go to the supermarket to get chocolate, and you wanted to drive to the supermarket, and you needed to get into your car, would you gain entry by ripping off the car door with a steam shovel? (No.) Instrumental value is a “leaky abstraction,” as we programmers say; you sometimes have to toss away the cached value and compute out the actual expected utility. Part of being efficient without being suicidal is noticing when convenient shortcuts break down. Though this formalism does give rise to instrumental values, it does so only where the requisite regularity exists, and strictly as a convenient shortcut in computation.
But if you complicate the formalism before you understand the simple version, then you may start thinking that instrumental values have some strange l
ife of their own, even in a normative sense. That, once you say B is usually good because it leads to C, you’ve committed yourself to always try for B even in the absence of C. People make this kind of mistake in abstract philosophy, even though they would never, in real life, rip open their car door with a steam shovel. You may start thinking that there’s no way to develop a consequentialist that maximizes only inclusive genetic fitness, because it will starve unless you include an explicit terminal value for “eating food.” People make this mistake even though they would never stand around opening car doors all day long, for fear of being stuck outside their cars if they didn’t have a terminal value for opening car doors.
Instrumental values live in (the network structure of) the conditional probability function. This makes instrumental value strictly dependent on beliefs-of-fact given a fixed utility function. If I believe that penicillin causes pneumonia, and that the absence of penicillin cures pneumonia, then my perceived instrumental value of penicillin will go from high to low. Change the beliefs of fact—change the conditional probability function that associates actions to believed consequences—and the instrumental values will change in unison.
In moral arguments, some disputes are about instrumental consequences, and some disputes are about terminal values. If your debating opponent says that banning guns will lead to lower crime, and you say that banning guns will lead to higher crime, then you agree about a superior instrumental value (crime is bad), but you disagree about which intermediate events lead to which consequences. But I do not think an argument about female circumcision is really a factual argument about how to best achieve a shared value of treating women fairly or making them happy.
This important distinction often gets flushed down the toilet in angry arguments. People with factual disagreements and shared values each decide that their debating opponents must be sociopaths. As if your hated enemy, gun control/rights advocates, really wanted to kill people, which should be implausible as realistic psychology.
I fear the human brain does not strongly type the distinction between terminal moral beliefs and instrumental moral beliefs. “We should ban guns” and “We should save lives” don’t feel different, as moral beliefs, the way that sight feels different from sound. Despite all the other ways that the human goal system complicates everything in sight, this one distinction it manages to collapse into a mishmash of things-with-conditional-value.
To extract out the terminal values we have to inspect this mishmash of valuable things, trying to figure out which ones are getting their value from somewhere else. It’s a difficult project! If you say that you want to ban guns in order to reduce crime, it may take a moment to realize that “reducing crime” isn’t a terminal value, it’s a superior instrumental value with links to terminal values for human lives and human happinesses. And then the one who advocates gun rights may have links to the superior instrumental value of “reducing crime” plus a link to a value for “freedom,” which might be a terminal value unto them, or another instrumental value . . .
We can’t print out our complete network of values derived from other values. We probably don’t even store the whole history of how values got there. By considering the right moral dilemmas, “Would you do X if Y,” we can often figure out where our values came from. But even this project itself is full of pitfalls; misleading dilemmas and gappy philosophical arguments. We don’t know what our own values are, or where they came from, and can’t find out except by undertaking error-prone projects of cognitive archaeology. Just forming a conscious distinction between “terminal value” and “instrumental value,” and keeping track of what it means, and using it correctly, is hard work. Only by inspecting the simple formalism can we see how easy it ought to be, in principle.
And that’s to say nothing of all the other complications of the human reward system—the whole use of reinforcement architecture, and the way that eating chocolate is pleasurable, and anticipating eating chocolate is pleasurable, but they’re different kinds of pleasures . . .
But I don’t complain too much about the mess.
Being ignorant of your own values may not always be fun, but at least it’s not boring.
*
149
Leaky Generalizations
Are apples good to eat? Usually, but some apples are rotten.
Do humans have ten fingers? Most of us do, but plenty of people have lost a finger and nonetheless qualify as “human.”
Unless you descend to a level of description far below any macroscopic object—below societies, below people, below fingers, below tendon and bone, below cells, all the way down to particles and fields where the laws are truly universal—practically every generalization you use in the real world will be leaky.
(Though there may, of course, be some exceptions to the above rule . . .)
Mostly, the way you deal with leaky generalizations is that, well, you just have to deal. If the cookie market almost always closes at 10 p.m., except on Thanksgiving it closes at 6 p.m., and today happens to be National Native American Genocide Day, you’d better show up before 6 p.m. or you won’t get a cookie.
Our ability to manipulate leaky generalizations is opposed by need for closure, the degree to which we want to say once and for all that humans have ten fingers, and get frustrated when we have to tolerate continued ambiguity. Raising the value of the stakes can increase need for closure—which shuts down complexity tolerance when complexity tolerance is most needed.
Life would be complicated even if the things we wanted were simple (they aren’t). The leakyness of leaky generalizations about what-to-do-next would leak in from the leaky structure of the real world. Or to put it another way:
Instrumental values often have no specification that is both compact and local.
Suppose there’s a box containing a million dollars. The box is locked, not with an ordinary combination lock, but with a dozen keys controlling a machine that can open the box. If you know how the machine works, you can deduce which sequences of key-presses will open the box. There’s more than one key sequence that can trigger the machine to open the box. But if you press a sufficiently wrong sequence, the machine incinerates the money. And if you don’t know about the machine, there’s no simple rules like “Pressing any key three times opens the box” or “Pressing five different keys with no repetitions incinerates the money.”
There’s a compact nonlocal specification of which keys you want to press: You want to press keys such that they open the box. You can write a compact computer program that computes which key sequences are good, bad or neutral, but the computer program will need to describe the machine, not just the keys themselves.
There’s likewise a local noncompact specification of which keys to press: a giant lookup table of the results for each possible key sequence. It’s a very large computer program, but it makes no mention of anything except the keys.
But there’s no way to describe which key sequences are good, bad, or neutral, which is both simple and phrased only in terms of the keys themselves.
It may be even worse if there are tempting local generalizations which turn out to be leaky. Pressing most keys three times in a row will open the box, but there’s a particular key that incinerates the money if you press it just once. You might think you had found a perfect generalization—a locally describable class of sequences that always opened the box—when you had merely failed to visualize all the possible paths of the machine, or failed to value all the side effects.
The machine represents the complexity of the real world. The openness of the box (which is good) and the incinerator (which is bad) represent the thousand shards of desire that make up our terminal values. The keys represent the actions and policies and strategies available to us.
When you consider how many different ways we value outcomes, and how complicated are the paths we take to get there, it’s a wonder that there exists any such thing as helpful ethical advice. (Of which the strangest of all advices, and
yet still helpful, is that “the end does not justify the means.”)
But conversely, the complicatedness of action need not say anything about the complexity of goals. You often find people who smile wisely, and say, “Well, morality is complicated, you know, female circumcision is right in one culture and wrong in another, it’s not always a bad thing to torture people. How naive you are, how full of need for closure, that you think there are any simple rules.”
You can say, unconditionally and flatly, that killing anyone is a huge dose of negative terminal utility. Yes, even Hitler. That doesn’t mean you shouldn’t shoot Hitler. It means that the net instrumental utility of shooting Hitler carries a giant dose of negative utility from Hitler’s death, and a hugely larger dose of positive utility from all the other lives that would be saved as a consequence.
Many commit the type error that I warned against in Terminal Values and Instrumental Values, and think that if the net consequential expected utility of Hitler’s death is conceded to be positive, then the immediate local terminal utility must also be positive, meaning that the moral principle “Death is always a bad thing” is itself a leaky generalization. But this is double counting, with utilities instead of probabilities; you’re setting up a resonance between the expected utility and the utility, instead of a one-way flow from utility to expected utility.
Or maybe it’s just the urge toward a one-sided policy debate: the best policy must have no drawbacks.
In my moral philosophy, the local negative utility of Hitler’s death is stable, no matter what happens to the external consequences and hence to the expected utility.
Of course, you can set up a moral argument that it’s an inherently good thing to punish evil people, even with capital punishment for sufficiently evil people. But you can’t carry this moral argument by pointing out that the consequence of shooting a man holding a leveled gun may be to save other lives. This is appealing to the value of life, not appealing to the value of death. If expected utilities are leaky and complicated, it doesn’t mean that utilities must be leaky and complicated as well. They might be! But it would be a separate argument.
Rationality- From AI to Zombies Page 58