Reference Frames for Expected Value

Puzzle 1: George mortgages his house to invest in lottery tickets. He wins and becomes a millionaire. Did he make a good choice?

This looks like a tree-falls-in-forest-did-it-make-a-sound question. The expected value was negative, the outcome was positive, "good choice" can mean either assessment, distinguish them, mystery dissolved.

‘expected value’ is typically defined in reference to a specific set of information and intelligence rather than an objective truth about the world.

Expected value is subjectively objective. It depends on the knowledge one has, but what knowledge one has is also an objective fact about the world.

After all, if there is any sort of free will, perhaps we have the ability to make decisions that are sub-optimal by our expected value functions. Perhaps we commonly do so (else it wouldn’t be much in the sense of ‘free’ will.)

Is this Sartre's concept of free will as actions coming out of nowhere, free of all considerations of what would actually be a good idea, with suicide as the ultimate free act? Eliezer has provided the answer to the Problem of Free Will here.

You come to what is more or less the right consequentialist answer in the end, but it seems to me that your path is needlessly convoluted. Why are we judging past actions? Generally, the reason is to give us insight into and perhaps influence future decisions. So we don't judge the lottery purchase to have been good, because it wouldn't be a good idea to imitate it (we have no way to successfully imitate "buy a winning lottery ticket" behavior, and imitating "buy a lottery ticket" behavior has poor expected utility, and similarly for many broader or narrower classes of similar actions), and so we want to discourage people from imitating it, not encourage them. If we're being good consequentialists, what other means could it possibly be appropriate to use in deciding how to judge other than basing it on the consequences of judging in that way?

I read most of this post with a furrowed brow, wondering what you were getting at, until I got to the point on free will, which I think makes some sense.

If good choices are relative to states of knowledge and abilities, then how are not all choices good choices, given that these things are beyond our control?

I think, yes, in order to have the concept of 'good' and 'bad' choices in hindsight, one has to assume the person could have acted differently, even though in a very strict free-will sense, they couldn't have.

However there are fundamental limits to how differently they could have acted — nobody can predict the outcome of a lottery for example. So I suppose we draw the line at what reasonable expectations for a human being are. But we still make individual exceptions — if you were to find out someone had a cognitive disability, you're not going to judge them as harshly for making a bad decision. This is different to saying it's not a bad decision — it is — it's just you're not going to hold them responsible for it. It still should not be emulated, as Protagoras put it.

I'm also pretty convinced that large scale random events are more often than not quantum random (that is, quantum randomness, though initially small in classical systems, is amplified by classical chaos such that different Everett branches get different lottery results and coin flips). So if you ask yourself "If I were in that persons position, should I have bought the lottery ticket?", well, the outcome is actually totally not predetermined. Not that I think any argument here should rely on the quantum vs classical randomness distinction, but I thought I'd mention it anyway.

But it seems like it's not even a coherent concept, to judge based on actual results rather than expected, so apart from the free will angle and pointing out that some people might have badly calculated expectations, I don't think it's an idea worth putting too much thought into, and I think that those interpreting consequentialist ethics in this way must be very confused people indeed.

Say the player thought that they were likely win the lottery, that it was a good purchase. This may seem insane to someone familiar with probability and the lottery system, but not everyone is familiar with these things.

I would say this person made a good decision with bad information.

Perhaps we should attempt to stop placing so much emphasis on individualism and just try to do the best we can while not judging others nor other decisions much.

There are lots of times when it's important to judge people e.g. for hiring or performance reviews.

One would be ethical if their actions end up with positive outcomes, disregarding the intentions of those actions. For instance, a terrorist who accidentally foils an otherwise catastrophic terrorist plan would have done a very ‘morally good’ action.

This seems intuitively strange to many, it definitely is to me. Instead, ‘expected value’ seems to be a better way of both making decisions and judging the decisions made by others.

If the actual outcome of your action was positive, it was a good action. Buying the winning lottery ticket, as per your example, was a good action. Buying a losing lottery ticket was a bad action. Since we care about just the consequences of the action, the goodness of an action can only be evaluated after the consequences have been observed - at some point after the action was taken (I think this is enforced by the direction of causality, but maybe not).

So we don't know if an action is good or not until it's in the past. But we can only choose future actions! What's a consequentialist to do? (Equivalently, since we don't know whether a lottery ticket is a winner or a loser until the draw, how can we choose to buy the winning ticket and choose not to buy the losing ticket?) Well, we make the best choice under uncertainty that we can, which is to use expected values. The probability-literate person is making the best choice under uncertainty they can; the lottery player is not.

The next step is to say that we want as many good things to happen as possible, so "expected value calculations" is a correct way of making decisions (that can sometimes produce bad actions, but less often than others) and "wishful thinking" is an incorrect way of making decisions.

So the probability-literate used a correct decision procedure to come to a bad action, and the lottery player used an incorrect decision procedure to come to a good action.

The last step is to say that judging past actions changes nothing about the consequences of that action, but judging decision procedures does change something about future consequences (via changing which actions get taken). Here is the value in judging a person's decision procedures. The terrorist used a very morally wrong decision procedure to come up with a very morally good action: the act is good and the decision procedure is bad, and if we judge the terrorist by their decision procedure we influence future actions.

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I think it's very important for consequentialists to always remember that an action's moral worth is evaluated on its consequences, and not on the decision theory that produced it. This means that despite your best efforts, you will absolutely make the best decision possible and still commit bad acts.

If you let it collapse - if you take the shortcut and say "making the best decision you could is all you can do", then every decision you make is good, except for inattentiveness or laziness, and you lose the chance to find out that expected value calculations or Bayes' theorem needs to go out the window.

Thanks for taking the time to try to debunk some of the sillier aspects of classic utilitarianism. :)

‘Actual value’ exists only theoretically, even after the fact.

You've come close to an important point here, though I believe its expression needs to be refined. My conclusion is that value has real existence. This conclusion is primarily based on the personal experience of possessing real preferences, and my inference (to a high level of confidence) that other humans routinely do the same. We might reasonably doubt the a priori correspondence between actual preference, and the perception of preference, but even so, the assumption that I make decisions entails that I'm motivated by the pursuit of value.

Perhaps, then, you would agree that it is more correct to say that the relative value of an action can be judged only theoretically.

Thus, we account for the fact that if the action had not been performed, the outcome would be something different, the value of which we can at best only make an educated guess about, making a non-theory-laden assessment of relative value impossible. The further substitution of my 'can be judged' in place of your 'exists' seems to me necessary, to avoid committing the mind projection fallacy.

The main question in this essay, the harder question, is if we can judge previous decisions based on their respective expected values, ...

If it is the decision that is being judged (as the question specifies), rather than its outcome, then clearly the answer is "yes." There can not be anything better than expected value to base a decision on. In a determined bid to be voted captain obvious, I examined this in some detail, in a blog post, Is rationality desirable?

... and how to possibly come up with the relevant expected values to do so.

This is called science! You are right, though, to be cautious. It strikes me that many assume they can draw conclusions about the relative rationality of two agents, when really, they ought to do more work for their conclusions to be sound. I once listened to a talk in which it was concluded that the test subjects in some psychological study were not 'Bayesian optimal.' I asked the speaker how he knew this. How had he measured their prior distributions? their probability models? their utility functions? These things are all part of the process of determining a course of action.

I feel like one of the most important distinctions one can make about consequentialism or a specific consequentialist system is to separate the value system form the decision procedure. In fact, I find that the ability to do this (implicitly or explicitly) is a prerequisite for having productive discussions about it.

It seems to me that there's two different hidden questions pointed at by "Was this decision ethical", and depending on why you're asking you come up with different answers.

If you're asking "Was this the correct choice", you want to know if from the perspective of perfect knowledge, how close to optimal was this action, which corresponds fairly closely to actual result (though there's complications with MWI, and possibly some other parts of the large universe. Or maybe that goes away if you swap out perfect knowledge for something more like "from the perspective of the observer after the event", in which case the ethical status of a decision can be literally physically undefined until some time after the decision is made?). However, a lot of the time what you're actually asking is "How does this choice impact my assessment of a person's ability to make correct choices", in which case you're just interested in knowing whether the choice made using a method which reliably produces correct choices (which includes things like gathering relevant information on probability before remortgaging your house and blowing it on lottery tickets).

The first question is relatively easy to judge since you have evidence on how well a decision went, though lack of knowing the results other options gives some uncertainty, but does not provide useful information about trustworthiness of a person in general. The second seems much more useful since it should relate better to future behaviour, but is basically impossible to even approach quantifying in any realistically complicated situation. So.. you ask the first question, trying to get evidence about the second which is what you usually want to know?

If, once you know whether a decision in the past was correct (with reference to whatever morals you pick), and whether the method used to make that decision generally produces correct decisions, you still feel the need to ask "but was it really ethical", it looks like a disguised query.

Optimizing Future Decisions: Actual vs. Expected Value

Not sure what you mean here. Future is never actual, only expected (or, more often, unexpected).