Inference and Preference
‘Beginning to reason is like stepping onto an escalator that leads upward and out of sight. Once we take the first step, the distance to be travelled is independent of our will and we cannot know in advance where we shall end.’
— Peter Singer (1982)
‘You seriously believe a universe in which billions of sentient beings on this planet alone die horrible deaths in war, famine and plauge [sic], a universe in which people have a fleetingly short time to live before their health and strength drain away, a universe in which misunderstanding is endemic and barriers between minds are unbreechable, a universe in which most sentients are forced to serve others to obtain the basic necessities of life and in which a great many live under fear and repression, a universe where the only known planet with sentient life is under constant threat of being wiped clean by a whole range of disasters, where the entire population is under some degree of harmful delusion, doesn’t suck?’
There are many situations where we lack knowledge to move the world from an undesired state to a more desired state. We call these situations problems. In the following, I describe what I see as one of the major challenges that a technical solution to the problem of problem solving faces.
If we cannot ignore a problem, what we do is this: We take our limited knowledge about the world, our limited knowledge about what we want, and use our limited reasoning capabilities to find out what we should do to move the world closer to how we want it to be. Given that we believe the world to be like this, and given that we would like the world to be like that, we infer what action we should take.
In general, inference denotes the process of assuming that certain statements about the world are true and deriving what follows for the truth of other statements. Machines are potentially much better at inference than the human mind is. Programs have the potential to encode much more and much more precise knowledge than any one of us could learn in a lifetime. The laws of probability theory and approximations thereof can be used to infer precise knowledge about the world from data and to reason using this knowledge.
The fact that we can use machine inference to solve problems that are too difficult to be solved using human reasoning makes research into inference methods important. When we use machine inference to figure out what the dynamics of protein folding are in order to solve diseases like Alzheimer’s, we do so because, given all our data and our wish to cure the disease, our human minds still cannot figure out the cure on their own. A prerequisite for the use of machine inference is to have the problem statement available formally, as a program, a mathematical object. By singling out a small, well-defined problem, we can formally write down knowledge about the problem domain (or a program for inferring such knowledge from data) and a program that uses this knowledge to solve a particular reasoning task, i.e. to help us in determining how to change things for the better.
Any such small, formal problem statement captures only very little about what we want things to be like more generally. What do we want things to be like? We know that there are some things we want because they lead to other good things — these we call instrumental values — and there are some we want for their own sake — terminal values. We can make guesses about what our terminal values are, what we value for its own sake — joy, freedom, discovery, beauty, kindness — but ultimately, what we want the world to be like is not summed up well by any (or all) of the individual concepts behind our guesses. The name for that which does capture all about what we want is preference.
Because preference is stored opaquely in our brains, we cannot directly access its content, we can only use it to some extent. Similarly, we have little access to how our minds represent concepts like “tree”, “word”, or “spring”. This does not mean that there is no precise structure behind any given concept. On the contrary, the theories that best predict human concept learning and reasoning in recent psychological experiments are those that assume that concepts are represented as probabilistic programs.
Likewise in the case of preference: Our meager introspective abilities obscure the fact that the term ‘preference’ denotes a precise informational structure. This is easy to see where limitations of reasoning make us more uncertain than dictated by what can be deduced from the information that we know is stored in our brains, but is likely to be true more generally.
Take our search for a cure for Alzheimer’s: We have an intuitive idea what results are good and what results are bad — those that actually cure the disease and that do so without side-effects are the good ones. Nonetheless, we are uncertain about how our preferences rank different states of the world; without using machine inference to figure out the dynamics of protein folding, we do not know how preference orders possible states of the world because we cannot tell which state corresponds to a cure and which to a useless substance. By using machine inference to determine which state corresponds to a cure and which does not, we factor out a small part of our preferences that we assume to be independent from the rest (although it is not!). We thus hope to improve our understanding of what this part of our preferences says about the world.
When we — or our machines — work towards the solution of any particular subproblem without taking into account our preferences as a whole, we commit what could be called a mistaken factorization of preference. Preference as a whole makes a statement about what is the best choice at any given point in time, and if we look at only a small part of this statement, we lose value. On the other hand, if we can access the formal statement that our preferences make as a whole, then we may be able to use the reasoning capabilities of machines to determine much more precisely what the best choice looks like than would be possible through introspection.
If preference is a mathematical structure — even if it is currently implemented in our brains in a distributed and implicit way — then what kind of structure could it be? I do not know the answer to this question, but there are situations that are similar in the sense that they also take an intuitive idea and reify it into a mathematical object.
In computer science, there is the notion of the future of a computation. For example, at point # in the program (* 3 (+ 4 #)), what the future holds is that whatever value we hand it, it will add 4, multiply the result by 3, and then do whatever it does to the return value of a program that has finished, e.g. print the result to the screen. The notion of a continuation captures the idea of taking the future of a computation and storing it in an object. If we capture the continuation at #, the future starting from this point becomes a mathematical object, a value that we can pass around just like any other object and that we can reason about formally.
Analogously, we would like to take the diffuse notion of the preferences of a decision-making system (like you and me) and reify it into a formal object. And analogously, we expect this object to be a computational structure that contains information about what will — or, in the case of preference, should — be done in the future, but it may take lots of computation to determine what exactly this information says.
The project of formalizing preference has two parts: understanding the structure of preference (i.e. what kind of object are preferences, how do they compose) and getting at the actual content of human preference (i.e. extracting or pointing to the preferences of a given agent).
There are proposals for what the structure of preference could look like (e.g. preference logics, utility theory), but they seem insufficient in non-trivial situations. Two examples of such situations are (1) that we want our preferences not to lose meaning when it turns out that we have been mistaken about some of the things our preferences talk about (the so-called ontology problem), and (2) that we may have preferences about how we want preferences to interact. Different people appear to want different things, and even within a single mind, seemingly contradicting wishes exist. For example, there are things we want to do and there are things we actually enjoy doing, and these are often not the same. How do we figure out the statement that such a system of preferences makes about what should be done? This is called preference aggregation across agents and could be called compositionality of preference within a single agent.
Formalizing the content of our preferences, i.e. pointing to preference in a precise, machine-readable way, poses similarly challenging problems. The strongest illustration of this that I can currently think of is the following: If our preferences determine which method of formalizing their content is the correct one (namely the one that results in our actual preferences), and if we cannot know or use our preferences with precision until they are available as mathematical objects, then how can we find the correct formalization method? I can imagine that knowing the structure of preference would clarify what properties a method needs to have that allows us to formally refer to the preference content of any given agent, but to what extent this is the case is an open question.
To summarize, the fundamental problem is this: We have only limited access to what we want, and we cannot really figure out what follows from that which we do know about what we want. Machines are potentially much better at reasoning about what follows if we can give a formal description of what we want. However, if we formalize only a few small problems, we lose value due to our limited reasoning about the remaining part of our preferences and due to assuming independence between preferences when in reality they are intertwined. We need to understand preference as a formal object if we want to use machine inference to figure out what should be done to make this world a nicer place.
I thank Vladimir Nesov for useful discussion and for originating many of the ideas mentioned here.

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Dennett introduces three levels of abstraction we can use to describe intentional systems: Descriptions on the level of physics, a functional perspective and the intentional stance. In order to determine in how far these levels presuppose optimal design and rational behavior, I am first going to explain what Dennett means when he talks about intentional systems, then describe each of the three different levels of abstraction and finally analyze what role the notions of optimality and rationality play for each of them.