Three ways to Model Beliefs
Starting this week, I am going to start writing blog entries that outline my research ideas, both for people to comment and make suggestions, but also to explore the possibility that the internet is a useful medium to conduct research. Let me know if you have any thoughts about this matter.
Recently, I have been thinking a lot about beliefs and how they are embodied. Beliefs, like other mental states, are rather complex — they are a combination of cognitive, emotional and social elements. Like any other mental state which involves intentionality, it is rather hard to model the actual intention or emotion behind a belief. It is a lot easier to see the behavior or action that a person commits than to model the intention that resulted in the action. However, human beings tend to interpret actions as intentional events committed within an interpretive context (often shared by the parties in question). For example, suppose you cancelled a meeting with a friend at the last moment you might send them an email saying “I am sorry, something urgent came up, can we have lunch tomorrow instead?” Now, apart from the bare information in the email (Saying that you need to do something else) the email also conveys an intentional state (being apologetic) and also has a built in expectation that the recipient will excuse your action — and assumes that in the context of a friendship appointments can be broken without serious repercussions. In other words, behaviors that communicate beliefs have many unstated assumptions. Any attempt to model beliefs has to take these unstated intentional and contextual assumptions into account. So how should one model beliefs?
First, note that mathematical modeling by its very nature is cognitive. Emotional and affective aspects of beliefs are represented in a mathematical model by quantitative surrogates. For example, if a certain community believes in the use of violence to attain political goals, a computational model may replace actual emotional content by the scale that measures the strength of the proposition “How willing are you to use violence to achieve your goals?” on a scale of 1–5. No allowance is made for the actual depth of the feeling or the subjective sense of the viability of using violence. For this reason, the least interpretive and most behaviorist modeling strategy is: “Do not speculate about the actual intention behind a behavior and model the data coming from surveys (such as the one illustrated above)”. This approach, the first of the three that I want to describe, can be called the statistical approach to modeling beliefs.
So, for example, using the statistical method on the violence problem, a researcher might take all the data from surveys (such as the rate from 1–5 question above) along with other variables such as age/gender/geographical distribution and then make hypotheses about who and where are most likely to use violence. The statistical method does not say anything about why people may want to use violence and what drives a person to use violence in the first place.
The second modeling strategy, that I call the decision-theoretic strategy, goes one step further into modeling the internal structure of beliefs. In this strategy, it is assumed that beliefs are formed and communicated within a rational framework, i.e., the agents forming, holding and communicating their beliefs do so on the basis of a rational (could be bounded rationality) system for evaluating and changing their beliefs. Of course, there can be several mathematical models of rationality in behavior– Logic, Game theory and Probability are all competing models of rationality and can all be used profitably in modeling the rational norms for holding and justifying a belief. For example, one could assume that people who advocate the use of violence do so because they have studied the use of violence in the past or see themselves as playing a game with the authorities and have a rational means to evaluate the extent to which violence will further their goals. A game theoretic model may study how the two sides are willing to make concessions and how one of the sides, by using violence as one of its moves can bargain for better concessions. In this game theoretic framework, violence as a move would have an optimal state, and presumably agents using violence would try to attain this optimal state.
However even the decision theoretic model does not really tell us how is it that violence came to be a part of the set of acceptable moves. Furthermore, the decision theoretic model assumes that the agent making decisions is fundamentally rational (or approximates one, so that deviations from rationality are errors). Unfortunately, we know that humans do not act rationally — certainly not when it comes to sacred values, and even not in dry economic endeavors; Kahnemann and Tversky put paid to that notion. So one is left with an intriguing third possibility — while human beliefs are not created and acted upon for rational reasons, they might still have some underlying structure. The elucidation of this structure is the goal of the mathematical scientist at the “structural level”. Of course this “structural” strategy is controversial — one could argue that the origin of beliefs, say violent beliefs, is primarily a topic in psychology and mathematical modeling has nothing to say about it. I would like to argue otherwise, that belief states and structures that are seen as psychological or emotional in origin hide plenty of cognitive and mathematical structure. A good model for our study is the computational modeling of language. Language, the primary human means for conveying emotion, affect and other internal states also has plenty of structure (syntactic, semantic etc). Furthermore this structure is not rational — no one has been able to argue successfully that human language was designed rationally with some engineering like goal in mind. But Chomsky and his followers have shown that language can be studied mathematically, yielding insights into language that cannot even be stated in the old historical and comparative approaches. Why not apply the same idea to beliefs?