How do you predict a cognitive bias theoretically using dual process theory? Disclaimer: I am a complete layman in psychology, with no education in the field whatsoever. This question was prompted by my reading Kahneman's "Thinking Fast and Slow", in which he discusses the model of System 1 and System 2 extensively. 

I thought many of the cognitive biases and other psychological effects were fascinating to read about, and I really enjoyed it. But every time he brought the "two systems" into the discussion of a particular cognitive bias (such as the affect heuristic or hindsight bias), it felt like he was using it as a post hoc explanation of how the effect could be described by certain characteristics of the two systems. It was never clear to me how you can show that the dual process implies the existence of the discussed effect.

I think he did a far better job showing how certain psychological effects result from prospect theory. It's easy to show, for example, how prospect theory implies the endowment effect, as shown in the given link. Even though knowledge of the endowment effect existed before prospect theory, it's easy to see how the endowment effect could have been predicted by prospect theory. You can even prove that it would exist, given the utility function of prospect theory and the right axioms.

But I'm confused about how you can do the same with dual process theory, and the cognitive biases that it supposedly explains. How can you use dual process theory to predict the existence of a cognitive bias? Are there examples of cognitive biases that were, or can be explicitly predicted using DPT? 

If this is just a poorly framed question--if predicting cognitive biases is not one of the purposes of the theory--then what is the purpose of dual process theory?



EDIT: I want to make a few clarifications here.
My concern is neither with the predictive success of DPT - or other theories to which I compare it - nor is it with whether the things that DPT can predict have already been discovered before DPT. The example I used - prospect theory, and its "prediction" of the endowment effect - is both retroactive (the effect was known before the theory), and according to the answer by Fizz, has questionable predictive verification. However, the manner by which you can use the theory to make the prediction is quite clear. If we assume the value curve given by prospect theory, and the claim of prospect theory that a person's perceived value of a gain or loss is relative to their current position rather than absolutely dependent on the final state, then it follows logically that an individual's perceived gain in value for acquiring something is lower than their perceived loss in value for losing the same thing. This can be answered in theory, on pen and paper, given the framing of the scenario and the axioms of prospect theory.

With dual process theory I want to understand:


what kind of predictions it can make about human behavior
how to make those predictions using the theory


Since this is seemingly a very celebrated modern theory of human behavior, I just want to know how it's used. I don't mind if every known consequence of dual process theory was discovered before the theory, nor do I mind if the method is not as rigorous as that of a physics theory.
Well, whether something is truly predicted or a post-hoc explanation can be difficult to disentangle in this area. What you're asking for is that dual-process theory predicts the existence of a new type of bias previously unobserved. And that's a tall order because observational psychology has been around for a log time. 

Probably the area in which I buy the dual-process explanations the most is belief bias; dual-process theory predicts that our intuitions (T-1 processes) bias us for plausible conclusions (and against implausible ones), even if the reasoning (T-2 process) is faulty (and respectively correct).

Predicting an entirely new type of bias is not the only way to test dual-process theory. One can test it quantitatively by looking at known biases and verifying experimentally if the timing affects the level of bias. And in the case of belief bias, that seems to be the case.

The purpose of any scientific theory is to explain some aspect of the real world. Just because we don't continuously discover (qualitatively) new facts based on that theory doesn't invalidate it as scientific theory.

In psychology in general, experimental data is fairly easy to come by, so evidence often leads theory. It's not like in modern physics where you predict the Higgs boson and it takes decades to discover it in actual experiment. Or you predict the string structure of the universe, but it's unlikely we'll ever be able to test that.



By request, here's the introductory / "theoretical" part of the paper:


  [Dual-process] theories posit two distinct
  processes of reasoning that compete for control of the response that
  participants make in reasoning tasks. Heuristic or System1 processes are
  characterised as rapid, implicit, associative, and heavily contextualised,
  whereas analytic or System2 processes are described as slow and sequential
  but capable of abstraction and generalisation. Note that a key difference is
  the speed of processing. The reason for this is that analytic processing is a
  sequential process requiring use of central working memory and is
  constrained by its limited capacity. By contrast, heuristic processes operate
  through massively parallel implicit systems that exert an unconscious
  influence on responding. In support of this distinction is evidence of
  substantial correlations between general intelligence and working memory
  capacity with abstract deductive reasoning but not pragmatic, belief-based
  reasoning (Stanovich, 2004).
  
  While a mass of evidence has been recorded supporting the idea that there
  are two different processes of reasoning, more research is needed to confirm
  the characteristics that theorists have attributed to the cognitive systems that
  may underlie these observations. A relevant methodological innovation
  reported by Roberts and Newton (2002) is the rapid-response reasoning
  task. The idea is that by constraining participants to respond within a short
  period of time, the slower analytic process of reasoning will be differentially
  inhibited. For example, on the Wason selection task, there is a well established
  non-logical tendency, known as ‘‘matching bias’’ (Evans, 1998),
  to select cards that match the explicit content of conditional statements,
  regardless of the presence of negations. Roberts and Newton (2002) showed
  that measures of matching bias were significantly increased when a rapid response
  version of the selection task was compared with a free-time version.
  This is as dual-process theory would predict, since any influence of analytic
  reasoning to inhibit the bias would be suppressed by the requirement to
  respond quickly.
  
  A central phenomenon in dual-process accounts of reasoning is that of
  ‘‘belief bias’’—the tendency to evaluate the validity of an argument on
  the basis of whether or not one agrees with the conclusion, rather than
  on whether or not it follows logically from the premises. The
  phenomenon is one of the earliest reported in the psychology of
  reasoning (Wilkins, 1928) but the modern study of the effect dates from
  the paper of Evans, Barston, and Pollard (1983), which established the
  phenomenon with all relevant experimental controls. Evans et al. showed
  that participants’ evaluations of conclusions were substantially affected
  both by the logical validity of the arguments and by the believability of
  the conclusions. With the help of protocol analyses Evans et al.
  characterised the effect as involving a within-participant conflict between
  logic-based (analytic) processes and belief-based (heuristic) processes.
  Such a conflict is to be expected in view of contemporary dual-process
  theories. In support of this, it has been shown that participants high in
  general intelligence are more able to resist belief biases (Stanovich &amp;
  West, 1997) and that logical and belief-based responding are neurologically
  differentiated (Goel &amp; Dolan, 2003).
  
  In this study, we extend the rapid-response methodology of Roberts and
  Newton (2002) to the study of belief bias in syllogistic reasoning. Using a
  conclusion-evaluation paradigm with problems similar to those of Evans
  et al. (1983), we compare performance under rapid-response and free-time
  tasks. We predict that the participants required to respond rapidly will show
  (a) an increased level of belief bias and (b) a reduced level of logical
  responding.




And regarding prospect theory; quoting from Wikipedia page on it:


  Critics from the field of psychology argued that even if Prospect Theory arose as a descriptive model, it offers no psychological explanations for the processes stated in it.


So I don't see how it is any less of a reverse-fitting of (arguably more math-oriented) description to prior data.

Furthermore, the endowment effect is not even certain to exist, if wikipedia is correct (There are some failed replications, no meta-analysis that I can find.) There are a lot of other (possible) theoretical explanations given for it there as well. In fact there is more theory than there are experiments. Also, being much closer to economics, it's generally more likely to have mathematical models for it.