What decision problems are better answered with analytic thinking, and what are better answered with intuition? Most Western philosophy and psychology argue that deliberating carefully and rationally is the right way of reaching a decision. "Don't let emotions turn you" they might say. The splitting of the mind into the two systems (intuitive System 1 vs. rational System 2) have just sharpened this attitude. In contrast, many studies have shown the superiority of making decision by not thinking about it (e.g. Dijksterhuis), or by relying on intuition (e.g. Kahneman and a long list of many others).

It seems that there is no absolute way that is better then the other, rather some decision problems are better handled with careful thinking, while others are solved better with "gut feeling". What are the characteristics that differentiate the two?
Keith Stanovich summaries a school of thought on this debate nicely in his review of Kahneman's 'Thinking, Fast and Slow'.

Essentially, system 1 excels in 'benign' environments, where the cues that system 1 is adept at using are reliable indicators of the true state of the world, and no one else is trying to manipulate you by faking these cues.
System two is necessary in 'hostile' environments, either because the relationships between cues and reality have changed from what system 1 expects (and has come to expect through natural selection: for millions of years, these cues were reliable), or because there are other agents who are manipulating these cues deliberately (Stanovich cites 'advertisements,
or the deliberate design of supermarket floorspace to maximize revenue').

In a similar vein, Gerd Gigerenzer, although not strictly speaking a dual process theorist, has long argued the positive role of heuristics (as opposed to the 'heuristics and biases' approach).  His main claim is that simple, automatic decision rules often outperform more complex reasoning, or even statistical approaches like linear regression.

His examples include:


A recognition heuristic - whatever the decision (predicting elections, sports, stock performances, consumer behaviour, etc.), the response you recognize is more likely to do well than the one you don't.
Fluency - If you recognize both, the one that was easier to recognize will do better.
If you're not presented with multiple choice responses, the first response to come to mind is likely the best.
One-reason choices - it's more effective to rely on one reliable cue than to analytically compute all the available information (example: running to catch a high ball, try to modulate your speed to keep the angle between the ball and the ground constant).


There's plenty more in this review (warning: paywall).

Finally, a really interesting recent approach has been to compare decisions 'made by the head' to analogous choices 'made by the hand', or in other words, design fast, action-based analogues to classic decision making tasks (see this review).

I'll not go into details here, but essentially, we're extremely good at intuitively computing the probabilities involved in executing movements under uncertainty, presumably because mammals have been doing it for millions of years, but can be pretty awful at explicitly working out the right strategy for the same problem.



In summary, **automatic, innate, intuitive processes work well for the evolutionary old tasks they were designed for, like movement planning, and a lot of real world decision making (for a certain value of 'designed': natural selection, etc.), but can lead up astray in evolutionary novel situations that human culture places us in, ranging from supermarkets, to psychology labs.

Hope this helps, sorry about the rambling!