Psychology of Planning, Proof, Insight & Choice

Problem Decomposition

Problem Decomposition

Breaking down complex problems into smaller, manageable tasks, which can follow different approaches:

Breadth-first: Minimal commitments to parts of the problem.

Depth-first: Immediate feedback but higher cognitive effort.

Opportunistic: Leveraging the current state for decisions.

The Problem Space (Newell & Simon, 1972)

Represents all possible paths between an initial state and a goal state in problem-solving. Larger problem spaces are harder to navigate due to increased possibilities.

Bounded Rationality

Humans are limited in processing all available information, so they use satisficing (choosing an option that is "good enough") to make decisions.

Problem Representation

The way a problem is presented influences how it is approached. Factors include format, thematic content, and external conditions like urgency or risk.

Means-Ends Analysis

A heuristic that breaks problems into sub-goals and reduces the gap between the current state and the goal state (e.g., fixing a car step by step).

Heuristics in Problem Solving

Mental shortcuts for decision-making:

Hill-Climbing: Always moving closer to the goal.

Trial and Error: Testing solutions without a clear plan.

Sampling Heuristics: Using anchoring or representativeness to guide choices.

Consequences of Not Planning

Acting without planning often leads to suboptimal solutions, as demonstrated in studies like Ormerod et al. (2013) and the N-ball problem.

Sub-goals and Decomposition

Breaking problems into smaller parts improves efficiency and success when solving complex tasks.

Deduction

Drawing specific conclusions from general premises, used in proofs and logical reasoning (e.g., "If all mammals have fur, and dogs are mammals, then dogs have fur.").

Induction

Forming general conclusions based on specific observations (e.g., "Every swan I’ve seen is white; therefore, all swans are white.").

Abduction

Inferring the best explanation for an observation (e.g., "The grass is wet; it likely rained last night.").

Modus Ponens

A valid logical structure:
"If A, then B. A is true; therefore, B is true."

Modus Tollens

A valid logical structure:
"If A, then B. B is false; therefore, A is false."

Mental Models (Johnson-Laird, 1983)

Reasoners construct possible outcomes that align with premises to draw conclusions. Limited by working memory capacity and constrained by the principle of truth (focusing on true elements).

Information Gain

The process of reasoning by reducing uncertainty through the assessment of event rarity or likelihood, as explained in Bayesian frameworks.

Dual-System Theory

Decision-making involves two systems:

System 1: Fast, intuitive, and heuristic-driven but error-prone.

System 2: Slow, logical, and deliberate but requires more cognitive effort.

Insight

A sudden realization of a solution to a problem, often preceded by fixation or impasse. The "Aha moment" occurs after representational change.

Representational Change Theory (Knoblich et al., 1999)

Insight arises when knowledge constraints are overcome, allowing new mental representations to form and enable problem-solving.

Incubation

Taking a break from a problem to allow unconscious processing, which improves divergent thinking, linguistic insight, and visual problem-solving.

Prospect Theory (Kahneman & Tversky, 1979)

A descriptive model of decision-making that explains behaviours like:

Loss Aversion: Preference for certain gains over uncertain losses.

Probability Weighting: Overestimating unlikely events and underestimating likely ones.

Preference Reversals

When framing changes (e.g., presenting as a gain or loss), people may reverse their preferences, as shown by Lichtenstein and Slovic (1971).

Anchoring

Initial information influences subsequent judgments and decisions disproportionately, as seen in decisions about credit card payments or pricing.

Sleep and Problem-Solving

Sleep facilitates analogical transfer and problem-solving by consolidating memory and enabling creative thinking (Monaghan et al., 2000).