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What is the Prosecutor's Fallacy?

 , updated on October 21, 2023
The Prosecutor's Fallacy is a type of invalid interpretation of a valid statistic.
Consider a person who is accused of cheating on a lottery. A prosecutor may point out that there was only a 1 in 10,000,000 chance of the person winning, so they must have cheated. This may neglect the fact that 20,000,000 tickets were sold and someone had to win.

False Positives

As another example, consider a crime that is investigated by scanning a database of 10,000,000 people. A match is found to a suspect and at trial the prosecutor may state there was only a 2% false positive rate. They fail to mention that this is extremely significant whereby a total of 200,000 false positives would be generated by scanning all 10,000,000 entries.
Number of False Positives = Population Size × False Positive Rate
Number of False Positives = 10,000,000 × 0.02
Number of False Positives = 200,000 false positives

Significance

The Prosecutor's Fallacy is not specific to law. It has implications for scientific analysis, business analysis, problem solving and decision making.
Overview: Prosecutors Fallacy
Type
Statistical Fallacy
Definition
An invalid interpretation of a valid statistic.
Common Cause
Using a specific probability while ignoring a more general probability.
Neglecting the importance of margin of error and sample size.
Pointing out that the sequence of events that make someone innocent have a low probability without considering that the sequence of events that make someone guilty are equally improbable.
Related Concepts
Next: Base Rate Fallacy
More about statistical analysis:
Abductive Reasoning
Abstract Thinking
Abstraction
Aesthetics
Analogy
Analysis Paralysis
Analytical Thinking
Anomie
Argument
Argument From Silence
Arrow Of Time
Assertions
Automaticity
Backward Induction
Base Rate Fallacy
Benefit Of Doubt
Big Picture
Brainstorming
Call To Action
Catch 22
Causality
Choice Architecture
Circular Reasoning
Cognition
Cognitive Abilities
Cognitive Biases
Cold Logic
Collective Intelligence
Complexity Bias
Concept
Consciousness
Constructive Criticism
Convergent Thinking
Counterfactual Thinking
Creative Tension
Creeping Normality
Critical Thinking
Culture
Curse Of Knowledge
Decision Fatigue
Decision Framing
Decision Making
Defensive Pessimism
Design Thinking
Divergent Thinking
Educated Guess
Emotional Intelligence
Epic Meaning
Essential Complexity
Excluded Middle
Failure Of Imagination
Fallacies
Fallacy Fallacy
False Analogy
False Balance
False Dichotomy
False Equivalence
First Principles
Formal Logic
Four Causes
Fuzzy Logic
Gambler's Fallacy
Generalization
Golden Hammer
Good Judgement
Grey Area
Groupthink
Heuristics
Hindsight Bias
Hope
Idealism
Ideas
If-By-Whiskey
Illogical Success
Imagination
Independent Thinking
Inductive Reasoning
Inference
Influencing
Informal Logic
Information
Information Cascade
Introspection
Intuition
Inventive Step
Learning
Lifestyle
Logic
Logical Argument
Logical Thinking
Ludic Fallacy
Magical Thinking
Meaning
Mental Experiences
Mental State
Mindset
Misuse of Statistics
Motivated Reasoning
Natural Language
Nirvana Fallacy
Norms
Not Even Wrong
Objective Reason
Objectivity
Opinion
Overthinking
Perception
Personal Values
Perspective
Positive Thinking
Practical Thinking
Pragmatism
Premise
Problem Solving
Proof By Example
Propositional Logic
Prosecutor's Fallacy
Radical Chic
Rational Thought
Realism
Reality
Reason
Reasoning
Red Herring
Reflective Thinking
Reification
Relativism
Salience
Scarcity Mindset
Scientism
Selective Attention
Serendipity
Situational Awareness
Sour Grapes
State Of Mind
Storytelling
Subjectivity
Systems Thinking
Thinking
Thought Experiment
Unknown Unknowns
Visual Thinking
Want To Believe
Whataboutism
Win-Win Thinking
Wishful Thinking
Worldview
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