Are Two Heads Better Than One? · eieio.games

Summary

The article explores a probability puzzle where adding a second, equally unreliable source of information doesn't improve accuracy. Accuracy only improves when an odd number of sources are used, acting as tiebreakers. This phenomenon is related to Condorcet's jury theorem.

Key Takeaways

1. Adding a second source of information that is as reliable as the first does not improve the accuracy of guessing a coin flip.
2. Accuracy improves when an odd number of sources are used, as the additional source can act as a tiebreaker when the initial sources disagree.
3. The phenomenon is related to Condorcet's jury theorem, which recognizes that an even number of voters doesn't add any information.

Statement Breakdown

• Claimed Facts: 60% of statements the article presents as facts
• Opinions: 20% of statements classified as editorial or subjective
• Claims: 20% of statements surfaced for additional reader evaluation

Credibility & Bias Reasoning

Credibility assessment: The article presents a clear problem, simulation code, and mathematical proof to support its claims. The author provides the code used for the simulation, allowing for verification. The logic is explained step-by-step, enhancing transparency and credibility.

Bias assessment: Analytical Exploration. The article focuses on exploring a mathematical concept through simulation and logical deduction. The author presents the findings objectively, without promoting a specific agenda or viewpoint. The primary goal is to share an interesting observation and its implications.

Note: The article's claims are supported by simulation and mathematical reasoning, increasing its reliability. However, readers should independently verify the code and calculations.

Credibility flag: Well-supported

Claimed Facts (7)

• This is a given condition of the problem.
• This is the accuracy achieved by trusting Alice.
• This refers to the improvement in accuracy when adding Bob.
• This is the accuracy when using both Alice and Bob.
• This is the result of the simulation with only Alice.
• This is the result of the simulation with both Alice and Bob.
• This is a calculation of the probability of both telling the truth.

Opinions (6)

• This is the author's reaction to the simulation results.
• This is the author's attempt to guide the reader's understanding.
• This is the author's interpretation of the situation when Alice and Bob disagree.
• This is the author's subjective assessment of the result.
• This reflects the author's personal experience and initial reaction.
• This is the author's personal feeling about the result.

Claims (6)

• While less frequent, the term "pretty unlikely" is subjective without a specific probability.
• The claim that it would be better to ask only Alice is not strictly true; the accuracy remains the same.
• The term "substantially" is subjective without a specific quantification of the improvement.
• This is a generalization that may not apply to all voting scenarios.
• This statement assumes a specific betting or decision-making context without providing broader applicability.
• This is an emotional appeal to the reader.

Key Sources

• Author — Blogger
• Simulation Code — Python Script