Write a short note on Allais paradox and Ellsberg paradox.

Allais Paradox vs. Ellsberg Paradox

Allais Paradox:

1. Definition: The Allais Paradox is a phenomenon in decision theory where individuals exhibit inconsistent choices in certain types of decision-making scenarios involving risk and uncertainty.

2. Scenario: In the classic Allais Paradox scenario, individuals are presented with two choices:

   • Choice A: A guaranteed amount of money (e.g., $1 million) with certainty.
   • Choice B: A gamble with two possible outcomes:
     • Outcome 1: $0
     • Outcome 2: $1 million with a probability of 10% and $0 otherwise.

3. Inconsistency: Despite the expected value of both choices being the same ($100,000), many individuals tend to prefer choice A over choice B, even though choice B offers a higher potential payoff.

Ellsberg Paradox:

1. Definition: The Ellsberg Paradox is a similar phenomenon in decision theory involving ambiguity and uncertainty, named after the American economist Daniel Ellsberg.

2. Scenario: In the classic Ellsberg Paradox scenario, individuals are presented with an urn containing 90 red balls and 10 black balls. They are then asked to make two choices:

   • Choice 1: Choose between drawing a red ball from the urn or drawing from a second urn with unknown composition (e.g., 50 red balls and 50 black balls).
   • Choice 2: Choose between drawing a black ball from the urn or drawing from a second urn with unknown composition (e.g., 50 red balls and 50 black balls).

3. Inconsistency: Despite the information being the same for both choices in each pair (e.g., 50% chance of drawing a red or black ball from the second urn), individuals tend to exhibit inconsistent preferences, often showing a preference for the known probabilities over unknown probabilities.

Key Differences:

1. Risk vs. Ambiguity: The Allais Paradox involves choices between known probabilities (risk), while the Ellsberg Paradox involves choices between unknown probabilities (ambiguity).

2. Certainty Effect: The Allais Paradox is often attributed to a "certainty effect," where individuals prefer certain outcomes over uncertain outcomes, even when the uncertain outcomes offer higher expected value. The Ellsberg Paradox, on the other hand, is often attributed to a preference for known probabilities over unknown probabilities, known as the "ambiguity aversion."

In summary, while both paradoxes highlight inconsistencies in decision-making under risk and uncertainty, the Allais Paradox focuses on choices between known probabilities, while the Ellsberg Paradox focuses on choices between unknown probabilities.