
Problems & Paradoxes
1. St. Petersburg Paradox 2. Allais Paradox 3. Equity Premium Puzzle 4. Risk Aversion 5. Gains and Losses 6. Loss Aversion 7. Overweighting of low Probabilities 8. Underweighting of high Probabilities 9. "FourFoldPattern" 10. Shape of Probability Weighting Function 11. Ellsberg Paradox 12. Preference Reversals

The Allais paradox (modified)
Suppose Mr. Somebody offers you a choice of only one of the following: A guaranteed gain of $99. Or A lottery: The gain of $100 with the probability P(preliminary) = 99% or $0 with the (preliminary) probability 1%. (For experiment's accuracy, both $99 and $100 should be in $1 banknotes. So 99 and 100 banknotes of $1) The mathematical expectations of guarantee and lottery outcomes are exactly the same. But the welldetermined experimental fact is: in similar experiments the obvious majority of people chose the guaranteed gain instead of the lottery Top
Gains and Losses
Compare two experiments: 1) Mr. Somebody offers you a choice of only one of the following: A guaranteed gain of $99. Or A lottery: The gain of $100 with the probability P(preliminary) = 99% or $0 with the (preliminary) probability 1%. 2) Mr. Somebody offers you a choice of only one of the following: A guaranteed loss of $99. Or A lottery: The loss of $100 with the probability P(preliminary) = 99% or $0 with the (preliminary) probability 1%. The mathematical expectations of the guarantee and lottery outcomes are exactly the same in both experiments. But in similar experiments, the overwhelming majority of people chose:  in the case of gains  the guaranteed gain instead of the lottery one.  in the case of losses  the lottery loss instead of the guaranteed one. The possible wellknown "natural and clear explanation" of gains in the Allais paradox by means of risk aversion cannot supply any uniform explanation for both gains and losses. The result of this explanation is gains' risk aversion and losses' risk seeking. Top
Overweighting of low Probabilities
Suppose Mr. Somebody offers you a choice of only one of the following: A guaranteed gain of $1. Or A lottery: The gain of $100 with the probability P(preliminary) = 1% or $0 with the (preliminary) probability 1%. The mathematical expectations of guarantee and lottery outcomes are exactly the same. But the welldetermined experimental fact is: in similar experiments the obvious majority of people chose the lottery instead of the guaranteed gain. Top
FourFoldPattern
The welldetermined facts are: For positive (gains) risky prospects, people typically 1) overweight low probabilities but 2) underweight high probabilities. For negative (losses) risky prospects, people typically 3) underweight low probabilities but 4) overweight high probabilities. Top


