# Новые результаты. Решения, объяснения проблем, парадоксов       New Results.
Solution & Explanation
Contents   (in new windows)

1.   Solution of Problems
(of St. Petersburg Paradox   of Allais Paradox   of Equity Premium Puzzle   of Risk Aversion   of Gains and Losses   of Loss Aversion   of Overweighting of low Probabilities   of Underweighting of high Probabilities of "Four-Fold-Pattern"   of Shape of Probability Weighting Function   of Ellsberg Paradox   of Preference Reversals )
2.   New Results
( "Impossibilities" in Forecasting   "Necessities" in Planning )
------------------------------------------------------------------------

1. Solution & Explanation
Solution & Explanation
of the Four-Fold-Pattern

The well-determined 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.

Denoting the real value of probability,
which value is near 100% as Phigh real ,
the (positive) value of gain as G
and the (negative) value of loss as -G ,
we obtain
Phigh real < Phigh planned
and
G * Phigh real < G * Phigh planned
-G * Phigh real > -G * Phigh planned
2) the underweight of high probabilities gains and
4) the overweight of high probabilities losses.
"Low probabilities can increase" does not mean they will necessarily increase. But this is a sufficient reason to prefer low probabilities in the state of equilibrium.
Denoting the real value of probability,
which value is near 0% as Plow real
we obtain
Plow real possible > Plow planned
and
G * Plow real possible > G * Plow planned
-G * Plow real possible < -G * Plow planned
1) the overweight of low probabilities gains and
3) the underweight of low probabilities losses.
Thus, the above facts can be explained naturally and uniformly.

Top
------------------------------------------------------------------------

2. New Results
"Impossibilities" in Forecasting

Possible conclusions from the first consequence of the principle:

"Absolutely exact extrapolation forecasting is impossible"

"Exact middle-range extrapolation forecasting is unattainable"

Possible conclusions from the first and second consequences of the principle:

"Absolutely reliable extrapolation forecasting is impossible"

"Exact long-range extrapolation forecasting is impossible"

"Quantitative extra-long-range extrapolation forecasting is impossible"
(Growing quantitative uncertainties and unforeseen events may modify an essential parameter for more than 50% from its maximal value)

Possible conclusion from the second consequence of the principle:

"Complete qualitative extra-long-range extrapolation forecasting is impossible"
(Unforeseen events may add an unforeseen qualitative feature in a complete picture)

"Necessities" in Planning

Possible conclusions from the principle in the scope of the concept
"Future as the extrapolated Present":

"Future is Modifications and Changes"

"Short-term and Medium-term Planning is Necessary to be Flexible"

"The Necessary Features of Long-term Planning should be
Robustness & Resourcefulness"

Top      