Editing Decision Making and Rationality (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Calculating Expected Value vs. Utility (The St. Petersburg Paradox):'''
<syntaxhighlight lang="python">
import math

def expected_value(p_win, win_amount, p_loss, loss_amount):
    """Calculates the mathematical expected value of a gamble."""
    return (p_win * win_amount) + (p_loss * loss_amount)

def logarithmic_utility(amount):
    """Bernoulli's proposal: Utility increases logarithmically with wealth."""
    return math.log(amount) if amount > 0 else -float('inf')

# Gamble: 50% chance to win $200, 50% chance to lose $50
ev = expected_value(0.5, 200, 0.5, -50)
print(f"Expected Value: ${ev}") # +$75

# Now consider utility for someone with $1000 base wealth
base_wealth = 1000
u_no_gamble = logarithmic_utility(base_wealth)
u_gamble = 0.5 * logarithmic_utility(base_wealth + 200) + \
           0.5 * logarithmic_utility(base_wealth - 50)

print(f"Utility of not gambling: {u_no_gamble:.4f}")
print(f"Utility of gambling: {u_gamble:.4f}")
# If u_gamble > u_no_gamble, a rational agent (Bernoulli sense) takes the bet.
</syntaxhighlight>

; Practical Applications
: '''Finance''' → Avoiding panic-selling during market dips (loss aversion).
: '''Medicine''' → Understanding how "80% survival" vs "20% mortality" frames patient choices.
: '''Public Policy''' → Designing "Save More Tomorrow" programs that leverage hyperbolic discounting.
: '''Management''' → Overcoming the "planning fallacy" (underestimating time/cost) in projects.
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