Executive summary: Maximizing the geometric expectation of utility, as an alternative to maximizing expected utility, has some appealing properties but also some drawbacks that make it an imperfect replacement for expected utility maximization in ethical decision making.
Key points:
Maximizing the geometric expectation of utility is equivalent to maximizing the time-averaged growth rate of utility under repeated multiplicative gambles, and is the optimal strategy for long-term wealth growth in betting (the Kelly Criterion).
The geometric expectation avoids some counterintuitive implications of expected utility maximization, such as accepting Pascal’s mugging and gambles that risk total extinction for a chance of high payoff.
However, the geometric expectation violates the Von Neumann-Morgenstern axiom of Continuity, leading to potential money-pump situations and inability to distinguish between gambles with any probability of zero utility.
The geometric expectation can conflict with the choices of rational agents behind a veil of ignorance, who would vote to maximize expected utility.
The geometric expectation rejects background independence, making decisions sensitive to irrelevant background conditions, although this may not be entirely unreasonable.
While the geometric expectation resolves some issues with expected utility maximization, it introduces problems, suggesting that no single decision may ethical intuitions.
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Executive summary: Maximizing the geometric expectation of utility, as an alternative to maximizing expected utility, has some appealing properties but also some drawbacks that make it an imperfect replacement for expected utility maximization in ethical decision making.
Key points:
Maximizing the geometric expectation of utility is equivalent to maximizing the time-averaged growth rate of utility under repeated multiplicative gambles, and is the optimal strategy for long-term wealth growth in betting (the Kelly Criterion).
The geometric expectation avoids some counterintuitive implications of expected utility maximization, such as accepting Pascal’s mugging and gambles that risk total extinction for a chance of high payoff.
However, the geometric expectation violates the Von Neumann-Morgenstern axiom of Continuity, leading to potential money-pump situations and inability to distinguish between gambles with any probability of zero utility.
The geometric expectation can conflict with the choices of rational agents behind a veil of ignorance, who would vote to maximize expected utility.
The geometric expectation rejects background independence, making decisions sensitive to irrelevant background conditions, although this may not be entirely unreasonable.
While the geometric expectation resolves some issues with expected utility maximization, it introduces problems, suggesting that no single decision may ethical intuitions.
This comment was auto-generated by the EA Forum Team. Feel free to point out issues with this summary by replying to the comment, and contact us if you have feedback.