Questions tagged [decision-theory]
For questions regarding formal decision problems. In contrast, questions involving strategic aspects (where the solution depends on the behavior of others) are discussed in game theory.
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Optimal stopping in red vs black card game deck of 52 cards
I have a optimal stopping problem that is solved by recursion. I was stumped by this question in an interview once. I am hoping someone can walk me through the reasoning so I can reproduce it on ...
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Can I use the "Secretary Problem" to find the worst candidate, too?
As you know, we use the "Secretary Problem" to choose the single best candidate. Now I would like to know can we use this rule to find the worst candidate, too? If yes, how to accomplish this?
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What is the relationship of $\mathcal{L}_1$ (total variation) distance to hypothesis testing?
Kullback-Leibler divergence (a.k.a. relative entropy) has a nice property in hypothesis testing: given some observed measurement $m\in \mathcal{Q}$, and two probability distributions $P_0$ and $P_1$ ...
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Inadmissibility of Simpson's rule
Let $B_t$, $t\ge0$ be a standard Brownian motion and suppose $0<x_1<x_2<\cdots<x_n<1$. Then the conditional expectation
$$
\mathbb E\left(\int_0^1 B_t\,dt \,\middle\vert\, B_0, B_{x_1},...
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Can we make a voting system where it is cryptographically hard to find a dictator
As Wikipedia says, Arrow's impossibility theorem states that no rank-order electoral system can be designed that always satisfies these three "fairness" criteria:
If every voter prefers ...
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Mistake in Wikipedia article on St Petersburg paradox?
I suspect that there is a mistake in the Wikipedia article on the St Petersburg paradox, and I would like to see if I am right before modifying the article.
In the section "Solving the paradox", the ...
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Is the question whether the value of a given definite integral has a closed-form decideable?
Suppose, we have a definite convergent integral (possibly improper) with an elementary function as an integrand.
Is there an algorithm deciding whether the value of the integral has a closed-form ...
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Which route is better for a Neutral-risk person?
There are two routes, 1 and 2.
It is known that route 1 takes 60 minutes and route 2 takes 41 minutes.
If there is problems in the traffic:
Route 1 will increase to 70 minutes;
Route 2 will ...
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0
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1
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Identifying random variables with their generated distribution function - Necessity of countable additivity?
Let the state space $\Omega=[0,1]$ and $\lambda$ be the Lebesgue measure defined on the Borel $\sigma$-algebra on $[0,1]$. Consider measurable functions (random variables) $f:\Omega\to\mathbb{R}$ and ...
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Agent's expected utility depends only on mean and variance
Consider an agent with the expected utility function $U(L) = \sum_{s=1}^{S}\pi_s U(Y_s)$ over the lottery $L = (Y_s, \pi_s)$ where $\pi_s$ is the probability of state $s$, $Y_s$ are state $s$ payoffs, ...
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