# 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 ...
• 251
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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 $P_1$ ...
• 5,466
156 views

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 ...
• 335
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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 ...
1 vote
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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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1 vote
117 views

### 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 ...
• 940
193 views

### 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 ...
• 109
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, ...