# Tag Info

• 1,111
Accepted

### Proving a (Representing Utility) Function is Continuous

This answer is for proving $\alpha(x)$ is continuous on $\mathbb{R}^L_+$. Before we proceed, we need a proposition: Proposition$\quad$ Consider a sequence $\{x_n\}$ on $X$. Suppose $\{x_n\}$ lies in ...
• 56

### Sum of two stopping times is a stopping time?

There is a brief proof in the book S. W. He et al., Semimartingale Theory and Stochastic Calculus, CRC Press Inc, 1992.''(p.84, Th.3.7.(3)). The proof is based on following fact(Th.3.7.(1)): If $S$...
• 5,451

### Sum of two stopping times is a stopping time?

Nates' answer is on the right track but assumes right continuity. The definition of stopping time is $\{\sigma \le t\}\in \mathcal{F}_t$ (instead of $\{\sigma < t\}\in \mathcal{F}_t$). Stefan's ...
• 2,037

### Gittins Index for a simple example

Gittins indices are hard to compute. This paper offers a good overview of various algorithms: http://www.ece.mcgill.ca/~amahaj1/projects/bandits/book/2013-bandit-computations.pdf

Accepted

### Solving an optimal stopping problem with pulling a card of a certain color

You can prove by induction that the value of the game is always the current proportion of red cards, and you obtain this value whether you stop or continue, so it doesn’t matter when you stop.
• 240k

### Can we make a voting system where it is cryptographically hard to find a dictator

After reading some of the literature mentioned in the comments, I am convinced that my original question was flawed. Specifically, I accept that there is no way to meet the first two fairness criteria ...
• 335
Accepted

### Does this proof of a voting related lemma work? if so, how?

It would be more clear if we separated out the claim into two parts: If $v$ is decisive for $(a,b)$ and $c$ is any third candidate, then $v$ is decisive for $(a,c)$. If $v$ is decisive for $(a,b)$ ...
• 146k
Accepted

### "Markov Decision Process" with target states and shortest path as only constraints

Your approach looks reasonable if you set $R=1$ for transitions from transient to target states, $R=0$ for all other transitions, and $\gamma>0$. Because your state space and action sets are ...
• 48.2k

• 349k
1 vote
Accepted

### Proving that the language is not recursive enumerable

The language above defines the set of Turing machines which never halt on any input. Note, this is the same thing as visiting a state an infinite number of times, assuming that the number of states ...
• 4,749

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