论文标题
与多个代理的矛盾预测
Contradictory predictions with multiple agents
论文作者
论文摘要
令$ x_1 $，$ x_2 $，$ \ ldots $，$ x_n $是一系列连贯的随机变量，即满足均等$ x_j = \ mathbb {p}（a | \ mathcal {g}事件$ a $。本文包含估计$$ \ MATHBB {p} \ big（\ max_ {1 \ le i <j \ le n} | x_i-x_j | x_j |geδ\ big） （\ frac {1} {2}，1] $是一个给定的参数。不平等是清晰的：对于任何$δ$，右上的不断持续不可用任何较小的数字代替。该论点基于几个新颖的组合和对称性参数，并结合了Dynamitive of Dynamsive of Dynamiss of Dynamerive of Droment of ty-verative of k. burds s。
Let $X_1$, $X_2$, $\ldots$, $X_n$ be a sequence of coherent random variables, i.e., satisfying the equalities $$ X_j=\mathbb{P}(A|\mathcal{G}_j),\qquad j=1,\,2,\,\ldots,\,n,$$ almost surely for some event $A$. The paper contains the proof of the estimate $$\mathbb{P}\Big(\max_{1\le i < j\le n}|X_i-X_j|\ge δ\Big) \leq \frac{n(1-δ)}{2-δ} \wedge 1,$$ where $δ\in (\frac{1}{2},1]$ is a given parameter. The inequality is sharp: for any $δ$, the constant on the right cannot be replaced by any smaller number. The argument rests on several novel combinatorial and symmetrization arguments, combined with dynamic programming. Our result generalizes the two-variate inequality of K. Burdzy and S. Pal and in particular provides its alternative derivation.
