8、Two candidates, A and B, participate in an election, with A receiving $n$ votes and B receiving $m$ votes $(n>m)$. The probability that A's cumulative vote count always exceeds B's cumulative vote count during the vote counting process is $\qquad$ .
8. $\frac{m-n}{m+n}$

Analysis: The ballot counting record is represented by an $(m+n)$-tuple of real numbers $\left(a_{1}, a_{2}, \mathrm{~L}, a_{m+n}\right)$. When the $k$-th vote is for candidate A, we set $a_{k}=1$; otherwise, we set $a_{k}=-1$. Let $b_{k}=a_{1}+a_{2}+\mathrm{L}+a_{k}(k=1,2, \mathrm{~L}, m+n)$, and connect the following grid points from left to right: $\left(1, b_{1}\right),\left(2, b_{2}\right), \mathrm{L},\left(k, b_{k}\right), \mathrm{L},\left(m+n, b_{m+n}\right)$, forming a broken line with $m+n-1$ segments. It is easy to see that $b_{k}>0(k=1,2, \mathrm{~L}, m+n)$, and $b_{1}=1, b_{m+n}=m-n$. Thus, the broken line is a line connecting $(1,1)$ and $(m+n, m-n)$ that does not intersect the $x$-axis. It is clear that the set of all broken lines corresponds one-to-one with the set of all ballot counting records. Therefore, by the broken line method, the number of valid ballot counting records is $\frac{m-n}{m+n} C_{m+n}^{m}$, so the probability is $\frac{m-n}{m+n}$.