  We investigate the two-body decay modes $\rho\rho, \pi\pi^{\ast}(1300)$ and
$\sigma \sigma$ of the $f_0(1500)$, all leading to the $4\pi$ decay channel, in
a three-state mixing scheme, where the $f_0(1500)$ is a mixture of the
lowest-lying scalar glueball with the nearby isoscalar states of the $0^{++}
Q\bar{Q}$ nonet. In the leading order of this scheme, the decay mechanism of
the $f_0(1500)$ proceeds dominantly via its quarkonia components, which can be
described in the framework of the $^3P_0$ $Q\bar Q$ pair creation model. We
predict the hierarchy of decay branching ratios B with $B(\rho \rho)
^{>}_{\sim} B(\pi\pi) ^{>}_{\sim} B(\sigma \sigma) > B(\pi\pi^{\ast})$,
providing a key signature for the proposed mixing scheme in this leading order
approach.
