  We study superconducting transition temperature ($T_c$) of oxygen-doped
double-layer high-temperature superconductors YBa$_2$Cu$_3$O$_{6+\delta}$ (0
$\le$ $\delta$ $\le$ 1) as a function of the oxygen dopant concentration
($\delta$) and planar hole-doping concentration ($P_{pl}$). We find that $T_c$,
while clearly influenced by the development of the chain ordering as seen in
the $T_c$ $vs.$ $\delta$ plot, lies on a universal curve originating at the
critical hole concentration ($P_c$) = 1/16 in the $T_c$ $vs.$ $P_{pl}$ plot.
Our analysis suggests that the universal behavior of $T_c$($P_{pl}$) can be
understood in terms of the competition and collaboration of chemical-phases and
electronic-phases that exist in the system. We conclude that the global
superconductivity behavior of YBa$_2$Cu$_3$O$_{6+\delta}$ as a function of
doping is electronically driven and dictated by pristine electronic phases at
magic doping numbers that follow the hierarchical order based on $P_c$, such as
2 $\times$ $P_c$, 3 $\times$ $P_c$ and 4 $\times$ $P_c$. We find that there are
at least two intrinsic electronic superconducting phases of $T_c$ = 60 K at 2
$\times$ $P_c$ = 1/8 and $T_c$ = 90 K at 3 $\times$ $P_c$ = 3/16.
