  Despite decades of polarization observations and high-significance polarized
$\gamma$-ray, X-ray, optical, and radio emissions in gamma-ray bursts (GRBs)
have been accumulating in dozens of cases, people have yet to find a consistent
scenario for understanding the globally observed timing properties of GRB
polarization to date. Here, we report that the observed properties of GRB
polarization exhibit a four-segment timing evolution at the cosmological
distance: (I) an initial hump early on (within the first few seconds); (II) a
later on power-law decay (from $\sim$10$^{1}$ to $\sim$10$^{4}$ s), which takes
the form of $\pi_{\rm obs} \propto t^{-0.50 \pm 0.02}$; (III) afterwards a
late-time rebrightening hump (from $\sim$10$^{4}$ to $\sim$10$^{5}$ s); and
(IV) finally a flatting power-law decay (from $\sim$ 10$^{5}$ to $\sim$
10$^{7}$ s), with the the form of $\pi_{\rm obs} \propto t^{-0.21 \pm 0.08}$.
These findings may present a challenge to the mainstream of polarization models
that assume the polarization time evolution change in different emission
regions. We show that these results can be explained by relativistic and
geometric effects of a highly relativistic and magnetized jet generated by the
central engine, and "magnetic patches" distributed as a globally random but
locally coherent form. Our analysis suggests that there is a single dominant
mechanism that might account for the global observational properties of GRB
polarization, and other emission mechanisms and effects might play a role in
spatially local and temporally short effects on GRB polarization.
