Despite decades of polarization observations and high significance of polarized {gamma}-ray, X-ray, optical, and radio emissions in gamma-ray bursts (GRBs) 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 a cosmological distance: (i) an initial hump early on (within the first few seconds); (ii) a later-on power-law decay (from ~10^1^ to ~10^4^s), which takes the form of {Pi}obs{propto}t^-0.50+/-0.02^; (iii) afterward a late-time rebrightening hump (from ~10^4^ to ~10^5^s); and (iv) finally a flattening power-law decay (from ~10^5^ to ~10^7^s), with the form of {Pi}obs{propto}t^-0.21+/-0.08^. We show that these results can be explained by relativistic and geometric effects of a highly relativistic and magnetized jet generated by a central engine, and "magnetic patches" distributed as a globally random but locally coherent form. The long-term timing evolution of observed GRB polarization follows a scaling law {Pi}obs{propto}1/S_obs_, dominantly determined by how "magnetic patches" are randomly distributed in the observed emission region Sobs on the jet plane of 1/{Gamma} cone. It predicts the polarization hump and tail form in accordance with the luminosity jet-break phenomenon. Our analysis suggests that there is a single dominant mechanism (relativistic and geometric effects) that may account for the global observational properties of GRB polarization, and other emission mechanisms and effects may play a role in spatially local and temporally short effects on GRB polarization.

Cone search capability for table J/ApJS/280/39/table1 (A full catalog of GRB polarimetric observations)