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While radio emission in quasars can be contributed to by a variety of processes (involving star forming regions, accretion disk coronas and winds, and jets), the powering of the radio loudest quasars must involve very strong jets, presumably launched by the Blandford-Znajek mechanism incorporating the magnetically arrested disk (MAD) scenario. We focus on the latter and investigate the dependence of their fraction on redshift. We also examine the dependence of the radio-loud fraction (RLF) on BH mass ($M_{\rm BH}$) and Eddington ratio ($��_{\rm Edd}$) while excluding the redshift bias by narrowing its range. In both these investigations we remove the bias associated with: (1) the diversity of source selection by constructing two well-defined, homogeneous samples of quasars (first within $0.7 \leq z < 1.9$, second within $0.5 \leq z < 0.7$); (2) a strong drop in the RLF of quasars at smaller BH masses by choosing those with BH masses larger than $10^{8.5} M_{\odot}$. We confirm some previous results showing the increase in the fraction of radio-loud quasars with cosmic time and that this trend can be even steeper if we account for the bias introduced by the dependence of the RLF on BH mass whereas the bias introduced by the dependence of the RLF on Eddington ratio is shown to be negligible. Assuming that quasar activities are triggered by galaxy mergers we argue that such an increase can result from the slower drop with cosmic time of mixed mergers than of wet mergers., 15 pages, 4 figures. Accepted for publication in ApJ