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More than one third of the Large Bright Quasar Survey (LBQS) has been observed at 8.4 GHz with the VLA. There is no correlation between radio luminosity and absolute blue magnitude for $-28 < {\rm M_{B}} < -24$, and the radio-loud (8.4 GHz luminosity $> 10^{25}$ W ${\rm Hz}^{-1}$) fraction (10\%) does not depend on absolute blue magnitude. There is some evidence for a substantially increased radio-loud fraction (36\%) among objects with ${\rm M_{B}} < -28$. The frequency of powerful radio emitters appears to decrease smoothly with decreasing optical luminosity for ${\rm M_{B}} > -24$, a result which is probably not a selection effect (98\% confidence) and represents a physical change in the radio properties of quasars. This was determined by applying the quantitative LBQS selection criteria to a test spectrum simulating a quasar embedded in a red elliptical host galaxy, in which the quasar and host galaxy have equal $M_{B}$. The radio-loud fraction among all objects in the radio sample with ${\rm M_{B}} > -24$ is 3\%. The radio-loud fraction remains constant at $\sim 10 \%$ from $z = 0.5$ to $z > 3.5$, and there is some evidence that this holds for $z < 0.5$. The distribution of log R (ratio of radio to optical luminosity) appears to be bimodal, with a gap at $\log R \sim 1$ for all redshifts and absolute magnitudes.
