  In this paper we derive a full expression for the propagation of weak lensing
shape measurement biases into cosmic shear power spectra including the effect
of missing data. We show using simulations that terms higher than first order
in bias parameters can be ignored and the impact of biases can be captured by
terms dependent only on the mean of the multiplicative bias field. We identify
that the B-mode power contains information on the multiplicative bias. We find
that without priors on the residual multiplicative bias $\delta m$ and
stochastic ellipticity variance $\sigma_e$ that constraints on the amplitude of
the cosmic shear power spectrum are completely degenerate, and that when
applying priors the constrained amplitude $A$ is slightly biased low via a
classic marginalisation paradox. Using all-sky Gaussian random field
simulations we find that the combination of $(1+2\delta m)A$ is unbiased for a
joint EE and BB power spectrum likelihood if the error and mean (precision and
accuracy) of the stochastic ellipticity variance is known to better than
$\sigma(\sigma_e)\leq 0.05$ and $\Delta\sigma_e\leq 0.01$, or the
multiplicative bias is known to better than $\sigma(m)\leq 0.07$ and $\Delta
m\leq 0.01$.
