We present a mitigation strategy to reduce the impact of non-linear galaxy bias on the joint `$3 times 2 $pt cosmological analysis of weak lensing and galaxy surveys. The $Psi$-statistics that we adopt are based on Complete Orthogonal Sets of E/B Integrals (COSEBIs). As such they are designed to minimise the contributions to the observable from the smallest physical scales where models are highly uncertain. We demonstrate that $Psi$-statistics carry the same constraining power as the standard two-point galaxy clustering and galaxy-galaxy lensing statistics, but are significantly less sensitive to scale-dependent galaxy bias. Using two galaxy bias models, motivated by halo-model fits to data and simulations, we quantify the error in a standard $3 times 2$pt analysis where constant galaxy bias is assumed. Even when adopting conservative angular scale cuts, that degrade the overall cosmological parameter constraints, we find of order $1 sigma$ biases for Stage III surveys on the cosmological parameter $S_8 = sigma_8(Omega_{rm m}/0.3)^{alpha}$. This arises from a leakage of the smallest physical scales to all angular scales in the standard two-point correlation functions. In contrast, when analysing $Psi$-statistics under the same approximation of constant galaxy bias, we show that the bias on the recovered value for $S_8$ can be decreased by a factor of $sim 2$, with less conservative scale cuts. Given the challenges in determining accurate galaxy bias models in the highly non-linear regime, we argue that $3 times 2$pt analyses should move towards new statistics that are less sensitive to the smallest physical scales.
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