## 1 Introduction  
One of the most damaging geological risks in the region where loess is distributed worldwide is loess slope instability. Under the combined influence of rainfall infiltration, freeze-thaw cycles, and human engineering activities (such as irrigation and excavation), loess is extremely vulnerable to landslide hazards due to its porous structure, susceptibility to wetting, and high sensitivity to hydrological conditions. These factors pose a serious threat to residential areas, farmland infrastructures, and traffic arterials [1, 2, 3, 4]. At the same time, the suddenness and multi-scale damage characteristics of such disasters (e.g., cave collapse, slope shoulder crack extension) further highlight the complexity of stability evaluation [5, 6]. About one-third of the annual geological disasters in China occur in the Loess Plateau, which not only causes casualties and infrastructure damage but also leads to huge direct economic losses [7, 8]. Moreover, with the fluctuation of groundwater levels and the frequent occurrence of extreme weather events, the risk of slope landslides and other disasters in the Loess Plateau region is also increasing [4, 9, 10]. However, traditional analysis methods, such as the limit equilibrium method and finite element numerical simulation,make it difficult to quantify the nonlinear interaction effects among indicators due to the over-reliance on idealized assumptions (e.g., homogeneous soils, fixed slip fracture surfaces) [7; 11; 12]. This makes the theory often inconsistent with the actual situation in practical applications and, thus, there is an urgent need to construct a novel analytical framework that can integrate multiple data sources. As the core of novel evaluation methods, the indicator screening mechanism is a widespread challenge. Among the existing methods, the subjective assignment method is susceptible to expert cognitive bias, leading to indicator redundancy or omission of key factors [13]. Objective methods such as principal component analysis can extract data features, but may screen out statistically significant indicators but lack engineering interpretability [14]; traditional methods have obvious human intervention in the screening process, such as the resolution coefficient in the grey correlation model, which needs to rely on empirical settings. In this example, the resolution coefficient in the grey correlation model relies on the empirical setting, and when the coefficient varies within a certain range, the variability of the correlation order of indicators is high [15]. However, the selection of indexes for slope stability evaluation typically depends too much on the knowledge and judgment of experts and is not supported by systematic verification procedures, raising questions about the repeatability and scientificity of index screening results [16; 17]. When redundant parameters are added, computational complexity is needlessly increased, and the reliability of the evaluation model output is directly impacted by the significant decline in the identification accuracy of important driving factors under the coupling effect of multiple parameters [18; 19]. Therefore, to minimize the subjectivity of index screening, guarantee the objectivity of the screening findings, and assure the correctness of slope stability evaluation, it is imperative to develop an objective index screening algorithm framework and a corresponding result verification method. This study developed a quantitative screening mechanism for the joint control of validity and reliability and creatively suggested a quantitative screening mechanism based on the Delphi method and the improved grey correlation model to address the main issues in the stability evaluation of loess slope.The two-stage framework used to optimize the index system eliminated redundancy through qualitative screening, fused subjective and objective data through quantitative screening, and quantified the quality of the fusion using validity and reliability coefficients.