If you have an ordering bias, that seems easily fixed by just rerunning the evaluation several times in different orders and taking the most common recommendations, and you can work around other biases by not including things like name, etc. Although you can probably unearth more subtle cultural biases in how resumes are written).

Not that i think you should allow LLMs to make decisions in this way -- it's better for summarizing and organizing. I don't trust any LLM's "opinion" about anything. It doesn't have a stake in the outcome.