Cash transfer programs are the most common anti-poverty tool in low- and middle-income countries, reaching more than one billion people globally. Benefits are typically targeted using prediction models. In this paper, we develop an extended targeting assessment framework for proxy means testing that accounts for societal sensitivity to targeting errors. Using a social welfare framework, we weight targeting errors based on their position in the welfare distribution and adjust for different levels of societal inequality aversion. While this approach provides a more comprehensive assessment of targeting performance, our two case studies show that bias in the data, particularly in the form of label bias and unstable proxy means testing weights, leads to a substantial underestimation of welfare losses, disadvantaging some groups more than others.