In this study, the existence of anchoring bias—people’s tendency to rely on, evaluate, and decide based on the first piece of information they receive—is examined in two multi-attribute decision-making (MADM) methods, simple multi-attribute rating technique (SMART), and Swing. Data were collected from university students for a transportation mode selection. Data analysis revealed that the two methods, which have different starting points, display different degrees of anchoring bias. Statistical analyses of the weights obtained from the two methods show that, compared to Swing (with a high anchor), SMART (with a low anchor) produces lower weights for the least important attributes, while for the most important attributes, the opposite is true. Despite their differences in anchoring bias, analytical approaches supported by empirical studies suggest that both methods (SMART and Swing) overweigh the less important attributes and under weigh the more important attributes. As such, we examined whether the best-worst method (BWM), which has two opposite anchors in its procedure (a possible promising anchoring debiasing strategy), could produce results that are less prone to anchoring bias. Our findings show that the BWM is indeed able to produce lower weights (compared to SMART and Swing) for the less important attributes and higher weights for the more important attributes. This study shows the vulnerability of MADM methods with a single anchor and supports the idea that MADM methods with multiple (opposite) anchors, like BWM, are less prone to anchoring bias.