There are numerous associations between psychological characteristics and political values, but it is unclear whether messages tailored to these psychological characteristics can influence political decisions. Two studies (N = 398, N = 395) tested whether psychological-based argument tailoring could influence participants’ decision-making. We constructed arguments based on the 2016 Brexit referendum; Remain supporters were presented with four arguments supporting the Leave campaign, tailored to reflect the participant’s strongest (/weakest) moral foundation (Loyalty or Fairness) or personality trait (Conscientiousness or Openness). We tested whether individuals scoring high on a trait would find the tailored arguments more persuasive than individuals scoring low on the same trait. We found clear evidence for targeting, particularly for Loyalty, but either no evidence or weak evidence, in the case of Conscientiousness, for tailoring. Overall, the results suggest that targeting political messages could be effective, but provide either no, or weak evidence that tailoring these messages influences political decision-making.