Reinforcement sensitivity theory (RST) most clearly relates to internalizing disorders. But a weak behavioural inhibition system (BIS as defined by RST) could underlie externalising, in general, and psychopathy in particular (Fowles, 1980). Conventional “rationally derived” RST scales (rRST) are not anchored in neurally defined RST systems (nRST). So, here, we use both rRST and nRST measures to assess psychopathy traits. We operationalised psychopathy via a four-factor model (affective | interpersonal | disinhibition | boldness). We operationalised rRST via the Heym, Ferguson & Lawrence (2008) updated version of Carver and White’s (1994) BIS/BAS scales (BAS | BIS | FFFS). We operationalised nRST (goal inhibition system, GIS; goal repulsion system, GRS) via previously validated (Shadli et al., 2021) rhythmic power in the stop signal task (SST) and (goal approach system, GAS) via previously validated ERPs in the doors task. Initial bivariate correlations of psychopathy factors with rRST scales were as expected. We found no significant associations between psychopathy factors and nRST measures. A series of post hoc exploratory repeated measures ANOVAs guarded against non-linearity between psychopathy and nRST constructs. These found that: (1) Disinhibition traits might be explained (unexpectedly) by increased sensitivity in the GIS (i.e., conflict) and GRS (i.e., repulsion) and decreased sensitivity in the GAS (i.e., attraction). (2) Affective traits might be explained, as expected, by decreased sensitivity in the GIS and GRS. But an unexpected positive association was also found in the alpha frequency range for the GRS. So, nRST systems (particularly GIS) do not explain psychopathy. rRST scales were more aligned with expectations but were explained via their “rational” basis not RST per se. Unlike internalizing, nRST does not appear strongly related to externalising disorders in general and psychopathy in particular. rRST appears distinct from nRST.