We argue that cognition linking risk to innovation is influenced by two distinct cognitive paradigms which have deep roots in personality and culture and are closely bound up with political identity. We differentiate between a paradigm of Promethean conservatism where innovation is perceived as threatening, and a paradigm of ‘Strategic Resilience’, where the status quo is perceived as threatening and innovation is perceived to reduce this threat. We find an evidence base for these paradigms in the personality psychology literature, which shows a strong tendency for psychometric measures of risk and innovation to correlate positively with each other and negatively with measures of conservatism and authoritarianism. We develop four theoretical elaborations from this greatly underutilised evidence base: (1) we seem to possess powerful ‘implicit personality theories’ (IPTs) which conflate the risk taker with the innovator; (2) these IPTs lead us to evaluate risk‐taking innovation either positively or negatively; (3) these evaluations also manifest the positions we adopt, as we undertake identity work, along the rich and complex personological and cultural continuum that contrasts risk‐averse conservatism with liberal radicalism; and (4) this highly political self‐positioning carries multiple implications for how we identify and evaluate risk within the context of organisational innovation.