We find that segments of society that have shorter life expectancy can expect a lower income from their pensions and lifetime utility due to the longevity of other groups participating in the same pension scheme. Linking the pension age to average life expectancy magnifies the negative effect on the lifetime utility of those who suffer low longevity. Furthermore, when the income of those with greater longevity increases, those with shorter life expectancy become even worse off. Conversely, when the income of those with shorter life expectancy increases, they end up paying more into the pension scheme, which benefits those who live longer. The relative sizes of the low‐ and high‐longevity groups in the population determine the magnitude of these effects. We calibrate the model based on data on differences in life expectancy of different socioeconomic groups and find that low‐income workers suffer from a 10–13% drop in pension benefits from being forced to pay into the same scheme as high‐income workers.