The population of young, non-recycled pulsars with spin down energies Edot >10^35 erg/s is sampled predominantly at gamma-ray and radio wavelengths. A total of 137 such pulsars are known, with partial overlap between the sources detectable in radio and gamma-rays. We use a very small set of assumptions in an attempt to test whether the observed pulsar sample can be explained by a single underlying population of neutron stars. For radio emission we assume a canonical conal beam with a fixed emission height of 300~km across all spin periods and a luminosity law which depends on Edot^{0.25}. For gamma-ray emission we assume the outer-gap model and a luminosity law which depends on Edot^{0.5}. We synthesise a population of fast-spinning pulsars with a birth rate of one per 100 years. We find that this simple model can reproduce most characteristics of the observed population with two caveats. The first is a deficit of gamma-ray pulsars at the highest Edot which we surmise to be an observational selection effect due to the difficulties of finding gamma-ray pulsars in the presence of glitches without prior knowledge from radio frequencies. The second is a deficit of radio pulsars with interpulse emission, which may be related to radio emission physics. We discuss the implications of these findings.
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