The efficiency of light-emitting diodes (LEDs) made from organic semiconductors is determined by the fraction of injected electrons and holes that recombine to form emissive spin-singlet states rather than non-emissive spin-triplet states. If the process by which these states form is spin-independent, the maximum efficiency of organic LEDs will be limited to 25 per cent. But recent reports have indicated fractions of emissive singlet states ranging from 22 to 63 per cent, and the reason for this variation remains unclear. Here we determine the absolute fraction of singlet states generated in a platinum-containing conjugated polymer and its corresponding monomer. The spin-orbit coupling introduced by the platinum atom allows triplet-state emission, so optically and electrically generated luminescence from both singlet and triplet states can be compared directly. We find an average singlet generation fraction of 22 +/- 1 per cent for the monomer, but 57 +/- 4 per cent for the polymer. This suggests that recombination is spin-independent for the monomer, but that a spin-dependent process, favouring singlet formation, is effective in the polymer. We suggest that this process is a consequence of the exchange interaction, which will operate on overlapping electron and hole wavefunctions on the same polymer chain at their capture radius.