Three years of optical monitoring of the low-mass X-ray binary (LMXB) 4U 1957+11 is presented. The source was observed in V, R and i bands using the Faulkes Telescopes North and South. The light curve is dominated by long-term variations which are correlated (at the >3σ level) with the soft X-ray flux from the All Sky Monitor on board the Rossi X-ray Timing Explorer. The variations span 1mag in all three filters. We find no evidence for periodicities in our light curves, contrary to a previous short-time-scale optical study in which the flux varied on a 9.3-h sinusoidal period by a smaller amplitude. The optical spectral energy distribution is blue and typical of LMXBs in outburst, as is the power-law index of the correlation β = 0.5, where Fν,OPT ~ FβX. The discrete cross-correlation function reveals a peak at an X-ray lag of 2-14 days, which could be the viscous time-scale. However, adopting the least-squares method we find the strongest correlation at a lag of 0 +/- 4 d, consistent with X-ray reprocessing on the surface of the disc. We therefore constrain the optical lag behind X-ray to be between -14 and +4 d. In addition, we use the optical-X-ray luminosity diagram for LMXBs as a diagnostic tool to constrain the nature of the compact object in 4U 1957+11, since black hole and neutron star sources reside in different regions of this diagram. It is found that if the system contains a black hole (as is the currently favoured hypothesis), its distance must exceed ~20 kpc for the optical and X-ray luminosities to be consistent with other soft-state black hole systems. For distances <20 kpc, the data lie in a region of the diagram populated only by neutron star sources (black hole systems are 10 times optically brighter for this X-ray luminosity). 4U 1957+11 is unique: it is either the only black hole LMXB to exist in an apparent persistent soft state or a neutron star LMXB which behaves like a black hole.