  We apply the Bayesian concept of `evidence' to reveal systematically the
nature of dark energy from present and future supernova luminosity distance
measurements. We express the unknown dark energy equation of state w(z) as a
low order polynomial in redshift and use evidence to find the polynomial order,
thereby establishing the minimum order required by the data. We apply this
method to the current supernova data, and with a prior -1 < w(z) < 1 and
Omega_m = 0.3 \pm 0.05, obtain a large probability of 91% for the cosmological
constant model, with the remaining 9% assigned to the two more complex models
tested. We also investigate the use of evidence for future supernova data sets
such as distances obtainable from surveys like the Supernova Acceleration Probe
(SNAP). Given a low uncertainty on the present day matter density we find that,
if the underlying dark energy model is only modestly evolving, then a constant
$w(z)$ fit is sufficient. However, if the evolution of the dark energy equation
of state to linear order is larger than |w_1| ~ 0.5, then the evolution can be
established with statistical significance. For models where we can assume the
prior -1 < w(z) < 1, the correct polynomial order can be established even for
modestly evolving equations of state.
