  In the framework of the Constrained Minimal Supersymmetric Standard Model
(CMSSM) we evaluate the electroweak fine tuning measure that provides a
quantitative test of supersymmetry as a solution to the hierarchy problem.
Taking account of current experimental constraints we compute the fine tuning
at two-loop order and determine the limits on the CMSSM parameter space and the
measurements at the LHC most relevant in covering it. Without imposing the
LEPII bound on the Higgs mass, it is shown that the fine tuning computed at
two-loop has a minimum $\Delta=8.8$ corresponding to a Higgs mass $m_h=114\pm
2$ GeV. Adding the constraint that the SUSY dark matter relic density should be
within present bounds we find $\Delta=15$ corresponding to $m_h=114.7\pm 2$ GeV
and this rises to $\Delta=17.8$ ($m_h=115.9\pm 2$ GeV) for SUSY dark matter
abundance within 3$\sigma$ of the WMAP constraint. We extend the analysis to
include the contribution of dark matter fine tuning. In this case the overall
fine tuning and Higgs mass are only marginally larger for the case SUSY dark
matter is subdominant and rises to $\Delta=28.7$ ($m_h=116.98\pm 2$ GeV) for
the case of SUSY dark matter saturates the WMAP bound. For a Higgs mass above
these values, fine tuning rises exponentially fast. The CMSSM spectrum that
corresponds to minimal fine tuning is computed and provides a benchmark for
future searches. It is characterised by heavy squarks and sleptons and light
neutralinos, charginos and gluinos.
