  Only recently progress has been made in obtaining
$o(\log(\mathrm{rank}))$-competitive algorithms for the matroid secretary
problem. More precisely, Chakraborty and Lachish (2012) presented a
$O(\sqrt{\log(\mathrm{rank})})$-competitive procedure, and Lachish (2014) later
presented a $O(\log\log(\mathrm{rank}))$-competitive algorithm. Both these
algorithms and their analyses are very involved, which is also reflected in the
extremely high constants in their competitive ratios.
  Using different tools, we present a considerably simpler
$O(\log\log(\mathrm{rank}))$-competitive algorithm for the matroid secretary
problem. Our algorithm can be interpreted as a distribution over a simple type
of matroid secretary algorithms which are easy to analyze. Due to the
simplicity of our procedure, we are also able to vastly improve on the hidden
constant in the competitive ratio.
