  We give a combinatorial proof of the result of Kahn, Kalai, and Linial, which
states that every balanced boolean function on the $n$-dimensional boolean cube
has a variable with influence of at least Omega(\frac{log n}{n}).
  The methods of the proof are then used to recover additional isoperimetric
results for the cube, with improved constants. We also state some conjectures
about optimal constants and discuss their possible implications
