Combinatorial Hodge Theory recently arises with a growing number of
applications in statistical ranking, game theory, and computer vision etc.
As classical Hodge Theory is a milestone connecting topology and geometry,
such a combinatorial version brings computational topology and geometry into
these fields. Here we particularly focus on statistical ranking via crowdsourcing, 
where Hodge theory leads to an orthogonal decomposition of pairwise ranking 
data on a graph into gradient flow, harmonic flow, and curl flow. It enables us 
to pursue both global ranking and the intrinsic inconsistency as cyclic rankings 
which plays a central role in Arrow's impossibility theorem in social choice theory. 
Several developments with applications are introduced for such a decomposition, 
which shows elements of applied Hodge theory in connection to computer science 
and statistics where paired comparison data grow rapidly with crowdsourcing technology.