you didn't phrase this quite right.  hashes are not "votes on which chain is longest".  when a miner receives notification of a block, he checks to verify that the submitted hash conforms to the target (certain # leading 0's) and verifies that all tx's within it are valid.  once verified, he adds it on top of the chain he has in memory and immediately starts hashing away on a new header in a race to create a hash that is once again below the target and would create yet another new block.  

here's where "voting" comes in.  if 2 different blocks are seen on the network simultaneously, the Northern Hemisphere might decide to build on one block (call it block #1) while the Southern Hemisphere decides to build off the other block (call it block #2).  this temporarily creates a fork for theoretically 10 minutes.  it would be exceedingly rare for another pair of blocks to arrive once again simultaneously extending this fork.  instead, the next single block the network sees will resolve the fork.  so if the Northern Hemisphere sees a new block first (block #3) it will add that block on top of its side of the fork (on top of block #1) and then immediately the Southern Hemisphere will see that it made a mistake and will "orphan" the block #2 it had been incorrectly trying to build off of and rejoin the Norhern Hemisphere and add block #1 and block #3 to its chain and then race to build a new block on top of block #3.

"voting" only consists of deciding to abandon (orphan) the chain it was working on to move to the other chain that is longer and has nothing to do with measuring hashes in a direct sense. in fact, no one on the network can actually measure the # of hashes performed by a block that has shown up.  nodes and miners only infer this by the time it took to show up since the last block.  by the mere fact that the other chain is longer means that it has performed the highest amount of POW via hashing.