In this day and age there are still human brokers on the trading floor. Computers are perfectly capable of negotiating a deal (buy/sell) in milliseconds when ordered to do so. So why are there still humans brokering on the trading floor? Also, is there a 'human-broker-free' stock exchange in existence?
There are still human brokers on the floor primarily due to tradition. Their numbers have certainly dwindled, however, and it's reasonable to expect the number of floor traders to decrease even more as electronic trading continues to grow.
A key reason for human brokers, however, is due to privacy. Certain private exchanges such as dark pools maintain privacy for high profile clients and institutional investors, and human brokers are needed to execute anonymous deals in these venues. Even in this region, however, technology is supplanting the need for brokers.
I don't believe there is any human-broker-free stock exchange, but Nasdaq and other traditionally OTC (over the counter) exchanges are as close as it gets since they never even had trading floors.