Trading once per day and randomizing the order of trades would work nicely I think. There was a recent very good example of this concerning Apple : When Steve Jobs died, they kept the information secret and agreed with the stock exchange to suspend trading for a day. The time for everyone to think about what it meant for the company instead of hysterically following a random trend. A big event, obviously changing the company's intrinsic value, was interpreted with a daily period. Everything I read about high frequency trading indicates that it is mainly noise.
I mean, stock exchanges close at night and during week ends. There are 48 hours without quotations. How does one concile that with nano-second trading.