[tptacek]

I don't think you've thought this through very carefully. Most orders in the market aren't "market orders"; they specify a price. Meanwhile, assume you resolve pricing in an automated auction: there's a spectrum of prices. Who gets the better prices?

[CyberDildonics]

If prices are given as a floor for selling and ceiling for buying they can be fit in a fair and methodical way through many different methods with any remainder being left over for the next tick. I'm surprised it is even such a controversial idea that a fair and fluid exchange can be made without resorting to a first come first serve structure.

[tptacek]

This suggestion supposes that there is a reasonable "floor" and "ceiling" for prices in batch auctions. But in fact that spread of prices is exactly what market makers figure out organically.

If you instead mean that individual traders could input orders with floor and ceiling prices, that's something that already exists, but now you're back to the original problem of resolving whose orders execute when (inevitably) most of the orders don't match.

[CyberDildonics]

It's not back to the same problem, there are many ways to do it including but not limited to matching the sells with the lowest floors to the buys with the highest ceilings, working inward from the extremes of the spread. Why are you so convinced that a fair exchange is impossible?