The way I think it could work is that a stock exchange is an ebay like environment (sorry for the analogy, but I can't think of a better one) where buyers and seller meet and declare what they have to offer or what they are looking for.
A piece of software in the middle matches buyers and sellers according to some public algorithm and takes care of the escrow so that the buyer gets their stock and the seller his money or nothing at all happens.
So how is this different than a limit-order book? Some exchanges work exactly like this (esp European electronic markets.) This explains both the structure and the "algorithm."
You would not have an Ebay-like system, because stock is fungible. One share of IBM is exactly like another share of IBM. You don't need reputation, etc, because of the way clearing works.
I don't understand how you are able to think that this is not in some way an exchange.
I never said it would not in 'some way be an exchange', I wrote that 'the way they are right now' they are outdated.
I figure buildings full of people and rooms full of traders are way past their expiry dates, if there is one thing that you could trade exclusively online it's stocks.
Of course I understand that you do not need reputation and so on, I already made it clear that ebay is a very imperfect analogy.
Currently there is much lack of transparency, stock market data is delayed from many exchanges to the general public, sometimes up to 15 minutes (for nasdaq, nyse and a whole bunch of others), people are riding in the slipstream of big traders because they have access to sensitive data. All that could go out the window (and the brokerage fees as well) by using a relatively simple in concept (but probably extremely complex in scope and execution) system that would take care of these functions automatically.
Redefine the stock market in terms of an API and let users either run software, use a website or have big traders write their own.
All the statistics would be live and available through the API.
Again, I realize that I'm just dreaming here but I'm pretty sure that if the will were there it could be done.
You do not understand what an exchange is. You have made up a mental model that is not even close to reality and are now arguing against that. Please do a little research before having an opinion.
What you are describing is actually a great deal like how many exchanges work. Open outcry pits or whatever are not the prevailing model. There is NO room with screaming people for NASDAQ.
The pricing data is delayed because it is free. You can buy realtime pricing data. It's hard to support a large infrastructure for free, of course, and you are making money on it.
Big traders, especially block traders, execute at least partially off-exchange anyway.
"All the statistics" are not necessarily stored or generated by the exchange. Other companies do this (Reuters, etc.) We had to calculate "all the statistics" ourselves when we did automated trading systems.
I'm not sure how APIs magically make all fees and costs "go away" in some magical fashion.
Currently there is much lack of transparency, stock market data is delayed from many exchanges to the general public, sometimes up to 15 minutes
No, there is no lack of transparency. You get what you pay for. If you don't pay for anything, don't expect real-time quotes. Wall Street is not Santa Claus.
Where would people find counterparties in your system?
In what way would price discovery work?
Exchanges in the US are vastly overcomplicated, but that doesn't mean the concept is bad.