Currently, there are NOT millions of Bitcoin users out there, if you take a look at the simultaneous online nodes statistics and/or client download statistics. Also nice "if everyone in ... would ..." ideas don't work - if they would even KNOW of Bitcoin, the price would soar much higher and your "stable" ~3/BTC would be like my offer of 21 EUR in comparison and a return to a rate of 3/BTC would be seen as "crash" + "failure".
I don't set up such a company, because Tradehill is currently doing the same - and being under the jurisdiction of Chile I figure it might be easier for them than me under EU law.
Also:
How/why does it hurt a currency if it is being exchanged for another currency at various prices or even if it is a meta-currency (like SDRs
http://en.wikipedia.org/wiki/Special_Drawing_Rights)?If you are not holding that money and the system is voluntary, you have the exact same thing as you already have on MtGox: People have a pile of USD in their account and when they think the price is right, they buy BTC. All you would do is to say: "As there are 21 million USD on MtGox right now that I know of, it does not make sense to set offers below 1 USD!". I still don't see how this would stabilize anything, if you cannot even remotely approach the current prices.
Most central banks DO have reserve requirements (
http://en.wikipedia.org/wiki/Reserve_requirement) but it again only works because they are central. You're free to try it out with an alternate chain. If you let people come and go at will, your "backing" is also completely unstable so there's no trust in it.
In the scenario you described, you have successfully devaluated BTC into nothingness, even though your bot was correctly working someone could still play pump + dump. To me this sounds like a complete failure of this bot.
For a backing to work EVERYONE who trades fiat for BTC needs to put the same amount of fiat into the fund as well (I buy 10 BTC @ 10 USD --> I pay 100 USD to the seller + 100 USD to the fund to keep the value up). Then over time the fund will become large enough to really back Bitcoin. If you only pay in a lower amount of fiat into the fund than you trade, you have a fractional reserve and risk that amount you overpay (If you trade 10 BTC@10 USD and pay 80USD to the fund, over time the fund will only grow to a maximum of 80% of the then current trade price).
All in all your bot's a nice idea and all, but it has 3 shortcomings:
1) It won't work for ceilings (no BTC will be traded above x USD) as the amount of USD is unknown (depending of the money amount you take into account) or so high, that you will need far over 20 million BTC in that fund to bring it down to current sub-100 USD levels.
2) It requires people to publicly tell a lot of people how much buying power in fiat they have and pledge to use to back Bitcoin.
3) It is voluntary, so panics + dumps can still occur (floors will most likely be magnitudes below current values and your system only works if noone needs their fiat money for anything else but backing Bitcoin. Ever.). You even gave an example in your last post.
Anyways, I still haven't seen a single line of code yet! If it is such a great idea, just do it, don't listen to me and argue with me - prove me wrong!