I would consider legitimate (i.e. not "fake") any transaction between competing people or organizations, whether it is done manually or with the help of scripts and robots. Any such transaction contributes to define the true "market price" of the item. To a first approximation, it should not matter if the same coins are being traded back and forth many times, or how many distinct people are trading, as long as each transaction happens because both sides believe that the price is good. To me a transaction is "fake" only if the buyer and seller are the same, or are colluding outside the market place.
Methinks that the volume of legitimate transactions is a good measure of the importance of a market.
Although I agree with your basic premise behind a legitimate transaction, I think that how many people trade the system and how many actual coins make-up the market hold important implications for true value approximation - first approximations are too general for me. This information becomes even more important if you really dissect the concept of a "fake" transaction.
Lax regulation, back-room deals for large holders, and a highly interconnected group of large stakeholders (listen to Andreas towards the middle of the talk when he speaks of how the various "good" actors reacted to the Mt. Gox press release
http://letstalkbitcoin.com/e85-mtgox-and-malleability/#.UwQ8K4V_e_y) create a perfect breeding ground for acts like self-trading and collusion. Houbi is likely rife with less than legitimate transactions if we use the strict definition of "fake" as per your text. Unfortunately, since these forms of collusion often are hard to discern from volume and technical analysis even in good market conditions, an unlimited algo assisted trade environment does not make the task any easier. I know I kind of went on a rant there, but the point is to acknowledge the grey nature of the environment and see that certain technical metrics are less effective at understanding the reality of the stakeholders within this market.
The higher the volume, the higher the liquidity and the smaller is the spread, therefore the price is pinned down more accurately. At BTC-e, forexample, the price often is bouncing rapidly up and down by a few dollars, so that the 1-minute plot look like a broad belt. You hardly see that at Huobi; the plot looks more like a line than a belt.
Usually, the higher the volume, the smaller is the effect on the price of buying or selling a fixed amount of coins. Therefore, arbitrage trading between a high-volume market and a low-volume market generally has little effect on the price of the former, instead copies the price to the latter. For example, I would guess that the sharp steps one can see in the 1-minute plots of BTC-China and Bitstamp (but not on Huobi's), at periods when there seems to be little real activity, are arbitrage transactions aligning their prices with the global market.
For all I have seen in the past 2-3 months, I believe that most of Huobi's volume is legitimate in this sense. At the other exchanges, I am not so sure; but even if it is all legitimate, the volume at non-Chinese exchanges is only 1/3 to 1/4 of the volume at Huobi and OKCoin. Whatever one may think of the "quality" or "meaningfulness" of their trade, it counts the same for the definition of BTC's price.
Ditto.
Also I do not think that there is any government interference with the bitcoin trading inside the exchanges. My understanding of the news is that the PBOC, having blocked the use of BTC as a currency in commerce, and prohibited banks from playing with it, now sees bitcoin trading within the exchanges as a kind of gambling, and therefore does not care about it at all.
Agreed, the government does not have direct influence inside the exchange per say, but they are still indirectly in control of how the future of trading bitcoin unfolds via regulation and other tools of submission.
Note that I said "bitcoin trading", not "bitcoin". Bitcoin development and other activities (such as promoting its commercial use) seem to be mostly "non-Chinese things". Given the restrictions on use of BTC in China, I do not expect that there will be any significant development or advocacy there, except perhaps in mining technology.
True, I should have read that sentence more carefully - BTC trading is but a part (a very large one) of the entire system and are not the same thing.