There is nothing obvious for node joining network because it has no knowledge of what network should look like. Node just sees two different networks one with no way to decide which one is "real one".
Easily deciding which chain is honest without relying on any authority is the most important thing in bitcoin and you can't really do decentralized database without this.
First of all, you have to rely on an authority, just not a central one. Bitcoin's authority is hashing power, Decrits' is consensus. Now while consensus at first may seem wishy-washy, the fact is that it is a very public, very distributed network where any collusion attempt by the consensus will be out in the open, recorded, for all to see and prove. But I think you are willing to agree on that point. Even in absolute worst-case scenarios where EvilCorp owns a significant amount of real shares and has a target's connection to the network surrounded, whatever manipulation was attempted will be recorded, and the victim can later prove malfeasance.
A bit of a side bar for sec. There is (brag) a bit of ingenuity in how the transaction block chain works (nb: as proposed in my notes). kokjo assumed earlier in this thread before asking that the order that transactions are approved in is ever in the control of one node or several nodes. It is not. The chain goes in a random order that is changed only by adding the hash of every single SH's signature on the prior CB to some random function. This is the reason why SHs will lose their deposit if they do not sign the CB. They either can't affect the randomness of this function, or lose 3,000 DCR or whatever the price may be for a share. They are also required to sign the "potential" CB (I have to clarify this in the OP) during their assigned TB, meaning that if they do not sign it then (by missing their TB), they will receive a soft strike*. The very last person to sign the CB could make for two potential outcomes [one of them might be better than losing 3,000 DCR], but I think there are ways to avoid that too--I'm going to go too far on a tangent though. Generating a distributed, unmanipulatable random number for the network is significantly important though, and was something I solved only recently. It's like 50 hours of ideating and 10 lines of code.
* - this is to prevent repeated attempts to learn information about other SH's signatures
The point of writing all that was to say this: even if EvilCorp controls, say, 80% of the shares and a strong enough control over the CN or is somehow man-in-the-middle attacking a MITM-resistant network (section 2.B) to pull off a massive currency heist, the odds of a TB being forcibly missed because EvilCorp temporarily can't let you see anything from TheGoodGuys during the time frame of this heist are very high. Say the transaction is for 100kDCR, a very prudent person would want to wait for enough transaction blocks to pass to cover at least 100kDCR, i.e. 34 (5 and a half minutes) if the share price is 3kDCR.. It would be another tangent to explain why covering it is important. Anyways, someone determine the odds of EvilCorp owning all 34 in a row. It's low. So if EvilCorp manages to pull this off, they must pull it off in a window where they control every single SH for as long as the victim wants to wait. Because if a TB in the chain is missing, the victim has a thought of "what if...?" Missing TBs are only slight hiccups for regular, every day transactions, but they have big implications for big transactions. This all requires a lot of detail though into how massively awesome I believe consensus-based security can be, and this post is already too long and hasn't answered
your question.
Now, as long as the client has the genesis block for the network it is interested in participating in and at no point has the consensus massively colluded to do something nefarious*, then the newbie node can very reasonably determine which network is the correct one in the face of competing networks.
* - This would be common knowledge, like mtgox being hacked or something, except a lot of people just sacrificed a lot of money.
There are two ways for money to be removed from the "share ledger"--1) being destroyed for doing something bad (such as not agreeing to the consensus, section 1.B.ii), 2) by the share's owner withdrawing it. In situation 1), we have no way to determine whether or not the shareholder actually did something bad--only that the consensus agreed he did. Even if we did store a record of a bad transaction block as proof, because the state of the network is routinely pruned, it will be meaningless evidence in the future. In situation 2), the shareholder signs a hash of the shareholder record as they remove their share. While the shareholder record would not likely be kept forever (an ongoing hash could though), it is pretty heavily bound by around 100 bytes for every share purchased and 100 bytes for every share legitimately removed. If you've had 500,000 shareholders in the history of the network, you have 50-100MB of data you need to download, plus the headers of the transaction blocks from present back to 100% consensus or whatever makes you feel comfortable (100 or so bytes X the number of current shareholders).
What this does is create an ongoing consensus. Each member who has left the network has written, "yup, everything's cool" and everyone else still there is around to confirm it. Members that are no longer in the network and did not sign out lost 3,000 DCR. If that percentage is, say, 1%, then there's a monumental chance that you are on the correct network.
A smart client would interpret the data this way: if there were originally 100 SHs in the genesis block, and 99 of them never signed out and are no longer present, the maximum consensus that this chain can have is 1%, even if there are now 500,000 SHs. In the future, the real network is likely to have somewhere around 95-98% consensus I would think, as 3,000DCR should be a lot of money to people if Decrits is useful and popular--but there will be people that accidentally or intentionally lose their shares over the history of the network. If the network is currently split in an ongoing attack, if EvilCorp was not in on it almost from the start of the network, it will be very, very difficult for EvilCorp to look like the better network, even to a complete newbie node, but the real network might also be below 50%, so it is not 100% cut and dried. Or maybe it is, because there will not be a rational reason to do this.
Essentially, if EvilCorp has a mad plan and buys up 101,000 shares when the network has currently 100,000 shares to perform a "51% attack", assuming no one signed out in the mean time, EvilCorp will have a network with 0% consensus and TheGoodGuys will have 49% consensus. That's why a 99% attack doesn't work either. This is not a network-enforced choice but it's a brain-dead obvious one.