This requires not just an honest guy, but a diligent one as well.
The risk is that honest guys will be lazy and rely on others to go far back in history to check all tx for double spending.

Even in bitcoin we've seen some miners being too lazy to do full node checking and instead relying on SPV, and thus risk building on top of invalid blocks.

Isn't there are problem with merger of a split tangle then. If the network was split, then tips of the stronger part will have greater cumulative weight and will always be chosen to be referenced. The weaker subtangle just dies off.

The party which is interested in the survival of the weaker subtangle would "connect" it to the stronger subtangle by referencing 1 tx from here and 1 from there. If both subtangles are legit, they'll quickly merge.

So transaction security is actually reliant on the subsequent transaction volume for the overall network?
I imagine that the picture above would look quite different if the attacker simply chooses to mount his attack during a period of negligible transaction volume (thus low weight build-up on the legitimate tangle). I'm probably missing something (or a lot)...

That is precisely how I would have answered. It is quite clear that everyone has a strong incentive to be on a correct branch, else any time down stream someone can broadcast a notice that a branch is incongruent then that branch gets abandoned.

But doesn't this mean that there is a great incentive to not include tips in your branch, because these don't yet have enough veracity to be sure they won't end up being a double-spend. In your system there is often no way to prove which of the double-spends were first, so they both are invalid.

Seems to me no one has an incentive to lengthen instead of broaden the tree. But I haven't absorbed the white paper. Did you address that?

Yes. As mentioned somewhere above on this page (or maybe on the previous one), the (default) referencing algorithm works in such a way that it prefers tips with bigger height. So, if you're too lazy and reference some very old tx's, you take the risk that your tx won't be referenced by others.

Anyhow, for that to happen, both double-spending tx's need to be broadcast more or less at the same time. Doesn't sound as a good idea for the attacker...

Valid point.

This is still a form of premine. You can convert all of you ICO funding to coins in any scenario while paying those funds to yourself. Since you can pay yourself numerous times, and recycle the funds to pay yourself again, there is no limit to the number of coins you can buy from yourself.

Even if you require all funds to be presented up front, that doesn't prevent you from taking out a loan which you can pay back fully because you buy the coins from yourself.

Even if you limit the supply of coins and force all offers to be tendered at once and randomly choose in a publicly verifiable process, you can still stack the bids to be sure you get the % of coins you want.

If you instead have a market driven price for the ICO and a fixed supply of coins, then you can bid on your own coins driving the price higher and generating more funds while obtaining some of the coins cheaper than others who have paid you to buy your coins cheaper.

The only way around this would be to verify the identify of every purchaser and make this information public (or audited by a trusted entity), which I doubt most purchasers would agree to.

The only solution I see for this dilemma is to identify each purchaser, but do it in a convenient and non-intrusive way. That is why I have been thinking to only sell up to say $500 to each user (no investors! so as to avoid creating an illegal unregistered investment security so you all don't all end up in jail in the future) and allowing these purchases only by credit card (or verified bank account funding via Paypal to avoid chargebacks) with an auditing process that insures each name on the card is unique. I suppose you are clever enough you can pay people to let you use their credit cards (or steal them), but this is a crime and probably easy to track down (especially during any SEC investigation), so it is very risky and one would assume legit developers won't risk crime (heck they are talented, and can earn a lot of money taking programming jobs outside of crypto).

The only other way is some mining distribution, but wastes resources that could be better used to fund development.

Or you can just tell everyone honestly that all they know is how many coins they have and the total supply of coins, but they can't know how many coins you have unless all the buyers get together and tally their purchases.

This a serious dilemma. I have thought about it a lot. Has anyone else devised a better solution?

Yes, normally the left yellow tx would have been referenced by many green ones already.