> Think of bitcoins as tokens or as tulip bulbs - it can be used for something

I do not see what that "something" is, which makes it a ponzi in my eyes. (An open, honest ponzi, but a ponzi nevertheless)

> If a bank lend out x times the value of the bitcoin you deposited, they will not be able to pay them out as bitcoins.

But of course, if x < 1 (as is in fractional reserve banking), the bank can pay out bitcoins.

> If you dont have access to your bitcoins as bitcoins, but only as a bank statement about how much they owe you, you effectivly traded your bitcoins to an IOU.

Exactly. And if that IOU is from a credible enough institution, there is no reason[1] why I would differentiate taking a payment in that IOU or bitcoin. In which case that IOU is bitcoin-denominated currency and the amount of bitcoin-denominated currency in circulation is no more constant.

[1]Well, actually there may be at least two reasons to differentiate. First, the IOU may pay interest unlike bitcoin. Second, the practicalities in transacting bitcoins or IOU's may differ, which in all probability dictate that I prefer the IOU...)

I think the confusion in this discussion lies in different interpretations of the word "Ponzi". You're using an interpretation that defines as Ponzi any investment where the value is solely anchored on the collective confidence of the holders. In the interpretation I have (and which I think is the standard one), a Ponzi scheme is something else entirely: a scheme where old investors are paid from the arrival of new ones in such a way that is mathematically unsustainable.

Note that by this standard definition, Bitcoin is not a Ponzi scheme. You may doubt whether Bitcoin is a wise investment, but calling it a Ponzi is bound to cause confusion.

I agree that there are many definitions by which bitcoin is not a ponzi, most clearly it is not fraudulent. But we can have a look how Wikipedia[1] defines a ponzi:

"a fraudulent investment operation where the operator, an individual or organization, pays returns to its investors from new capital paid to the operators by new investors, rather than from profit earned through legitimate sources."

Now, with the obvious note that bitcoin is not fraudulent, you must agree that "bitcoin (as an investment) pays returns to its investors from new capital paid to the network by new investors, rather than from profit earned through any other source"

And any claim that bitcoin offers sustainable positive returns is precisely as mathematically unsustainable than any ponzi scheme. That holds as long as there is new money flowing in. Not longer. That is very similar to a ponzi.

(And of course, any commodity bubble has this same property.)

Overall, I think there are so many similarities between the investment logic between bitcoin and a ponzi, that the comparison is justifiable.

[1]https://en.wikipedia.org/wiki/Ponzi_scheme

> Now, with the obvious note that bitcoin is not fraudulent

Which makes it not a ponzi, really that's all there is too it; fraud is a necessary pre-condition to call something a ponzi. No fraud, no ponzi.

If you remove the fraud element as you are attempting to do, then virtually every investment counts as a ponzi, all insurance counts as a ponzi, because paying investors with money from newcomers is a thing common to a lot more than just ponzi schemes. The world is Ponzi SCHEME, the scheme means fraudulent, scam, etc. If something isn't fraudulent it is not a ponzi no matter how many other traits it shares with ponzi schemes. The comparison is thus not justifiable.