I'm just looking at how to implement donations on my site and also read that I should use a new address for each transaction to increase anonymity.
Is this an ultimately pointless practice when tied to a single private website?
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Note that even if you don't publicly publish the donation address (thus associating the address with your site), the public blockchain would reflect that your donors all paid money to the same person.
While it might've been traceable anyway (especially when you spend the bitcoins), using one address does make it more obvious, and your donors might not appreciate that.
Whether this is actually important to you is a question only you and your donors can answer (but it probably isn't important, so using one address is fine).
A new address for each transaction is used for anonymity most of the time. For a donation website this isn't isn't that useful. Most people reuse because they feel that their address could be remembered and identified later on, even though this is hard to do it is possible.
Unless you want it to be hard to tell who and where the bitcoins are, it's better to reuse and not have to have a complex system that generates and keeps track of generated addresses.
Absolutely not pointless. So any answer should be read as "No, however...".
You are making a decision about other people's privacy which may cause them to decide to not donate. Or they may get into trouble if they do donate, depending on whether your site is wikileaks and what their government thinks about that.
Now that's worst case stuff and in practice it probably won't be such an issue and it's simply so much more convenient to not have to create dynamic new addresses for every visitor.
Hopefully stealth addresses will soon give us the best of both: a static qr code on your website yet still random new addresses for every donation.
When using the same address, you obviously allow everyone to check your balance.
After checking your balance, the user may think: "wow, he got so much money from donations, it should be enough for him" and he won't pay.
However, it's also possible: "So many person donated him, I also must do it!"