> The saying goes, "Anonymity loves company" which means that an anonymous communication system cannot provide high anonymity assurances if there are very few people using it.

I see this often repeated but never elucidated. It is particularly problematic in light of the stated non-goal:

> Hiding the fact that someone is utilizing an anonymity network is not an intrinsic goal of anonymity networks.

So here's a straightforward counter-example I mentioned before:

Create a PIR where messages-- let's say "tweet-sized" for this example-- are sent once daily, and the only allowed participants are Debian developers. If a participant has no message to send, they send a "tweet-sized" message composed of randomly chosen bits.

The clients try to decode all messages with their private key. The message or messages that are successfully decoded were the messages that were intended for that client.

Let's even put a single point of failure like a centralized server where all messages are sent and retrieved.

Now you've got:

* sender anonymity

* receiver anonymity

* sender and receiver anonymity with respect to third party observers

* maximum practical resistance to Sybil attacks

* resistance to timing correlation attacks

* resistance to compulsion attacks

Anyway, for this example the saying "anonymity loves company" is false.