Anonymity sets are central when discussing privacy. Basically, an anonymity set is the total number of people that have a characteristic we are looking for. In cryptocurrency that generally means the potential people that may be associated with a particular transaction.

Anonymity sets get reduced by filtering the total population using known data. For example, let's pretend a store has a camera at it's entrance, but not inside and 100 customers visited the store that day and one of them stole a box of cereal. We can reduce the anonymity set right away to 100 because know it must be one of the people that physically entered the store. Using the camera at the entrance, we can also reduce it by an additional 95 because 95 people did not carry a bag, etc, that would allow them to physically transport the cereal out of the store. So, based on this, we can narrow the possibilities to the 5 people that entered the store that day and who had the transport capacity to exit the store with the cereal. The anonymity set has been reduced to 5.

What is the anonymity set of a Pirate Chain transaction?

Due to the magic of zk-SNARKs the anonymity set of Pirate Chain is the total size of network participants. So, if there are 1 million users of Pirate Chain then, that is the anonymity set. This set will grow over time as more people use it. This is in contrast to other privacy technology like Monero mixins, which only provide an anonymity set of 16 that shrinks over time.