In anonymity systems increasing the size of an anonymity set does not provide linear gains in protection. Instead, the entropy-based measurement of anonymity (like Shannon entropy or k-anonymity) shows that beyond a certain threshold, additional participants contribute progressively less to actual anonymity gains.
Imagine you’re alone — your anonymity set (AS) is 1.
- Then, a second person joins you, increasing your AS to 2. This is a 50% increase in anonymity.
- A third person joins, bringing the AS to 3. But now, the increase is only 25%.
- A fourth person joins, making the AS 4, yet the increase is just 12.5%.
- And so on…
As the anonymity set grows, the relative gain in anonymity shrinks. The more participants you add, the less anonymity you gain per additional member.
The more anonymity set you gain, the less anonymity you gain.
