We introduce a family of information leakage measures called maximal
α,β-leakage, parameterized by real numbers α and β. The
measure is formalized via an operational definition involving an adversary
guessing an unknown function of the data given the released data. We obtain a
simple, computable expression for the measure and show that it satisfies
several basic properties such as monotonicity in β for a fixed α,
non-negativity, data processing inequalities, and additivity over independent
releases. Finally, we highlight the relevance of this family by showing that it
bridges several known leakage measures, including maximal α-leakage
(β=1), maximal leakage (α=∞,β=1), local differential
privacy (α=∞,β=∞), and local Renyi differential privacy
(α=β)