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You don't really look at the charge of the anion when determining its polarizability but rather its size and electronegativity. Polarizability increases as the ion gets larger and less electronegative since the electrons aren't held as tightly by the nucleus. One of the homework problems shows this nicely (2D.11 in 7th edition): O2- < N3- < Cl- < Br- for increasing polarizability.
Charge is less relevant when looking at anions, rather you should look at the number of electrons in relation to the number of protons in the nucleus, in addition to the size of the anion. For example, in the problem 2D.11 in 7th edition that was brought up, the polarizability of N3- is more than O2- since they both have the same number of electrons while nitrogen has one less proton in its nucleus. This makes it so that the polarizability of the nitrogen anion is greater. For Br- and Cl- in that problem, simply look at the size of the anion, whose shielding plays a large role in its high polarizabilities.
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