# How to analyse the sensitivity in argmax in exponential mechanism of differential privacy?

Consider we have a database $$D=[1,2,1,3]$$, and the query for $$\mathop{\arg\max}_{i} D_i$$. So how to analyse the sentivity of the utility function?

for the sensitivity of $$u$$ equals to $$\Delta u=\max_{i} \max_{D,D':\Vert D-D'\Vert_1\leq 1}\|\mathop{\arg\max}_{i} D_i-\mathop{\arg\max}_{i} D'_i\|$$

Is it necessary to set an upper bound of $$D_i$$ to have the sensitivity of the utility function?

• Thank you for your comment. So is it possible to normalize the data and have all $D_i \in [0,1]$? Thereby we have the sensitivity $\Delta u = 1$. – PINGCHUAN MA Mar 30 at 6:05