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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 in advance.

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  • $\begingroup$ The sensitivity is going to be very high. You cannot privately identify which person has the highest value. $\endgroup$ – Thomas Mar 29 at 5:18
  • $\begingroup$ 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 $\Delta u = 1$. $\endgroup$ – PINGCHUAN MA Mar 30 at 6:05

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