ArcMap 10.2.2 doesn’t respect the advanced sort in related tables, I couldn’t figure out why the ArcMap doesn’t respect the advanced sorted values when the sorted table is related to other feature calss?
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You could trick the display to show the years in the order you want by altering the Display tab expression field to do a formula that made an Ascending Sort behave like a Descending sort. At least at version 10.2, multiplying a positive number to become a negative number reverses the sort of the numbers of the related table in the Identify window and is in ascending numerical order not ascending alphabetical order (so -10001 is above -10000, which is above -2000, which is above -1000).
Set the Identify window to apply an Ascending Sort to the entire window. Then on the Display tab for your table make the expression: -1 * [ApprovalYear]
if ApprovalYear is a string field make the expression: -1 * CLng([ApprovalYear])
Explain that the "-" just means that you have removed the rest of the date and only retained the year portion and to otherwise ignore it.