If in the above visual, I add a column- city id, which also same granularity as a city, and from the same table, will I get the same ranks?

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No, you will get all 1. If a column does not participate in the table argument of the Rankx, and it is used in visual, Rank will be partitioned inside that new column. As city and city id has the same granularity, you will get all 1.