SCOOP1P welcome to Flyertalk.
This topic comes up from time to time. You might find these threads interesting to read.
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There are other discussions on this topic. Just do a search for "priority tag".

Personally, I no longer ask the ticket agent to put a Priority sticker on my bag. It doesn't seem to make any difference on domestic flights, and only sometimes matters on international flights.

(edited to correct link)

[This message has been edited by Flexible Flyer (edited 02-17-2003).]