I'd been used to passing prompt parameter values for Cognos reports in a URL by just simply using &p_<parameter_name>=<value>.
However, I came across a report where both the useValue and displayValue of the parameter were involved in the final output and I discovered that using &p_<parameter_name>=<value> seems to result in <value> being used as both the useValue and displayValue. This was no good as the report required the two different values as set up on the prompt page in the report.
After endless searching and guesswork I eventually stumbled across how to send the two values separately in a URL:
&p_<parameter_name>=<selectChoices><selectOption useValue="<useValue>" displayValue="<displayValue>"/></selectChoices>