  The Probability Ranking Principle (PRP) ranks search results based on their
expected utility derived solely from document contents, often overlooking the
nuances of presentation and user interaction. However, with the evolution of
Search Engine Result Pages (SERPs), now comprising a variety of result cards,
the manner in which these results are presented is pivotal in influencing user
engagement and satisfaction. This shift prompts the question: How does the PRP
and its user-centric counterpart, the Interactive Probability Ranking Principle
(iPRP), compare in the context of these heterogeneous SERPs? Our study draws a
comparison between the PRP and the iPRP, revealing significant differences in
their output. The iPRP, accounting for item-specific costs and interaction
probabilities to determine the ``Expected Perceived Utility" (EPU), yields
different result orderings compared to the PRP. We evaluate the effect of the
EPU on the ordering of results by observing changes in the ranking within a
heterogeneous SERP compared to the traditional ``ten blue links''. We find that
changing the presentation affects the ranking of items according to the (iPRP)
by up to 48\% (with respect to DCG, TBG and RBO) in ad-hoc search tasks on the
TREC WaPo Collection. This work suggests that the iPRP should be employed when
ranking heterogeneous SERPs to provide a user-centric ranking that adapts the
ordering based on the presentation and user engagement.
