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The Probability Ranking Principle (PRP) ranks search results based on theirexpected utility derived solely from document contents, often overlooking thenuances of presentation and user interaction. However, with the evolution ofSearch Engine Result Pages (SERPs), now comprising a variety of result cards,the manner in which these results are presented is pivotal in influencing userengagement and satisfaction. This shift prompts the question: How does the PRPand its user-centric counterpart, the Interactive Probability Ranking Principle(iPRP), compare in the context of these heterogeneous SERPs? Our study draws acomparison between the PRP and the iPRP, revealing significant differences intheir output. The iPRP, accounting for item-specific costs and interactionprobabilities to determine the ``Expected Perceived Utility" (EPU), yieldsdifferent result orderings compared to the PRP. We evaluate the effect of theEPU on the ordering of results by observing changes in the ranking within aheterogeneous SERP compared to the traditional ``ten blue links''. We find thatchanging 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 theTREC WaPo Collection. This work suggests that the iPRP should be employed whenranking heterogeneous SERPs to provide a user-centric ranking that adapts theordering based on the presentation and user engagement.

Ranking Heterogeneous Search Result Pages using the Interactive Probability Ranking Principle