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Traditionally the probabilistic ranking principle is used to rank the searchresults while the ranking based on expected profits is used for paid placementof ads. These rankings try to maximize the expected utilities based on the userclick models. Recent empirical analysis on search engine logs suggests aunified click models for both ranked ads and search results. The segregatedview of document and ad rankings does not consider this commonality. Further,the used models consider parameters of (i) probability of the user abandoningbrowsing results (ii) perceived relevance of result snippets. But how toconsider them for improved ranking is unknown currently. In this paper, wepropose a generalized ranking function---namely "Click Efficiency (CE)"---fordocuments and ads based on empirically proven user click models. The rankingconsiders parameters (i) and (ii) above, optimal and has the same timecomplexity as sorting. To exploit its generality, we examine the reduced formsof CE ranking under different assumptions enumerating a hierarchy of rankingfunctions. Some of the rankings in the hierarchy are currently used ad anddocument ranking functions; while others suggest new rankings. While optimalityof ranking is sufficient for document ranking, applying CE ranking to adauctions requires an appropriate pricing mechanism. We incorporate a secondprice based pricing mechanism with the proposed ranking. Our analysis provesseveral desirable properties including revenue dominance over VCG for the samebid vector and existence of a Nash Equilibrium in pure strategies. Theequilibrium is socially optimal, and revenue equivalent to the truthful VCGequilibrium. Further, we relax the independence assumption in CE ranking andanalyze the diversity ranking problem. We show that optimal diversity rankingis NP-Hard in general, and that a constant time approximation is unlikely.

Click Efficiency: A Unified Optimal Ranking for Online Ads and Documents