Distance and consensus for preference relations corresponding to ordered partitions

Ranking is an important part of several areas of contemporary research, including social sciences, decision theory, data analysis and information retrieval. The goal of this paper is to align developments in quantitative social sciences and decision theory with the current thought in Computer Science, including a few novel results. Specifically, we consider binary preference relations, the so-called weak orders that are in one-to-one correspondence with rankings. We show that the conventional symmetric difference distance between weak orders, considered as sets of ordered pairs, coincides with the celebrated Kemeny distance between the corresponding rankings, despite the seemingly much simpler structure of the former. Based on this, we review several properties of the geometric space of weak orders involving the ternary relation “between”, and contingency tables for cross-partitions. Next, we reformulate the consensus ranking problem as a variant of finding an optimal linear ordering, given a correspondingly defined consensus matrix. The difference is in a subtracted term, the partition concentration, that depends only on the distribution of the objects in the individual parts. We apply our results to the conventional Likert scale to show that the Kemeny consensus rule is rather insensitive to the data under consideration and, therefore, should be supplemented with more sensitive consensus schemes

Egalitarianism in the rank aggregation problem: a new dimension for democracy

Winner selection by majority, in an election between two candidates, is the only rule compatible with democratic principles. Instead, when the candidates are three or more and the voters rank candidates in order of preference, there are no univocal criteria for the selection of the winning (consensus) ranking and the outcome is known to depend sensibly on the adopted rule. Building upon XVIII century Condorcet theory, whose idea was to maximize total voter satisfaction, we propose here the addition of a new basic principle (dimension) to guide the selection: satisfaction should be distributed among voters as equally as possible. With this new criterion we identify an optimal set of rankings. They range from the Condorcet solution to the one which is the most egalitarian with respect to the voters. We show that highly egalitarian rankings have the important property to be more stable with respect to fluctuations and that classical consensus rankings (Copeland, Tideman, Schulze) often turn out to be non optimal. The new dimension we have introduced provides, when used together with that of Condorcet, a clear classification of all the possible rankings. By increasing awareness in selecting a consensus ranking our method may lead to social choices which are more egalitarian compared to those achieved by presently available voting systems.Comment: 18 pages, 14 page appendix, RateIt Web Tool: http://www.sapienzaapps.it/rateit.php, RankIt Android mobile application: https://play.google.com/store/apps/details?id=sapienza.informatica.rankit. Appears in Quality & Quantity, 10 Apr 2015, Online Firs

Network Medicine Framework for Identifying Drug Repurposing Opportunities for COVID-19

The current pandemic has highlighted the need for methodologies that can quickly and reliably prioritize clinically approved compounds for their potential effectiveness for SARS-CoV-2 infections. In the past decade, network medicine has developed and validated multiple predictive algorithms for drug repurposing, exploiting the sub-cellular network-based relationship between a drug's targets and disease genes. Here, we deployed algorithms relying on artificial intelligence, network diffusion, and network proximity, tasking each of them to rank 6,340 drugs for their expected efficacy against SARS-CoV-2. To test the predictions, we used as ground truth 918 drugs that had been experimentally screened in VeroE6 cells, and the list of drugs under clinical trial, that capture the medical community's assessment of drugs with potential COVID-19 efficacy. We find that while most algorithms offer predictive power for these ground truth data, no single method offers consistently reliable outcomes across all datasets and metrics. This prompted us to develop a multimodal approach that fuses the predictions of all algorithms, showing that a consensus among the different predictive methods consistently exceeds the performance of the best individual pipelines. We find that 76 of the 77 drugs that successfully reduced viral infection do not bind the proteins targeted by SARS-CoV-2, indicating that these drugs rely on network-based actions that cannot be identified using docking-based strategies. These advances offer a methodological pathway to identify repurposable drugs for future pathogens and neglected diseases underserved by the costs and extended timeline of de novo drug development

Element weighted Kemeny distance for ranking data

Preference data are a particular type of ranking data that arise when several individuals express their preferences over a finite set of items. Within this framework, the main issue concerns the aggregation of the preferences to identify a compromise or a “consensus”, defined as the closest ranking (i.e. with the minimum distance or maximum correlation) to the whole set of preferences. Many approaches have been proposed, but they are not sensitive to the importance of items: i.e. changing the rank of a highly-relevant element should result in a higher penalty than changing the rank of a negligible one. The goal of this paper is to investigate the consensus between rankings taking into account the importance of items (element weights). For this purpose, we present: i) an element weighted rank correlation coefficient as an extension of the Emond and Mason’s one, and ii) an element weighted rank distance as an extension of the Kemeny distance. The one-to-one correspondence between the weighted distance and the rank correlation coefficient is analytically proved. Moreover, a procedure to obtain the consensus ranking among several individuals is described and its performance is studied both by simulation and by the application to real datasets

Two algorithms for finding optimal solutions of the Kemeny rank aggregation problem for full rankings

The analysis of ranking data has recently received increasing attention in many fields (i.e. political sciences, computer sciences, social sciences, medical sciences, etc.).Typically when dealing with preference rankings one of the main issue is to find a ranking that best represents the set of input rankings.Among several measures of agreement proposed in the literature, the Kendall's distance is probably the most known. We propose a branch-and-bound algorithm to find the solution(s) even when we take into account a relatively large number of objects to be ranked. We also propose a heuristic variant of the branch-and-bound algorithm useful when the number of objects to rank is particularly high. We show how the solution(s) achieved by the algorithm can be employed in different analysis of rank data such as Mallow's phi model, mixtures of distance-based models, cluster analysis and so on