Structure in Dichotomous Preferences

Many hard computational social choice problems are known to become tractable when voters' preferences belong to a restricted domain, such as those of single-peaked or single-crossing preferences. However, to date, all algorithmic results of this type have been obtained for the setting where each voter's preference list is a total order of candidates. The goal of this paper is to extend this line of research to the setting where voters' preferences are dichotomous, i.e., each voter approves a subset of candidates and disapproves the remaining candidates. We propose several analogues of the notions of single-peaked and single-crossing preferences for dichotomous profiles and investigate the relationships among them. We then demonstrate that for some of these notions the respective restricted domains admit efficient algorithms for computationally hard approval-based multi-winner rules.Comment: A preliminary version appeared in the proceedings of IJCAI 2015, the International Joint Conference on Artificial Intelligenc

Proportional justified representation

Proceedings of: 31st AAAI Conference on Artificial Intelligence (AAAI-17), San Francisco, California, USA, February 4-9, 2017.The goal of multi-winner elections is to choose a fixed-size committee based on voters’ preferences. An important concern in this setting is representation: large groups of voters with cohesive preferences should be adequately represented by the election winners. Recently, Aziz et al. proposed two axioms that aim to capture this idea: justified representation (JR) and its strengthening extended justified representation (EJR). In this paper, we extend the work of Aziz et al. in several directions. First, we answer an open question of Aziz et al., by showing that Reweighted Approval Voting satisfies JR for k = 3; 4; 5, but fails it for k >= 6. Second, we observe that EJR is incompatible with the Perfect Representation criterion, which is important for many applications of multi-winner voting, and propose a relaxation of EJR, which we call Proportional Justified Representation (PJR). PJR is more demanding than JR, but, unlike EJR, it is compatible with perfect representation, and a committee that provides PJR can be computed in polynomial time if the committee size divides the number of voters. Moreover, just like EJR, PJR can be used to characterize the classic PAV rule in the class of weighted PAV rules. On the other hand, we show that EJR provides stronger guarantees with respect to average voter satisfaction than PJR does.This research was supported in part by the Spanish Ministerio de Economía y Competitividad (project HERMES-SMARTDRIVER TIN2013-46801-C4-2-R), by the Autonomous Community of Madrid (project e-Madrid S2013/ICE-2715), and by ERC Starting Grant 639945

Integrating Genome-Wide Genetic Variations and Monocyte Expression Data Reveals Trans-Regulated Gene Modules in Humans

One major expectation from the transcriptome in humans is to characterize the biological basis of associations identified by genome-wide association studies. So far, few cis expression quantitative trait loci (eQTLs) have been reliably related to disease susceptibility. Trans-regulating mechanisms may play a more prominent role in disease susceptibility. We analyzed 12,808 genes detected in at least 5% of circulating monocyte samples from a population-based sample of 1,490 European unrelated subjects. We applied a method of extraction of expression patterns—independent component analysis—to identify sets of co-regulated genes. These patterns were then related to 675,350 SNPs to identify major trans-acting regulators. We detected three genomic regions significantly associated with co-regulated gene modules. Association of these loci with multiple expression traits was replicated in Cardiogenics, an independent study in which expression profiles of monocytes were available in 758 subjects. The locus 12q13 (lead SNP rs11171739), previously identified as a type 1 diabetes locus, was associated with a pattern including two cis eQTLs, RPS26 and SUOX, and 5 trans eQTLs, one of which (MADCAM1) is a potential candidate for mediating T1D susceptibility. The locus 12q24 (lead SNP rs653178), which has demonstrated extensive disease pleiotropy, including type 1 diabetes, hypertension, and celiac disease, was associated to a pattern strongly correlating to blood pressure level. The strongest trans eQTL in this pattern was CRIP1, a known marker of cellular proliferation in cancer. The locus 12q15 (lead SNP rs11177644) was associated with a pattern driven by two cis eQTLs, LYZ and YEATS4, and including 34 trans eQTLs, several of them tumor-related genes. This study shows that a method exploiting the structure of co-expressions among genes can help identify genomic regions involved in trans regulation of sets of genes and can provide clues for understanding the mechanisms linking genome-wide association loci to disease

Large-scale genome-wide analysis identifies genetic variants associated with cardiac structure and function

BACKGROUND: Understanding the genetic architecture of cardiac structure and function may help to prevent and treat heart disease. This investigation sought to identify common genetic variations associated with inter-individual variability in cardiac structure and function. METHODS: A GWAS meta-analysis of echocardiographic traits was performed, including 46,533 individuals from 30 studies (EchoGen consortium). The analysis included 16 traits of left ventricular (LV) structure, and systolic and diastolic function. RESULTS: The discovery analysis included 21 cohorts for structural and systolic function traits (n = 32,212) and 17 cohorts for diastolic function traits (n = 21,852). Replication was performed in 5 cohorts (n = 14,321) and 6 cohorts (n = 16,308), respectively. Besides 5 previously reported loci, the combined meta-analysis identified 10 additional genome-wide significant SNPs: rs12541595 near MTSS1 and rs10774625 in ATXN2 for LV end-diastolic internal dimension; rs806322 near KCNRG, rs4765663 in CACNA1C, rs6702619 near PALMD, rs7127129 in TMEM16A, rs11207426 near FGGY, rs17608766 in GOSR2, and rs17696696 in CFDP1 for aortic root diameter; and rs12440869 in IQCH for Doppler transmitral A-wave peak velocity. Findings were in part validated in other cohorts and in GWAS of related disease traits. The genetic loci showed associations with putative signaling pathways, and with gene expression in whole blood, monocytes, and myocardial tissue. CONCLUSION: The additional genetic loci identified in this large meta-analysis of cardiac structure and function provide insights into the underlying genetic architecture of cardiac structure and warrant follow-up in future functional studies. FUNDING: For detailed information per study, see Acknowledgments.This work was supported by a grant from the US National Heart, Lung, and Blood Institute (N01-HL-25195; R01HL 093328 to RSV), a MAIFOR grant from the University Medical Center Mainz, Germany (to PSW), the Center for Translational Vascular Biology (CTVB) of the Johannes Gutenberg-University of Mainz, and the Federal Ministry of Research and Education, Germany (BMBF 01EO1003 to PSW). This work was also supported by the research project Greifswald Approach to Individualized Medicine (GANI_MED). GANI_MED was funded by the Federal Ministry of Education and Research and the Ministry of Cultural Affairs of the Federal State of Mecklenburg, West Pomerania (contract 03IS2061A). We thank all study participants, and the colleagues and coworkers from all cohorts and sites who were involved in the generation of data or in the analysis. We especially thank Andrew Johnson (FHS) for generation of the gene annotation database used for analysis. We thank the German Center for Cardiovascular Research (DZHK e.V.) for supporting the analysis and publication of this project. RSV is a member of the Scientific Advisory Board of the DZHK. Data on CAD and MI were contributed by CARDIoGRAMplusC4D investigators. See Supplemental Acknowledgments for consortium details. PSW, JFF, AS, AT, TZ, RSV, and MD had full access to all of the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis

On Detecting Nearly Structured Preference Profiles

Structured preference domains, such as, for example, the do-mains of single-peaked and single-crossing preferences, are known to admit efficient algorithms for many problems in computational social choice. Some of these algorithms ex-tend to preferences that are close to having the respective structural property, i.e., can be made to enjoy this property by performing minor changes to voters ’ preferences, such as deleting a small number of voters or candidates. However, it has recently been shown that finding the optimal number of voters or candidates to delete in order to achieve the desired structural property isNP-hard for many such domains. In this paper, we show that these problems admit efficient approxi-mation algorithms. Our results apply to all domains that can be characterized in terms of forbidden configurations; this in-cludes, in particular, single-peaked and single-crossing elec-tions. For a large range of scenarios, our approximation re-sults are optimal under a plausible complexity-theoretic as-sumption. We also provide parameterized complexity results for this class of problems.

Preference Restrictions in Computational Social Choice: A Survey

Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences. Many impossibility theorems disappear, the structure makes it easier to reason about preferences, and computational problems can be solved more efficiently. In this survey, we give a thorough overview of many classic and modern restricted preference domains and explore their properties and applications. We do this from the viewpoint of computational social choice, letting computational problems drive our interest, but we include a comprehensive discussion of the economics and social choice literatures as well. Particular focus areas of our survey include algorithms for recognizing whether preferences belong to a particular preference domain, and algorithms for winner determination of voting rules that are hard to compute if preferences are unrestricted.Comment: 116 pages, feedback welcom