BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Armajac Raventós Pujol (Universidad Autónoma de Madrid - Spain) DTSTART:20230303T160000Z DTEND:20230303T170000Z DTSTAMP:20260423T022921Z UID:GEOTOP-A/37 DESCRIPTION:Title: Simplicial complexes and the index lemma: A pathway to reach agreements fairly\nby Armajac Raventós Pujol (Universidad Autónoma de Madrid - Spain) as part of GEOTOP-A seminar\n\n\nAbstract\nAggregating individual p references is a fundamental problem in democracy:\nHow can we take collect ive decisions fairly based on individual preferences? Arrow's impossibilit y theorem (1951) proves that it is not possible to do it when we assume so me apparently mild conditions. Fortunately\, in some cases\, aggregation i s possible when the domain of individual preferences is restricted. That i s\, when voters can only report some preferences\, good aggregation rules exist. However\, no theorem characterizes the domains in which aggregation is possible\, and the\nproblem remains open.\n\nDespite the Arrovian mode l being purely combinatorial\, Baryshnikov (1993) used simplicial complexe s and homology to prove Arrow's theorem and exposed a conjecture which cha racterized restricted domains through homology groups. The main drawback o f using homology is that it is not affordable for most of the social scien tists. Therefore\, instead of homology\, we have used combinatorial topolo gy tools such as the Index Lemma (the combinatorial counterpart to Poincar e's Lemma) to tackle the problem. First\, we have proved the Arrow's impos sibility theorem\, showing that combinatorial topology is helpful for our purposes.\n\nSecond\, we have characterized the domains allowing aggregati on rules for the base case of two voters and three candidates. Our charact erization proves that homology groups are not enough to characterize such domains. Our result gives us hope to obtain a general characterization of the good domains for aggregating preferences. Moreover\, it could be imple mented computationally\, making it handled by practitioners in politics an d economics.\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/37/ END:VEVENT END:VCALENDAR