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Fractional approval voting is an electoral system using approval ballots (each voter selects one or more candidate alternatives), in which the outcome is fractional: for each alternative j there is a fraction pj between 0 and 1, such that the sum of pj is 1. It can be seen as a generalization of approval voting: in the latter, one candidate wins (pj = 1) and the other candidates lose (pj = 0). The fractions pj can be interpreted in various ways, depending on the setting. Examples are:
Time sharing: each alternative j is implemented a fraction pj of the time (e.g. each candidate j serves in office a fraction pj of the term).[1]
Budgetdistribution: each alternative j receives a fraction pj of the total budget.[2]
Probabilities: after the fractional results are computed, there is a lottery for selecting a single candidate, where each candidate j is elected with probability pj.[1]
Entitlements: the fractional results are used as entitlements (also called weights) in rules of apportionment,[3] or in algorithms of fair division with different entitlements.
Fractional approval voting is a special case of fractional social choice in which all voters have dichotomous preferences. It appears in the literature under many different terms: lottery,[1] sharing,[4] portioning,[3] mixing[5] and distribution.[2]
^ abcBogomolnaia, Anna; Moulin, Hervé; Stong, Richard (2005-06-01). "Collective choice under dichotomous preferences" (PDF). Journal of Economic Theory. 122 (2): 165–184. doi:10.1016/j.jet.2004.05.005. ISSN 0022-0531.
^ abBrandl, Florian; Brandt, Felix; Peters, Dominik; Stricker, Christian (2021-07-18). "Distribution Rules Under Dichotomous Preferences: Two Out of Three Ain't Bad". Proceedings of the 22nd ACM Conference on Economics and Computation. EC '21. New York, NY, USA: ACM. pp. 158–179. doi:10.1145/3465456.3467653. ISBN 9781450385541. S2CID 232109303.. A video of the EC'21 conference talk
^ abBrill, Markus; Gölz, Paul; Peters, Dominik; Schmidt-Kraepelin, Ulrike; Wilker, Kai (2020-04-03). "Approval-Based Apportionment". Proceedings of the AAAI Conference on Artificial Intelligence. 34 (2): 1854–1861. arXiv:1911.08365. doi:10.1609/aaai.v34i02.5553. ISSN 2374-3468. S2CID 208158445.
^Duddy, Conal (2015-01-01). "Fair sharing under dichotomous preferences". Mathematical Social Sciences. 73: 1–5. doi:10.1016/j.mathsocsci.2014.10.005. ISSN 0165-4896.
^Aziz, Haris; Bogomolnaia, Anna; Moulin, Hervé (2019-06-17). "Fair Mixing: The Case of Dichotomous Preferences" (PDF). Proceedings of the 2019 ACM Conference on Economics and Computation. EC '19. Phoenix, AZ, USA: Association for Computing Machinery. pp. 753–781. doi:10.1145/3328526.3329552. ISBN 978-1-4503-6792-9. S2CID 7436482.
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