Optimal apportionment (original) (raw)
Optimal apportionment is an approach to apportionment that is based on mathematical optimization. In a problem of apportionment, there is a resource to allocate, denoted by . For example, it can be an integer representing the number of seats in a house of representatives. The resource should be allocated between some agents. For example, these can be federal states or political parties. The agents have different entitlements, denoted by a vector of fractions with a sum of 1. For example, ti can be the fraction of votes won by party i. The goal is to find allocation - a vector with .
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| dbo:abstract | Optimal apportionment is an approach to apportionment that is based on mathematical optimization. In a problem of apportionment, there is a resource to allocate, denoted by . For example, it can be an integer representing the number of seats in a house of representatives. The resource should be allocated between some agents. For example, these can be federal states or political parties. The agents have different entitlements, denoted by a vector of fractions with a sum of 1. For example, ti can be the fraction of votes won by party i. The goal is to find allocation - a vector with . The ideal share for agent i is his/her quota, defined as . If it is possible to give each agent his/her quota, then the allocation is maximally fair. However, exact fairness is usually unattainable, since the quotas are not integers and the allocations must be integers. There are various approaches to cope with this difficulty (see mathematics of apportionment). The optimization-based approach aims to attain, for eacn instance, an allocation that is "as fair as possible" for this instance. An allocation is "fair" if for all agents i, that is, each agent's allocation is exactly proportional to his/her entitlement. in this case, we say that the "unfairness" of the allocation is 0. If this equality must be violated, one can define a measure of "total unfairness", and try to minimize it. (en) |
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| dbo:wikiPageWikiLink | dbc:Apportionment_(politics) dbr:Venice_Commission dbr:Leximin_order dbr:Mathematical_optimization dbr:Quota_rule dbr:Mathematics_of_apportionment dbc:Social_choice_theory dbc:Apportionment_method_criteria dbc:Mathematical_optimization dbc:Fairness_criteria dbr:Egalitarian_rule dbr:Webster/Sainte-Laguë_method dbr:Political_party dbr:Utilitarian_rule dbr:Federal_states dbr:Hamilton's_method dbr:Hill's_method |
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| dct:subject | dbc:Apportionment_(politics) dbc:Social_choice_theory dbc:Apportionment_method_criteria dbc:Mathematical_optimization dbc:Fairness_criteria |
| rdfs:comment | Optimal apportionment is an approach to apportionment that is based on mathematical optimization. In a problem of apportionment, there is a resource to allocate, denoted by . For example, it can be an integer representing the number of seats in a house of representatives. The resource should be allocated between some agents. For example, these can be federal states or political parties. The agents have different entitlements, denoted by a vector of fractions with a sum of 1. For example, ti can be the fraction of votes won by party i. The goal is to find allocation - a vector with . (en) |
| rdfs:label | Optimal apportionment (en) |
| owl:sameAs | wikidata:Optimal apportionment https://global.dbpedia.org/id/G5ETv |
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