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Wie man einen Sieger wählt: die Mathematik der Sozialwahl

Schnappschüsse moderner Mathematik aus Oberwolfach

Wie man einen Sieger wählt: die Mathematik der Sozialwahl

Angenommen, eine Gruppe von Einzelpersonen möch- te unter verschiedenen Optionen wählen, zum Bei- spiel einen von mehreren Kandidaten für ein poli- tisches Amt oder den besten Teilnehmer einer Eis- kunstlaufmeisterschaft. Man könnte fragen: Was ist die beste Methode, einen Sieger in dem Sinne zu wäh- len, dass er die individuellen Präferenzen der Grup- penmitglieder am besten widerspiegelt? Wir werden anhand einiger Beispiele sehen, dass viele Wahlver- fahren, die weltweit in Gebrauch sind, zu Paradoxa und nachgerade schlechten Ergebnissen führen kön- nen, und wir werden uns ein mathematisches Modell von Gruppenentscheidungen ansehen. Wir diskutie- ren das Unmöglichkeitstheorem von Arrow, das Fol- gendes besagt: Hat man mehr als zwei Wahlmöglich- keiten, dann gibt es in einem ganz exakten Sinn keine gute Methode für die Wahl eines Siegers. 

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Mathematisches Fachgebiet

Diskrete Mathematik und Grundlagen

Verbindung zu anderen Gebieten

Geistes- und Sozialwissenschaft

Autor(en)

Victoria Powers

Lizenz

DOI (Digital Object Identifier)

10.14760/SNAP-2015-009-EN

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2015-009-powers-de.pdf

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