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A Mathematical Analysis of an Election System Proposed by Gottlob Frege
Paul Harrenstein1,2, Marie-Louise Lackner3, Martin Lackner4
1Department of Computer Science, University of Oxford, Wolfson Building, 15 Parks Road, Oxford, OX1 3QD UK.
Erkenntnis
|November 18, 2022
Summary
Rediscovered election law by Gottlob Frege ensures proportional representation by carrying over votes for unelected candidates. A modified method strengthens minority representation and offers a novel solution to the apportionment problem.
Area of Science:
- * Political Science
- * Mathematics
- * Law
Background:
- * Gottlob Frege's lost election law proposal (1848-1925) was rediscovered in 1998.
- * Frege's method prioritizes minority representation in elections.
- * The core mechanism involves carrying over votes for unelected candidates and applying a 'cost of winning' for elected ones.
Purpose of the Study:
- * To analyze the long-term proportionality guarantees of Frege's election law.
- * To investigate potential improvements through modifications to Frege's original method.
- * To explore the application of a modified Frege method to the apportionment problem.
Main Methods:
- * Mathematical proof to demonstrate long-term proportionality.
- * Analysis of vote-carrying-over mechanisms.
- * Development and evaluation of a modified Frege method.
Main Results:
- * Frege's method guarantees proportional representation of political opinions in the long run.
- * A slight modification enhances proportionality guarantees.
- * The modified method presents a novel solution to the apportionment problem, distinct from existing methods.
Conclusions:
- * Frege's rediscovered election law offers significant benefits for proportional representation and minority rights.
- * Modifications can further optimize the method's fairness.
- * The approach provides a new perspective on solving the apportionment problem with strong proportionality properties.
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