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A unified approach to measuring unequal representation

Author

Listed:
  • Junichiro Wada

    (Yokohama City University)

  • Yuta Kamahara

    (Yokohama National University)

Abstract

The concept of unequal representation is commonly understood through the lenses of disproportionality and malapportionment, pertaining to inter-party and inter-district aspects, respectively. Popular indices used to measure such features are analyzed separately despite being mathematically identical. District-level wasted votes are not measured in terms of unequal representation, even though they can be conceptualized as intra-district unequal representation. A new component, intra-party unequal representation, which measures unequal representation across districts for voters who support each party, has not been considered to contribute to unequal representation. We propose a unified approach for measuring these components—disproportionality, malapportionment, wasted votes, and intra-party unequal representation—by using $${\alpha }$$ α -divergence. We show mathematically that the total of disproportionality and intra-party unequal representation equals that of malapportionment and wasted votes. We apply this approach to the Japanese political system and demonstrate the role of intra-party unequal representation in sustaining disproportionality in favor of the Liberal Democratic Party.

Suggested Citation

  • Junichiro Wada & Yuta Kamahara, 2024. "A unified approach to measuring unequal representation," Public Choice, Springer, vol. 201(1), pages 287-308, October.
    • Handle: RePEc:kap:pubcho:v:201:y:2024:i:1:d:10.1007_s11127-024-01159-z
    DOI: 10.1007/s11127-024-01159-z
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