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A Majoritarian Representative Voting System (1611.10154v1)

Published 30 Nov 2016 in cs.GT, cs.MA, and math.CO

Abstract: We present an alternative voting system that aims at bridging the gap between proportional representative systems and majoritarian, single winner election systems. The system lets people vote for multiple parties, but then assigns each ballot to a single party. This opens a whole range of possible systems, all representative. We show theoretically that this space is convex. Then among the possible parliaments we present an algorithm to produce the most majoritarian result. We then test the system and compare the results with a pure proportional and a majoritarian voting system showing how the results are comparable with the majoritarian system. Then we simulate the system and show how it tends to produce parties of exponentially decreasing size with always a first, major party. Finally we describe how the system can be used in a context of a parliament made up of two separate houses.

Summary

  • The paper proposes a novel voting system that balances representativity and governability by converting vote allocation into a convex optimization problem.
  • It establishes a theoretical framework demonstrating that the space of valid parliaments forms a convex subset where voter intentions align with party power distribution.
  • Empirical simulations with 5000 voters reveal an exponential decline in party sizes, resulting in a dominant leading party while mitigating clone candidate effects.

A Majoritarian Representative Voting System

The paper "A Majoritarian Representative Voting System" by Pietro Speroni di Fenizio and Daniele A. Gewurz introduces an innovative voting schema aiming to resolve the traditional tension between representativity and governability in electoral systems. It proposes a system that reconciles the proportional representation of diverse preferences with the concentration of power necessary for effective governance.

Overview of the Voting System

The proposed system enables voters to express support for multiple parties without ranking them, assigning each ballot to a single party based on predefined rules rather than voter intention. This mechanism transforms the vote allocation process into a convex space of potential representative parliaments. Among these, the authors present an algorithm designed to yield outcomes resembling majoritarian systems in terms of dominant party size, yet maintain representativity akin to proportional representation.

Theoretical Framework

The authors substantiate the convex nature of the solution space for representative parliaments, demonstrating that this space is a subset of the simplex of all possible parliaments. Each point within the space corresponds to a parliament where voter intention is honored within the constraints of a representative democracy. Consequently, the proposed system allows for different parliaments to exist simultaneously as valid solutions.

Simulation and Practical Application

The paper details simulations conducted with 5000 voters and 20 parties, revealing that party sizes decrease exponentially and consistently form a dominant leading party. Additionally, empirical testing with university students mirrored the simulation results, with outcomes showing substantial alignment with the outcomes derived from Italy's Italicum electoral system, despite a fundamentally different theoretical basis. Observations also indicated that typical pitfalls of clone candidates are mitigated as the system tends to consolidate similar party support into stronger singular representations.

Implications and Future Prospects

This framework offers substantial practical implications, potentially reshaping how electoral systems may be designed to balance governability and representativity. By avoiding the traditional trade-offs, this approach enables the formation of stable governments while ensuring that the composition of the parliament reflects the nuances of voter preferences.

The paper also opens avenues for further research, particularly in examining voter behavior under this system and assessing the dynamic interplay between electoral rules and party strategy. The resilience of the model in diverse electoral contexts and its adaptability to different political landscapes warrant further exploration.

Conclusion

The system detailed in the paper presents a compelling alternative to existing electoral frameworks, bridging a significant gap in the electoral design space. The authors provide a robust theoretical and empirical foundation for their claims, while cautiously identifying the potential for expansion and refinement of the voting model. This research contributes to an evolving dialogue on how democratic institutions can evolve to better suit the complexities of modern political representation.

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