Generalizing Instant Runoff Voting to Allow Voter Indifferences

Concetti Chiave

Approval-IRV, a generalization of Instant Runoff Voting (IRV) that allows voters to express indifferences between candidates, is the unique elimination scoring rule that satisfies independence of clones and respects cohesive majorities.

Sintesi

The content discusses a generalization of Instant Runoff Voting (IRV), called Approval-IRV, that allows voters to express indifferences between candidates by using weak orders instead of strict rankings.
The key highlights and insights are:

Approval-IRV interprets each weak order vote as an approval vote for the top-ranked candidates that have not yet been eliminated. It then repeatedly eliminates the candidate with the lowest approval score until only one candidate remains.

Approval-IRV satisfies two key properties that are characteristic of standard IRV for linear orders: independence of clones and respect for cohesive majorities. These axioms ensure that the rule is resistant to the spoiler effect and respects the preferences of majorities.

The authors prove that Approval-IRV is the unique elimination scoring rule that satisfies these two axioms. In contrast, the alternative generalization called Split-IRV fails both axioms.

For multi-winner elections, the authors define Approval-STV and show that it preserves the strong proportional representation properties of standard STV.

Experiments suggest that a non-negligible fraction of voters (around 0.4% in the 2019 San Francisco mayoral election) would benefit from the ability to express indifferences using Approval-IRV.

Overall, the content argues that Approval-IRV is a principled and desirable generalization of IRV that allows voters more expressive power without sacrificing key properties of the original rule.

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Approfondimenti chiave tratti da

Generalizing Instant Runoff Voting to Allow Indifferences

by Théo... alle arxiv.org 04-18-2024

https://arxiv.org/pdf/2404.11407.pdf

Domande più approfondite

How would the adoption of Approval-IRV impact election outcomes and voter behavior compared to standard IRV or other voting systems in practice

The adoption of Approval-IRV would likely have significant impacts on election outcomes and voter behavior compared to standard IRV or other voting systems. Approval-IRV allows voters to express indifferences by giving equal preference to multiple candidates, providing more flexibility and accuracy in reflecting voter preferences. This can lead to more nuanced and representative election results, as voters can support all candidates they approve of without worrying about strategic ranking.
In practice, Approval-IRV could lead to a reduction in the number of invalid ballots, as voters can easily indicate their approval for multiple candidates without the need to rank them all. This can increase voter participation and engagement, as the voting process becomes more straightforward and less burdensome. Additionally, Approval-IRV may reduce the likelihood of strategic voting, as voters can express their true preferences without fear of wasting their vote or inadvertently supporting a less preferred candidate.
Furthermore, the adoption of Approval-IRV could promote more diverse and inclusive election outcomes by allowing voters to support a wider range of candidates. This can lead to a more accurate representation of the electorate's preferences and potentially result in the election of candidates who better reflect the diversity of the population.

What are potential drawbacks or unintended consequences of allowing voters to express indifferences in an IRV election that the authors do not discuss

While the authors discuss the advantages of allowing voters to express indifferences in an IRV election, there are potential drawbacks and unintended consequences that should be considered. One possible drawback is the increased complexity of ballot design and voter instructions. Allowing voters to give equal preference to multiple candidates may require clearer guidelines and explanations to ensure that voters understand how to properly fill out their ballots. This could lead to confusion or errors in voting, potentially resulting in an increase in spoiled or invalid ballots.
Another unintended consequence could be the potential for manipulation or gaming of the system. Allowing voters to express indifferences opens up the possibility for strategic voting tactics, where voters strategically rank candidates to influence the outcome in their favor. This could undermine the integrity of the election process and lead to outcomes that do not accurately reflect the true preferences of the electorate.
Additionally, the introduction of indifferences in an IRV election could complicate the counting and tabulation process. Handling weak orders with indifferences may require more sophisticated algorithms and systems to accurately determine the winner, potentially increasing the complexity and cost of conducting elections.

What other voting rules or extensions beyond IRV could benefit from allowing voters to express indifferences, and how would the analysis and properties differ from the Approval-IRV case

Other voting rules or extensions beyond IRV that could benefit from allowing voters to express indifferences include Single Transferable Vote (STV) and Borda Count. In the case of STV, allowing voters to give equal preference to multiple candidates can enhance the proportional representation aspect of the voting system. By accommodating indifferences, STV can better capture the nuanced preferences of voters in multi-winner elections, leading to fairer and more representative outcomes.
Similarly, in the context of Borda Count, incorporating indifferences can provide voters with a more expressive way to rank candidates. By allowing voters to assign equal ranks to multiple candidates, the Borda Count method can better reflect the intensity of voter preferences and potentially mitigate the impact of strategic manipulation.
The analysis and properties of these voting rules with indifferences would differ from the Approval-IRV case in terms of the specific axioms and criteria used to evaluate the fairness and effectiveness of the voting system. Each voting rule may have unique characteristics and considerations when allowing voters to express indifferences, requiring a tailored analysis to assess their impact on election outcomes and voter behavior.