Abstract
In Italy, the referendum represents the main form of direct democracy. At the national level, there exist 2 main forms of referendum: an abrogative referendum, in which the electorate is called to vote on whether they wish to abolish an existing law, and a constitutional referendum, which can be requested in some cases when a new constitutional law is approved by the Parliament. In the first case, the referendum has to meet a certain turnout requirement in order to be valid, namely, a participation quorum threshold has to be reached. The rationale for such a requirement is that, to change the status quo, a large proportion of citizens should care about the issue at stake and take part in the decision. In our work, we provide a game theoretic analysis of a voting rule with a participation quorum threshold. In particular, we focus on a binary dichotomous voting rule, in which the choices are vote “yes” and vote “no”, on a 3-option dichotomous voting rule, in which there is the additional choice to “stay at home”, and on a quaternary dichotomous voting rule, in which it is also possible to “abstain”. The possible outcomes are two, namely “approval” and “rejection”. We provide a graphical representation of these aforementioned voting rules, which allows for an easier analysis of these well-known voting scenarios, in particular focusing on the case of the Italian referendum. We analyze how the decisiveness (as a measure of agility), the blocking power (as a measure of inertia) of such voting situations, both at a collective and at an individual level, and the configurations in which a voter can become a swing voter are strongly impacted by the quorum threshold.
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Notes
The referendums are usually used for deciding about the independence or the institutional status of a country. A well-known referendum involved in 2016 the citizens of the United Kingdom about the European Union membership. In Switzerland, the referendum is very popular and it is frequently used for very different subjects.
There exists also the propositional referendum for proposing a new law, but it can be used only at local level, e.g. in a region or in a province.
We adopt the same notation of Laruelle and Valenciano (2012), in which the set \(S^H\) was defined as the set of voters who “stayed at home”, from which the H superscript.
In Laruelle and Valenciano (2012), a weak null-support condition is required to include more real-world voting rules in the model. However, for our analysis, such a strong null-support condition is well-representative of our examples.
Observe that these weights are given by the corresponding binomial coefficient of a Pascal’s triangle.
Trivially, this happens each time a change in the structure of a strategic game is implemented, with a consequent change of the optimal strategy for the players.
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Acknowledgements
The authors gratefully acknowledge two anonymous reviewers for their useful comments and suggestions that allowed to improve the paper. The authors want to thank Guido Ortona for some discussions on the referendum rules.
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Appendix A: Abrogative referendums
Appendix A: Abrogative referendums
See Table 2.
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Chessa, M., Fragnelli, V. The Italian referendum: what can we get from game theory?. Ann Oper Res 318, 849–869 (2022). https://doi.org/10.1007/s10479-022-04927-6
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DOI: https://doi.org/10.1007/s10479-022-04927-6