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<p>In multi-winner elections, the goal is to select a pre-given size committee of members from a given set of candidates. We define the concept of T-power of a majority-group of voters (Total majority-power or Total tyranny-power) as the ability of the group to guarantee, under a given voting rule, that all the committee members belong to its favorite candidates, regardless of the preferences of the other voters. In this case, we say also that such a voting rule is exposed to T-power. This situation can be considered extreme and worrying in democracy. In this paper, we examine the T-power under classes of multi-winner scoring rules. We focus on some common rules, and it turns out that BLOC rule (<i>k</i>-<i>k</i>-Approval) is totally exposed to T-power, that is, any majority-group of any size has T-power under this rule. On the other hand, CCR, <i>k</i>-Plurality and <i>k</i>-Inverse-Plurality rules are almost notexposed to it, that is, no majority of any size has T-power. These last rules may providesome protection for minoritygroups in the sense of preventing T-power.</p>

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The T-power of a majority under multi-winner scoring rules

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月26日

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  • Muhammad Mahajne

摘要

In multi-winner elections, the goal is to select a pre-given size committee of members from a given set of candidates. We define the concept of T-power of a majority-group of voters (Total majority-power or Total tyranny-power) as the ability of the group to guarantee, under a given voting rule, that all the committee members belong to its favorite candidates, regardless of the preferences of the other voters. In this case, we say also that such a voting rule is exposed to T-power. This situation can be considered extreme and worrying in democracy. In this paper, we examine the T-power under classes of multi-winner scoring rules. We focus on some common rules, and it turns out that BLOC rule (k-k-Approval) is totally exposed to T-power, that is, any majority-group of any size has T-power under this rule. On the other hand, CCR, k-Plurality and k-Inverse-Plurality rules are almost notexposed to it, that is, no majority of any size has T-power. These last rules may providesome protection for minoritygroups in the sense of preventing T-power.