给定公投结果的公投悖论的可能性

P. Blavatskyy
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引用次数: 0

摘要

当大多数地区的大多数选民支持某一议题/候选人,但所有地区的大多数选民反对同一议题/候选人(反之亦然)时,就会出现公投(或复合多数)悖论。我们计算任何(可能很大的)奇数选区和每个选区任何(可能很大的)奇数选民的这种社会选择异常的可能性。当问题/候选人分裂时,悖论的可能性接近50%(所有选区的选民几乎是50%-50%)。当某个议题/候选人得到至少三分之二选民的支持/反对时,这个悖论实际上就消失了。
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The Likelihood of the Referendum Paradox for a Given Referendum Result
The referendum (or compound majority) paradox occurs when the majority of voters in the majority of districts supports an issue/candidate but the majority of voters across all districts opposes the same issue/candidate (or vice versa). We calculate the likelihood of this social choice anomaly for any (possibly large) odd number of districts and any (possibly large) odd number of voters per district. The likelihood of the paradox is close to 50% when the issue/candidate is divisive (voters across all districts are split almost 50%-50%). The paradox virtually disappears when the issue/candidate is supported/opposed by at least two-thirds of all voters.
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