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    "title": "BV2274 — The cost of districting — the best candidate wins no district at all",
    "description": "Two chapters of one club elect a single national delegate, and the same nine members are counted three ways. Ana is adored in Northside and unknown in Southside; Beto is the exact mirror image; Cleo is everybody's solid second choice. Race 1 counts Northside's five members and elects Ana. Race 2 counts Southside's four and elects Beto. Race 3 counts all nine together and elects CLEO — who won neither chapter. Nothing about anyone's ballot changed between the races. Only the map did. Ana's 23 points are concentrated in one chapter and Beto's 19 in the other, while Cleo's 33 are spread evenly across both, so a chapter-by-chapter count reads concentration and a combined count reads the total. Cleo also beats both rivals head-to-head, so she is the Condorcet winner as well as the points leader: both notions of 'best' agree, and the district map overrides both. This is the distortion of DISTRIBUTED voting, made countable. Computational social choice proves that splitting an electorate into k districts and then choosing among the district winners multiplies the worst-case welfare loss by k — and that the loss survives even when every district counts perfect utilities. Here at k=2 you can check it by hand: every chapter ran a full 0-5 score count and still discarded the best candidate, so no ballot reform touches this. What costs the club is the requirement that the delegate be somebody's chapter winner. Picking Ana costs 30% of the available satisfaction; picking Beto costs 42%. In the two chapter races every member of the OTHER chapter leaves the contest blank, which is how a real districted election works — you get one ballot paper and vote only your own district's contest. A blank adds zero to every total, so the counts match the 5- and 4-member tallies exactly. Read it fairly: this is a constructed example showing the mechanism, not a claim about how often real district maps do this. Published experiments on real-world data find the effect far milder than the worst-case bound, because real electorates are homogeneous. The library's other districting case (Exercise 1, two districts and one mayor) is the honest twin, where districting costs nothing at all and the combined count is the one that gives ground. Full lesson & tabulation: https://masiarek.github.io/star-voting-library/07_Concepts/topics/distributed_voting_distortion.html",
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    "create_date": "2026-08-06T02:29:35.504Z",
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