[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"branding":3,"analytics":7,"article-new-metric-measures-the-cost-of-paradox-proof-voting-rules":10,"sections":35},{"siteName":4,"siteTagline":5,"publisherName":4,"contactEmail":6},"The Revision","Tech news, decoded.","editor@therevision.news",{"gaMeasurementId":8,"adsenseClientId":9},"G-ZW2MV82GYR","ca-pub-8533917693782264",{"article":11},{"id":12,"slug":13,"title":14,"dek":15,"body_md":16,"tags_json":17,"published_at":18,"created_at":19,"updated_at":20,"status":21,"review_note":22,"review_notes":23,"image_url":22,"persona_id":22,"persona_name":22,"section":24,"tags":25,"sources":30,"feedback":34,"feedback_at":22,"cost_usd":34,"total_tokens":34},9663,"new-metric-measures-the-cost-of-paradox-proof-voting-rules","New Metric Measures the Cost of Paradox-Proof Voting Rules","A new study quantifies how many preference swaps separate an average voter's true ranking from the closest ballot a paradox-proof election system would allow.","A new paper puts a number on the tradeoff between flexible ballots and paradox-free elections.\n\nIn ranked-choice voting, a 'Condorcet paradox' happens when majority preferences form a loop: A beats B, B beats C, but C beats A. Condorcet domains are restricted sets of allowed rankings that guarantee this never happens, no matter how the votes combine. The catch is that restricting rankings also limits how well a ballot can reflect what a voter actually wants. The researchers introduce 'outer diversity,' a measure of how many preference swaps separate a random, unrestricted ranking from the closest ranking the domain actually allows. They crunch the numbers for domains with a handful of candidates, then work out the asymptotic math for several specific domain types.\n\nThe payoff is a concrete way to compare paradox-proof voting schemes instead of just arguing about them in the abstract. Election design has always traded completeness for consistency, and this gives that tradeoff an actual ruler instead of a hunch.\n\nIt will not change how any election runs tomorrow. But if ranked-choice systems keep spreading past city council races, having a precise measure of how much they bend voter intent to stay logically consistent is worth banking now.","[\"voting-theory\",\"social-choice\",\"ranked-choice-voting\",\"mathematics\"]","2026-10-02T04:00:00.000Z","2026-10-03T05:10:41.620Z","2026-10-03T05:10:47.914Z","published",null,[],"science",[26,27,28,29],"voting-theory","social-choice","ranked-choice-voting","mathematics",[31],{"name":32,"url":33},"arXiv cs.AI","https:\u002F\u002Farxiv.org\u002Fabs\u002F2610.00720",0,{"sections":36},[37,41,45,49,54,58,61,66,71,76,81,86,91,96],{"name":38,"slug":39,"count":40,"latest_published_at":18},"AI","ai",5978,{"name":42,"slug":43,"count":44,"latest_published_at":18},"Security","security",842,{"name":46,"slug":47,"count":48,"latest_published_at":18},"Policy","policy",438,{"name":50,"slug":51,"count":52,"latest_published_at":53},"Deals","deals",317,"2026-10-01T22:00:00.000Z",{"name":55,"slug":56,"count":57,"latest_published_at":18},"Hardware","hardware",199,{"name":59,"slug":24,"count":60,"latest_published_at":18},"Science",173,{"name":62,"slug":63,"count":64,"latest_published_at":65},"Consumer Tech","consumer-tech",155,"2026-10-01T19:54:10.000Z",{"name":67,"slug":68,"count":69,"latest_published_at":70},"Dev Tools","dev-tools",96,"2026-10-01T16:57:03.000Z",{"name":72,"slug":73,"count":74,"latest_published_at":75},"Software","software",93,"2026-09-30T21:41:11.000Z",{"name":77,"slug":78,"count":79,"latest_published_at":80},"Startups","startups",90,"2026-10-01T21:55:22.000Z",{"name":82,"slug":83,"count":84,"latest_published_at":85},"Gaming","gaming",53,"2026-10-02T02:50:39.000Z",{"name":87,"slug":88,"count":89,"latest_published_at":90},"General","general",50,"2026-09-30T21:37:54.000Z",{"name":92,"slug":93,"count":94,"latest_published_at":95},"Reviews","reviews",31,"2026-09-28T14:31:34.000Z",{"name":97,"slug":98,"count":99,"latest_published_at":100},"How-To","how-to",7,"2026-10-01T09:00:00.000Z"]