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The 2021 mayoral primary in New York City was done using Instant Runoff Voting ("Ranked Choice Voting"). This system does not necessarily elect the Condorcet winner, if one exists. (The candidate who would beat every other candidate in a head-to-head election.)

(For example, in the 2009 Burlington mayoral election, 54% of voters preferred Montroll over Kiss, but Kiss was selected as the winner by IRV.)

Is there a Condorcet winner, and is it the same as the IRV winner (Eric Adams)? Is it even possible to determine this from the ballot data that was collected/released by the city?

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The New York City Board of Elections released the cast vote record (CVR) on August 18th. There's no metadata or readme accompanying it, but Alec Barrett has published an 'unofficial' readme on GitHub.

I've written a quick 'n' dirty script to extract just the votes cast in the Democratic Mayoral race, and to evaluate each candidate against the other (excluding write-ins). The table below shows the results of each match-up. In a given cell, the first number is the number of ballots that favour the candidate on the x-axis, and the second number is the number of ballots that favour the candidate on the y-axis.

From this, we can see that Eric L. Adams is the Condorcet winner, as he beats every candidate in a head-to-head matchup. The closest matchup is against Kathryn A. Garcia, with 405,363 ballots favouring Adams compared to 398,167 favouring Garcia.

In graphical form - a green cell indicates that the candidate on the x-axis was successful in a head-to-head matchup against the candidate on the y-axis, while a red cell indicates the opposite. For example, Andrew Yang was successful against all candidates except Adams, Garcia & Wiley in a head-to-head matchup.

enter image description here

Eric L. Adams Paperboy Love Prince Aaron S. Foldenauer Shaun Donovan Kathryn A. Garcia Scott M. Stringer Art Chang Raymond J. McGuire Isaac Wright Jr. Andrew Yang Joycelyn Taylor Maya D. Wiley Dianne Morales
Eric L. Adams [532840, 532840] [51780, 529435] [24033, 528893] [174378, 494035] [398167, 405263] [239637, 474988] [70134, 524794] [112093, 495464] [15199, 530191] [250251, 448500] [40454, 528354] [358247, 435707] [179890, 505742]
Paperboy Love Prince [529435, 51780] [66403, 66403] [35261, 64526] [293418, 57228] [522302, 37141] [365513, 48342] [81333, 56663] [237541, 59400] [35761, 64469] [407980, 51687] [72932, 61512] [499997, 21913] [240488, 41643]
Aaron S. Foldenauer [528893, 24033] [64526, 35261] [36581, 36581] [294205, 30231] [525756, 26387] [366436, 28358] [83772, 32560] [235272, 31872] [35608, 35027] [408962, 24248] [74118, 33702] [500867, 28182] [243242, 30252]
Shaun Donovan [494035, 174378] [57228, 293418] [30231, 294205] [297535, 297535] [485249, 146148] [310147, 209661] [76511, 286303] [191316, 244350] [31975, 293442] [354237, 231367] [63918, 291953] [458666, 169184] [216645, 261414]
Kathryn A. Garcia [405263, 398167] [37141, 522302] [26387, 525756] [146148, 485249] [530328, 530328] [205071, 454095] [58340, 514908] [140077, 490231] [28585, 527334] [263503, 428842] [49687, 522363] [365689, 357291] [151751, 471723]
Scott M. Stringer [474988, 239637] [48342, 365513] [28358, 366436] [209661, 310147] [454095, 205071] [372027, 372027] [70080, 358752] [190255, 327905] [30193, 368616] [341909, 286709] [63417, 365722] [437154, 217856] [194830, 325147]
Art Chang [524794, 70134] [56663, 81333] [32560, 83772] [286303, 76511] [514908, 58340] [358752, 70080] [86826, 86826] [234953, 80534] [35133, 85588] [401747, 59565] [68107, 82333] [495929, 42678] [233828, 64538]
Raymond J. McGuire [495464, 112093] [59400, 237541] [31872, 235272] [244350, 191316] [490231, 140077] [327905, 190255] [80534, 234953] [239912, 239912] [29426, 236367] [364787, 174129] [66461, 234741] [467518, 165056] [228045, 219993]
Isaac Wright Jr. [530191, 15199] [64469, 35761] [35027, 35608] [293442, 31975] [527334, 28585] [368616, 30193] [85588, 35133] [236367, 29426] [37645, 37645] [408251, 28435] [72131, 33146] [501460, 20118] [244734, 30028]
Andrew Yang [448500, 250251] [51687, 407980] [24248, 408962] [231367, 354237] [428842, 263503] [286709, 341909] [59565, 401747] [174129, 364787] [28435, 408251] [413044, 413044] [54901, 407198] [437314, 296247] [200077, 378839]
Joycelyn Taylor [528354, 40454] [61512, 72932] [33702, 74118] [291953, 63918] [522363, 49687] [365722, 63417] [82333, 68107] [234741, 66461] [33146, 72131] [407198, 54901] [77439, 77439] [497995, 35799] [238098, 49948]
Maya D. Wiley [435707, 358247] [21913, 499997] [28182, 500867] [169184, 458666] [357291, 365689] [217856, 437154] [42678, 495929] [165056, 467518] [20118, 501460] [296247, 437314] [35799, 497995] [505416, 505416] [94866, 470986]
Dianne Morales [505742, 179890] [41643, 240488] [30252, 243242] [261414, 216645] [471723, 151751] [325147, 194830] [64538, 233828] [219993, 228045] [30028, 244734] [378839, 200077] [49948, 238098] [470986, 94866] [248670, 248670]
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    Notably, Maya Wiley would have defeated Kathryn Garcia in a head-to-head election, 365,689 to 357,291. This is despite the fact that Wiley was eliminated in round 7, before Garcia, with Wiley having 254,728 votes to Garcia's 266,932 (Eric Adams had 354,657 votes in round 7). This would mean that voters who ranked Adams highest of the three preferred Wiley to Garcia, 110,961 to 90,359 (with the remainder not ranking either Wiley or Garcia). [I got the round 7 numbers from the vote.nyc recap, I haven't confirmed if they match the CVR]
    – DanTilkin
    Commented Aug 20, 2021 at 21:52
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  1. A Condorcet winner is not guaranteed to exist since preferences might be cyclical (e.g., A > B, B > C, C > A).
  2. To find the Condorcet winner, you would need to observe the individual ballots. You require the individual ballots because you need to estimate how often candidate A is preferred to candidate B. The first choice, second choice, etc. aggregate numbers hint at what might happen, but they are consistent with a large number of individual preferences. Individual ballots are rarely posted. It's unlikely that NYC will release them for some time, if ever. However, if someone finds them, then I will be happy to update this post with an analysis.
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    Yeah I would also accept an answer that described the real-world counting procedure and showed that it is impossible to know who the Condorcet winner is because those votes are never actually counted by the system. (Though one answer says "They'll eventually release the full cast vote record as well")
    – endolith
    Commented Jul 9, 2021 at 21:14
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    It turns out that the individual ballot data has been released (see @CDJB's answer and analysis).
    – Don Hosek
    Commented Aug 19, 2021 at 16:39

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