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A B RIEF H ISTORY OF S OCIAL C HOICE Jos Rui Figueira A BRIEF HISTORY OF SOCIAL CHOICE 1. Introduction 2. Pioneers 2.1. J. Charles Jos Rui F IGUEIRA ( figueira@ist.utl.pt ) 1 2.2. M.J. de Caritat 3. But... 3.1. S. L

  1. 2. The “Pioneers” 2.1. Jean-Charles, chevalier de Borda (1733 - 1799) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Major publications-manuscripts Figueira 1. Introduction 1 Borda, Jean-Charles de (1784). “Mémoire sur les 2. “Pioneers” Élections au Scrutin”, Histoire de l’Académie Royale 2.1. J. Charles 2.2. M.J. de Caritat des Sciences. Année M. DCCLXXXI. 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 2 Avec les Mémoires de Mathématique et de Physique, 3.3. P . Daunou 4. The 19th pour la même Année. Paris 1784. Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  2. 2. The “Pioneers” 2.1. Jean-Charles, chevalier de Borda (1733 - 1799) A B RIEF New concepts: The Borda Count H ISTORY OF S OCIAL C HOICE 1 Criticized the Condorcet method: not workable in José Rui Figueira practice and no winner might occur. 1. Introduction 2 Proposed a new method: ranking candidates by giving 2. “Pioneers” 2.1. J. Charles each the points corresponding to their ranks. The 2.2. M.J. de Caritat voters give the candidate they favored least one point, 3. “But...” 3.1. S. L ’Huilier the next candidate two points, and so on. The winner is 3.2. J. Rodríguez 3.3. P . Daunou the candidate who got more points, after making the 4. The 19th summation of the points attributed to each candidate by Century 4.1. C.L. Dodgson each voter. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 3 Scoring technique: also used in multiple criteria 5.2. R. Llull 5.1. G.P . Secundus decision analysis. 6. Conclusions

  3. 2. The “Pioneers” 2.1. Jean-Charles, chevalier de Borda (1733 - 1799) A B RIEF New concepts: The Borda Count H ISTORY OF S OCIAL C HOICE 1 Criticized the Condorcet method: not workable in José Rui Figueira practice and no winner might occur. 1. Introduction 2 Proposed a new method: ranking candidates by giving 2. “Pioneers” 2.1. J. Charles each the points corresponding to their ranks. The 2.2. M.J. de Caritat voters give the candidate they favored least one point, 3. “But...” 3.1. S. L ’Huilier the next candidate two points, and so on. The winner is 3.2. J. Rodríguez 3.3. P . Daunou the candidate who got more points, after making the 4. The 19th summation of the points attributed to each candidate by Century 4.1. C.L. Dodgson each voter. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 3 Scoring technique: also used in multiple criteria 5.2. R. Llull 5.1. G.P . Secundus decision analysis. 6. Conclusions

  4. 2. The “Pioneers” 2.1. Jean-Charles, chevalier de Borda (1733 - 1799) A B RIEF New concepts: The Borda Count H ISTORY OF S OCIAL C HOICE 1 Criticized the Condorcet method: not workable in José Rui Figueira practice and no winner might occur. 1. Introduction 2 Proposed a new method: ranking candidates by giving 2. “Pioneers” 2.1. J. Charles each the points corresponding to their ranks. The 2.2. M.J. de Caritat voters give the candidate they favored least one point, 3. “But...” 3.1. S. L ’Huilier the next candidate two points, and so on. The winner is 3.2. J. Rodríguez 3.3. P . Daunou the candidate who got more points, after making the 4. The 19th summation of the points attributed to each candidate by Century 4.1. C.L. Dodgson each voter. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 3 Scoring technique: also used in multiple criteria 5.2. R. Llull 5.1. G.P . Secundus decision analysis. 6. Conclusions

  5. 2. The “Pioneers” 2.1. Jean-Charles, chevalier de Borda (1733 - 1799) A B RIEF New concepts: The Borda Count H ISTORY OF S OCIAL C HOICE 1 Criticized the Condorcet method: not workable in José Rui Figueira practice and no winner might occur. 1. Introduction 2 Proposed a new method: ranking candidates by giving 2. “Pioneers” 2.1. J. Charles each the points corresponding to their ranks. The 2.2. M.J. de Caritat voters give the candidate they favored least one point, 3. “But...” 3.1. S. L ’Huilier the next candidate two points, and so on. The winner is 3.2. J. Rodríguez 3.3. P . Daunou the candidate who got more points, after making the 4. The 19th summation of the points attributed to each candidate by Century 4.1. C.L. Dodgson each voter. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 3 Scoring technique: also used in multiple criteria 5.2. R. Llull 5.1. G.P . Secundus decision analysis. 6. Conclusions

  6. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF S OCIAL Short Biography C HOICE José Rui Figueira 1 Background: French philosopher, mathematician, and political scientist, . . . 1. Introduction 2. “Pioneers” 2.1. J. Charles 2 Living places: Ribemont (born), Bourg-la-Reigne, Paris, 2.2. M.J. de Caritat 3. “But...” . . . 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: Calculus (Integral), Inspector General of 4. The 19th the Mint, Secretary of the Académie des Sciences, Century 4.1. C.L. Dodgson probability and the philosophy of mathematics, 4.2. E.J. Nanson Elections, . . . 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  7. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF S OCIAL Short Biography C HOICE José Rui Figueira 1 Background: French philosopher, mathematician, and political scientist, . . . 1. Introduction 2. “Pioneers” 2.1. J. Charles 2 Living places: Ribemont (born), Bourg-la-Reigne, Paris, 2.2. M.J. de Caritat 3. “But...” . . . 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: Calculus (Integral), Inspector General of 4. The 19th the Mint, Secretary of the Académie des Sciences, Century 4.1. C.L. Dodgson probability and the philosophy of mathematics, 4.2. E.J. Nanson Elections, . . . 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  8. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF S OCIAL Short Biography C HOICE José Rui Figueira 1 Background: French philosopher, mathematician, and political scientist, . . . 1. Introduction 2. “Pioneers” 2.1. J. Charles 2 Living places: Ribemont (born), Bourg-la-Reigne, Paris, 2.2. M.J. de Caritat 3. “But...” . . . 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: Calculus (Integral), Inspector General of 4. The 19th the Mint, Secretary of the Académie des Sciences, Century 4.1. C.L. Dodgson probability and the philosophy of mathematics, 4.2. E.J. Nanson Elections, . . . 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  9. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF S OCIAL Short Biography C HOICE José Rui Figueira 1 Background: French philosopher, mathematician, and political scientist, . . . 1. Introduction 2. “Pioneers” 2.1. J. Charles 2 Living places: Ribemont (born), Bourg-la-Reigne, Paris, 2.2. M.J. de Caritat 3. “But...” . . . 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: Calculus (Integral), Inspector General of 4. The 19th the Mint, Secretary of the Académie des Sciences, Century 4.1. C.L. Dodgson probability and the philosophy of mathematics, 4.2. E.J. Nanson Elections, . . . 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  10. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF Source: commons.wikimedia.org / wiki / File: S OCIAL C HOICE Condorcet − NB.jpg José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  11. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF Major publications-manuscripts S OCIAL C HOICE José Rui 1 Condorcet, M.J.A.N.C. Marquis de, Essai sur Figueira l’Application de l’Analyse a la Probabilité des Décisions 1. Introduction Rendues la Pluralité des Voix. , L ’Imprimerie Royale, 2. “Pioneers” Paris (1785). 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Essai sur la constitution et les fonctions des 3.1. S. L ’Huilier 3.2. J. Rodríguez assemblées provinciales (1788). 3.3. P . Daunou 4. The 19th Century 3 Sur la nécessité d’établir en France une constitution 4.1. C.L. Dodgson 4.2. E.J. Nanson nouvelle (1793). 5. Before?! 5.2. N. von Kues 5.2. R. Llull 4 . . . 5.1. G.P . Secundus 6. Conclusions

  12. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF Major publications-manuscripts S OCIAL C HOICE José Rui 1 Condorcet, M.J.A.N.C. Marquis de, Essai sur Figueira l’Application de l’Analyse a la Probabilité des Décisions 1. Introduction Rendues la Pluralité des Voix. , L ’Imprimerie Royale, 2. “Pioneers” Paris (1785). 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Essai sur la constitution et les fonctions des 3.1. S. L ’Huilier 3.2. J. Rodríguez assemblées provinciales (1788). 3.3. P . Daunou 4. The 19th Century 3 Sur la nécessité d’établir en France une constitution 4.1. C.L. Dodgson 4.2. E.J. Nanson nouvelle (1793). 5. Before?! 5.2. N. von Kues 5.2. R. Llull 4 . . . 5.1. G.P . Secundus 6. Conclusions

  13. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF Major publications-manuscripts S OCIAL C HOICE José Rui 1 Condorcet, M.J.A.N.C. Marquis de, Essai sur Figueira l’Application de l’Analyse a la Probabilité des Décisions 1. Introduction Rendues la Pluralité des Voix. , L ’Imprimerie Royale, 2. “Pioneers” Paris (1785). 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Essai sur la constitution et les fonctions des 3.1. S. L ’Huilier 3.2. J. Rodríguez assemblées provinciales (1788). 3.3. P . Daunou 4. The 19th Century 3 Sur la nécessité d’établir en France une constitution 4.1. C.L. Dodgson 4.2. E.J. Nanson nouvelle (1793). 5. Before?! 5.2. N. von Kues 5.2. R. Llull 4 . . . 5.1. G.P . Secundus 6. Conclusions

  14. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF Major publications-manuscripts S OCIAL C HOICE José Rui 1 Condorcet, M.J.A.N.C. Marquis de, Essai sur Figueira l’Application de l’Analyse a la Probabilité des Décisions 1. Introduction Rendues la Pluralité des Voix. , L ’Imprimerie Royale, 2. “Pioneers” Paris (1785). 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Essai sur la constitution et les fonctions des 3.1. S. L ’Huilier 3.2. J. Rodríguez assemblées provinciales (1788). 3.3. P . Daunou 4. The 19th Century 3 Sur la nécessité d’établir en France une constitution 4.1. C.L. Dodgson 4.2. E.J. Nanson nouvelle (1793). 5. Before?! 5.2. N. von Kues 5.2. R. Llull 4 . . . 5.1. G.P . Secundus 6. Conclusions

  15. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF New concepts: The Condorcet method S OCIAL C HOICE 1 Condorcet method: It’s a pairwise election method José Rui Figueira where ranked ballots are used to simulate many 1. Introduction head-to-head elections. The winner of a Condorcet 2. “Pioneers” election is the candidate who wins all pairwise match 2.1. J. Charles 2.2. M.J. de Caritat ups 3. “But...” ( robla.net / 1996 / politics / condorcet.html ). 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 2 Cordorcet was aware of his Paradox of voting. 4. The 19th Century 4.1. C.L. Dodgson 3 Several methods can be used to solve this drawback: 4.2. E.J. Nanson 5. Before?! graph “kernel” in E LECTRE methods for choice problem 5.2. N. von Kues statements (B. Roy, 1985). 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  16. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF New concepts: The Condorcet method S OCIAL C HOICE 1 Condorcet method: It’s a pairwise election method José Rui Figueira where ranked ballots are used to simulate many 1. Introduction head-to-head elections. The winner of a Condorcet 2. “Pioneers” election is the candidate who wins all pairwise match 2.1. J. Charles 2.2. M.J. de Caritat ups 3. “But...” ( robla.net / 1996 / politics / condorcet.html ). 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 2 Cordorcet was aware of his Paradox of voting. 4. The 19th Century 4.1. C.L. Dodgson 3 Several methods can be used to solve this drawback: 4.2. E.J. Nanson 5. Before?! graph “kernel” in E LECTRE methods for choice problem 5.2. N. von Kues statements (B. Roy, 1985). 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  17. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF New concepts: The Condorcet method S OCIAL C HOICE 1 Condorcet method: It’s a pairwise election method José Rui Figueira where ranked ballots are used to simulate many 1. Introduction head-to-head elections. The winner of a Condorcet 2. “Pioneers” election is the candidate who wins all pairwise match 2.1. J. Charles 2.2. M.J. de Caritat ups 3. “But...” ( robla.net / 1996 / politics / condorcet.html ). 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 2 Cordorcet was aware of his Paradox of voting. 4. The 19th Century 4.1. C.L. Dodgson 3 Several methods can be used to solve this drawback: 4.2. E.J. Nanson 5. Before?! graph “kernel” in E LECTRE methods for choice problem 5.2. N. von Kues statements (B. Roy, 1985). 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  18. 2. The “Pioneers” 2.2. Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (1743 - 1794) A B RIEF H ISTORY OF New concepts: The Condorcet method S OCIAL C HOICE 1 Condorcet method: It’s a pairwise election method José Rui Figueira where ranked ballots are used to simulate many 1. Introduction head-to-head elections. The winner of a Condorcet 2. “Pioneers” election is the candidate who wins all pairwise match 2.1. J. Charles 2.2. M.J. de Caritat ups 3. “But...” ( robla.net / 1996 / politics / condorcet.html ). 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 2 Cordorcet was aware of his Paradox of voting. 4. The 19th Century 4.1. C.L. Dodgson 3 Several methods can be used to solve this drawback: 4.2. E.J. Nanson 5. Before?! graph “kernel” in E LECTRE methods for choice problem 5.2. N. von Kues statements (B. Roy, 1985). 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  19. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: Swiss mathematician, . . . 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Geneva, Poland, . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 Interested in: Mathematical analysis, topology, graphs, 3.3. P . Daunou elections, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  20. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: Swiss mathematician, . . . 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Geneva, Poland, . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 Interested in: Mathematical analysis, topology, graphs, 3.3. P . Daunou elections, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  21. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: Swiss mathematician, . . . 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Geneva, Poland, . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 Interested in: Mathematical analysis, topology, graphs, 3.3. P . Daunou elections, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  22. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: Swiss mathematician, . . . 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Geneva, Poland, . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 Interested in: Mathematical analysis, topology, graphs, 3.3. P . Daunou elections, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  23. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE Major publications-manuscripts José Rui Figueira 1 S.A.J. L ’Huilier (1794). Examen du mode d’élection 1. Introduction proposé à la Convention Nationale de France en février 2. “Pioneers” 2.1. J. Charles 1793, et adopté à Genève : présenté au Comité L 2.2. M.J. de Caritat égistalif para Simon L ’Huilier et imprimé par ordre du 3. “But...” 3.1. S. L ’Huilier Comité. Genève. Comité Legislatif. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 2 Facsimile reprint in Mathématiques et Sciences Century 4.1. C.L. Dodgson Humaines , 54, pp. 7-24. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  24. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE Major publications-manuscripts José Rui Figueira 1 S.A.J. L ’Huilier (1794). Examen du mode d’élection 1. Introduction proposé à la Convention Nationale de France en février 2. “Pioneers” 2.1. J. Charles 1793, et adopté à Genève : présenté au Comité L 2.2. M.J. de Caritat égistalif para Simon L ’Huilier et imprimé par ordre du 3. “But...” 3.1. S. L ’Huilier Comité. Genève. Comité Legislatif. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 2 Facsimile reprint in Mathématiques et Sciences Century 4.1. C.L. Dodgson Humaines , 54, pp. 7-24. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  25. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE Major publications-manuscripts José Rui Figueira 1 S.A.J. L ’Huilier (1794). Examen du mode d’élection 1. Introduction proposé à la Convention Nationale de France en février 2. “Pioneers” 2.1. J. Charles 1793, et adopté à Genève : présenté au Comité L 2.2. M.J. de Caritat égistalif para Simon L ’Huilier et imprimé par ordre du 3. “But...” 3.1. S. L ’Huilier Comité. Genève. Comité Legislatif. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 2 Facsimile reprint in Mathématiques et Sciences Century 4.1. C.L. Dodgson Humaines , 54, pp. 7-24. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  26. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: several José Rui Figueira 1 In the cyclical case, Condorcet produces an arbitrary 1. Introduction winner. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Condorcet method is manipulable. 3. “But...” 3.1. S. L ’Huilier 3 Assuming that all orderings are equiprobable, he 3.2. J. Rodríguez 3.3. P . Daunou identified all possible permutations of individual 4. The 19th Century preferences for a given outcome. Then, he determined 4.1. C.L. Dodgson 4.2. E.J. Nanson probability ratios. 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  27. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: several José Rui Figueira 1 In the cyclical case, Condorcet produces an arbitrary 1. Introduction winner. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Condorcet method is manipulable. 3. “But...” 3.1. S. L ’Huilier 3 Assuming that all orderings are equiprobable, he 3.2. J. Rodríguez 3.3. P . Daunou identified all possible permutations of individual 4. The 19th Century preferences for a given outcome. Then, he determined 4.1. C.L. Dodgson 4.2. E.J. Nanson probability ratios. 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  28. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: several José Rui Figueira 1 In the cyclical case, Condorcet produces an arbitrary 1. Introduction winner. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Condorcet method is manipulable. 3. “But...” 3.1. S. L ’Huilier 3 Assuming that all orderings are equiprobable, he 3.2. J. Rodríguez 3.3. P . Daunou identified all possible permutations of individual 4. The 19th Century preferences for a given outcome. Then, he determined 4.1. C.L. Dodgson 4.2. E.J. Nanson probability ratios. 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  29. 3. “But...” 3.1. Simon Antoine Jean L ’Huilier (or L ’Huillier) (1750 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: several José Rui Figueira 1 In the cyclical case, Condorcet produces an arbitrary 1. Introduction winner. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Condorcet method is manipulable. 3. “But...” 3.1. S. L ’Huilier 3 Assuming that all orderings are equiprobable, he 3.2. J. Rodríguez 3.3. P . Daunou identified all possible permutations of individual 4. The 19th Century preferences for a given outcome. Then, he determined 4.1. C.L. Dodgson 4.2. E.J. Nanson probability ratios. 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  30. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: Spanish mathematician. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Madrid, . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 Interested in: Mathematics and especial the theory of 3.3. P . Daunou elections. 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  31. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: Spanish mathematician. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Madrid, . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 Interested in: Mathematics and especial the theory of 3.3. P . Daunou elections. 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  32. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: Spanish mathematician. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Madrid, . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 Interested in: Mathematics and especial the theory of 3.3. P . Daunou elections. 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  33. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: Spanish mathematician. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Madrid, . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 Interested in: Mathematics and especial the theory of 3.3. P . Daunou elections. 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  34. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Major publications-manuscripts 1. Introduction 2. “Pioneers” 1 Joseph Isidoro Morales (1797). Memoria Matemática 2.1. J. Charles 2.2. M.J. de Caritat sobre el Cálculo de la Opinion en las Elecciones. 3. “But...” 3.1. S. L ’Huilier Madrid en la Imprenta Real. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  35. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Major publications-manuscripts 1. Introduction 2. “Pioneers” 1 Joseph Isidoro Morales (1797). Memoria Matemática 2.1. J. Charles 2.2. M.J. de Caritat sobre el Cálculo de la Opinion en las Elecciones. 3. “But...” 3.1. S. L ’Huilier Madrid en la Imprenta Real. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  36. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  37. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  38. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  39. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: ??? José Rui Figueira 1 “Rediscovered” the Borda Count? (see the book and 1. Introduction some articles by Panero and Lapresta). 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Made a distinction between votes on people and votes 3. “But...” 3.1. S. L ’Huilier on proposals. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 3 Borda count is more appropriate for the first and binary Century 4.1. C.L. Dodgson methods for the second. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  40. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: ??? José Rui Figueira 1 “Rediscovered” the Borda Count? (see the book and 1. Introduction some articles by Panero and Lapresta). 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Made a distinction between votes on people and votes 3. “But...” 3.1. S. L ’Huilier on proposals. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 3 Borda count is more appropriate for the first and binary Century 4.1. C.L. Dodgson methods for the second. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  41. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: ??? José Rui Figueira 1 “Rediscovered” the Borda Count? (see the book and 1. Introduction some articles by Panero and Lapresta). 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Made a distinction between votes on people and votes 3. “But...” 3.1. S. L ’Huilier on proposals. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 3 Borda count is more appropriate for the first and binary Century 4.1. C.L. Dodgson methods for the second. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  42. 3. “But...” 3.2. José Isidoro Morales Rodríguez (1758 - 1827) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: ??? José Rui Figueira 1 “Rediscovered” the Borda Count? (see the book and 1. Introduction some articles by Panero and Lapresta). 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Made a distinction between votes on people and votes 3. “But...” 3.1. S. L ’Huilier on proposals. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 3 Borda count is more appropriate for the first and binary Century 4.1. C.L. Dodgson methods for the second. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  43. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Short Biography Figueira 1. Introduction 1 Background: French statesman and historian (of the 2. “Pioneers” French Revolution and Empire). 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Living places: Boulogne-sur-Mer (born), Paris, . . . 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: History, Theory of Elections, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  44. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Short Biography Figueira 1. Introduction 1 Background: French statesman and historian (of the 2. “Pioneers” French Revolution and Empire). 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Living places: Boulogne-sur-Mer (born), Paris, . . . 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: History, Theory of Elections, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  45. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Short Biography Figueira 1. Introduction 1 Background: French statesman and historian (of the 2. “Pioneers” French Revolution and Empire). 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Living places: Boulogne-sur-Mer (born), Paris, . . . 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: History, Theory of Elections, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  46. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Short Biography Figueira 1. Introduction 1 Background: French statesman and historian (of the 2. “Pioneers” French Revolution and Empire). 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Living places: Boulogne-sur-Mer (born), Paris, . . . 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: History, Theory of Elections, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  47. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF Source: Wikipedia H ISTORY OF S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  48. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Major publications-manuscripts 1. Introduction 2. “Pioneers” 2.1. J. Charles 1 Daunou, P .Cl.F. (1803). “Mémoire sur les élections au 2.2. M.J. de Caritat scrutin”, Baudoin, Imprimeur de l’institut National. 3. “But...” 3.1. S. L ’Huilier Paris. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  49. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Major publications-manuscripts 1. Introduction 2. “Pioneers” 2.1. J. Charles 1 Daunou, P .Cl.F. (1803). “Mémoire sur les élections au 2.2. M.J. de Caritat scrutin”, Baudoin, Imprimeur de l’institut National. 3. “But...” 3.1. S. L ’Huilier Paris. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  50. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui New concepts: several (1) Figueira 1. Introduction 1 Abandoned the Borda count because its susceptibility 2. “Pioneers” to manipulation. 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Borda and Condorcet methods pinpoint to different 3.1. S. L ’Huilier directions; he preferred the Condorcet principle. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 3 He discussed plurality and runoff procedures. 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  51. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui New concepts: several (1) Figueira 1. Introduction 1 Abandoned the Borda count because its susceptibility 2. “Pioneers” to manipulation. 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Borda and Condorcet methods pinpoint to different 3.1. S. L ’Huilier directions; he preferred the Condorcet principle. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 3 He discussed plurality and runoff procedures. 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  52. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui New concepts: several (1) Figueira 1. Introduction 1 Abandoned the Borda count because its susceptibility 2. “Pioneers” to manipulation. 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Borda and Condorcet methods pinpoint to different 3.1. S. L ’Huilier directions; he preferred the Condorcet principle. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 3 He discussed plurality and runoff procedures. 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  53. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui New concepts: several (1) Figueira 1. Introduction 1 Abandoned the Borda count because its susceptibility 2. “Pioneers” to manipulation. 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 Borda and Condorcet methods pinpoint to different 3.1. S. L ’Huilier directions; he preferred the Condorcet principle. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 3 He discussed plurality and runoff procedures. 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  54. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL New concepts: several (2) C HOICE José Rui Figueira 1 Qualified majorities can be minority veto schemes. 1. Introduction 2 Borda could violates the independence w.r.t. irrelevant 2. “Pioneers” 2.1. J. Charles alternatives. 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3 Only unanimity would guarantee that a majority winner 3.2. J. Rodríguez 3.3. P . Daunou is also a Borda winner (pervasive implication). 4. The 19th Century 4.1. C.L. Dodgson 4 Demonstrated that a Borda looser cannot be a 4.2. E.J. Nanson Condorcet winner. 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  55. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL New concepts: several (2) C HOICE José Rui Figueira 1 Qualified majorities can be minority veto schemes. 1. Introduction 2 Borda could violates the independence w.r.t. irrelevant 2. “Pioneers” 2.1. J. Charles alternatives. 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3 Only unanimity would guarantee that a majority winner 3.2. J. Rodríguez 3.3. P . Daunou is also a Borda winner (pervasive implication). 4. The 19th Century 4.1. C.L. Dodgson 4 Demonstrated that a Borda looser cannot be a 4.2. E.J. Nanson Condorcet winner. 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  56. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL New concepts: several (2) C HOICE José Rui Figueira 1 Qualified majorities can be minority veto schemes. 1. Introduction 2 Borda could violates the independence w.r.t. irrelevant 2. “Pioneers” 2.1. J. Charles alternatives. 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3 Only unanimity would guarantee that a majority winner 3.2. J. Rodríguez 3.3. P . Daunou is also a Borda winner (pervasive implication). 4. The 19th Century 4.1. C.L. Dodgson 4 Demonstrated that a Borda looser cannot be a 4.2. E.J. Nanson Condorcet winner. 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  57. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL New concepts: several (2) C HOICE José Rui Figueira 1 Qualified majorities can be minority veto schemes. 1. Introduction 2 Borda could violates the independence w.r.t. irrelevant 2. “Pioneers” 2.1. J. Charles alternatives. 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3 Only unanimity would guarantee that a majority winner 3.2. J. Rodríguez 3.3. P . Daunou is also a Borda winner (pervasive implication). 4. The 19th Century 4.1. C.L. Dodgson 4 Demonstrated that a Borda looser cannot be a 4.2. E.J. Nanson Condorcet winner. 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  58. 3. “But...” 3.3. Pierre Claude François Daunou (1761 - 1840) A B RIEF H ISTORY OF S OCIAL New concepts: several (2) C HOICE José Rui Figueira 1 Qualified majorities can be minority veto schemes. 1. Introduction 2 Borda could violates the independence w.r.t. irrelevant 2. “Pioneers” 2.1. J. Charles alternatives. 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3 Only unanimity would guarantee that a majority winner 3.2. J. Rodríguez 3.3. P . Daunou is also a Borda winner (pervasive implication). 4. The 19th Century 4.1. C.L. Dodgson 4 Demonstrated that a Borda looser cannot be a 4.2. E.J. Nanson Condorcet winner. 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  59. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE Short Biography José Rui Figueira 1 Background: English author, mathematician, logician, 1. Introduction Anglican deacon, photographer, . . . 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Daresbury near Warrington (born), 3. “But...” 3.1. S. L ’Huilier Oxford, . . . , 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 3 Interested in: Word player, logic, fantasy, new ideas on Century elections and committees, . . . 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  60. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE Short Biography José Rui Figueira 1 Background: English author, mathematician, logician, 1. Introduction Anglican deacon, photographer, . . . 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Daresbury near Warrington (born), 3. “But...” 3.1. S. L ’Huilier Oxford, . . . , 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 3 Interested in: Word player, logic, fantasy, new ideas on Century elections and committees, . . . 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  61. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE Short Biography José Rui Figueira 1 Background: English author, mathematician, logician, 1. Introduction Anglican deacon, photographer, . . . 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Daresbury near Warrington (born), 3. “But...” 3.1. S. L ’Huilier Oxford, . . . , 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 3 Interested in: Word player, logic, fantasy, new ideas on Century elections and committees, . . . 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  62. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE Short Biography José Rui Figueira 1 Background: English author, mathematician, logician, 1. Introduction Anglican deacon, photographer, . . . 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: Daresbury near Warrington (born), 3. “But...” 3.1. S. L ’Huilier Oxford, . . . , 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th 3 Interested in: Word player, logic, fantasy, new ideas on Century elections and committees, . . . 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  63. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF Source: richardwiseman.wordpress.com / . . . / H ISTORY OF S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  64. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Major publications-manuscripts Figueira 1. Introduction 1 The Principles of Parliamentary Representation (1884). 2. “Pioneers” (PR.) 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 A Discussion . . . (1873). 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Suggestions as to the best method of taking votes, 4. The 19th Century where more than two issues are voted on. (1876). 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  65. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Major publications-manuscripts Figueira 1. Introduction 1 The Principles of Parliamentary Representation (1884). 2. “Pioneers” (PR.) 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 A Discussion . . . (1873). 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Suggestions as to the best method of taking votes, 4. The 19th Century where more than two issues are voted on. (1876). 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  66. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Major publications-manuscripts Figueira 1. Introduction 1 The Principles of Parliamentary Representation (1884). 2. “Pioneers” (PR.) 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 A Discussion . . . (1873). 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Suggestions as to the best method of taking votes, 4. The 19th Century where more than two issues are voted on. (1876). 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  67. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Major publications-manuscripts Figueira 1. Introduction 1 The Principles of Parliamentary Representation (1884). 2. “Pioneers” (PR.) 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 2 A Discussion . . . (1873). 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Suggestions as to the best method of taking votes, 4. The 19th Century where more than two issues are voted on. (1876). 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  68. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  69. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  70. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) Shakespeare and Company: Paris, Km 0 A B RIEF H ISTORY OF George Whitman (1912 - . . . ): The owner S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  71. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) Shakespeare and Company: Paris, Km 0 A B RIEF H ISTORY OF George Whitman (1912 - . . . ): The owner S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  72. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  73. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira 1. Introduction 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  74. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF New concepts: Several (1) S OCIAL C HOICE 1 In an election without a Condorcet winner, Dodgson’s José Rui Figueira method is designed to find the candidate that is 1. Introduction “closest” to being a Condorcet winner. 2. “Pioneers” 2.1. J. Charles 2 In case of cycles, for choosing a winner he proposed 2.2. M.J. de Caritat 3. “But...” voters to change their votes in order to produce a 3.1. S. L ’Huilier consensus ranking based on inversion. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 3 “The Dodgson winner if it can be made a Condorcet 4.1. C.L. Dodgson winner is “only” by interchanging as few adjacent 4.2. E.J. Nanson 5. Before?! alternatives in the individual rankings as possible” (F . 5.2. N. von Kues Brandt, 2009). 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  75. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF New concepts: Several (1) S OCIAL C HOICE 1 In an election without a Condorcet winner, Dodgson’s José Rui Figueira method is designed to find the candidate that is 1. Introduction “closest” to being a Condorcet winner. 2. “Pioneers” 2.1. J. Charles 2 In case of cycles, for choosing a winner he proposed 2.2. M.J. de Caritat 3. “But...” voters to change their votes in order to produce a 3.1. S. L ’Huilier consensus ranking based on inversion. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 3 “The Dodgson winner if it can be made a Condorcet 4.1. C.L. Dodgson winner is “only” by interchanging as few adjacent 4.2. E.J. Nanson 5. Before?! alternatives in the individual rankings as possible” (F . 5.2. N. von Kues Brandt, 2009). 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  76. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF New concepts: Several (1) S OCIAL C HOICE 1 In an election without a Condorcet winner, Dodgson’s José Rui Figueira method is designed to find the candidate that is 1. Introduction “closest” to being a Condorcet winner. 2. “Pioneers” 2.1. J. Charles 2 In case of cycles, for choosing a winner he proposed 2.2. M.J. de Caritat 3. “But...” voters to change their votes in order to produce a 3.1. S. L ’Huilier consensus ranking based on inversion. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 3 “The Dodgson winner if it can be made a Condorcet 4.1. C.L. Dodgson winner is “only” by interchanging as few adjacent 4.2. E.J. Nanson 5. Before?! alternatives in the individual rankings as possible” (F . 5.2. N. von Kues Brandt, 2009). 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  77. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF New concepts: Several (1) S OCIAL C HOICE 1 In an election without a Condorcet winner, Dodgson’s José Rui Figueira method is designed to find the candidate that is 1. Introduction “closest” to being a Condorcet winner. 2. “Pioneers” 2.1. J. Charles 2 In case of cycles, for choosing a winner he proposed 2.2. M.J. de Caritat 3. “But...” voters to change their votes in order to produce a 3.1. S. L ’Huilier consensus ranking based on inversion. 3.2. J. Rodríguez 3.3. P . Daunou 4. The 19th Century 3 “The Dodgson winner if it can be made a Condorcet 4.1. C.L. Dodgson winner is “only” by interchanging as few adjacent 4.2. E.J. Nanson 5. Before?! alternatives in the individual rankings as possible” (F . 5.2. N. von Kues Brandt, 2009). 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  78. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: Several (2) José Rui Figueira 1 Counterexamples related to the majority rule and 1. Introduction Condorcet’s method. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Proportion Representation rule for assigning seats. 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 The idea of “the giving to each candidate the power of 3.3. P . Daunou 4. The 19th transferring to any other candidate the votes given for Century 4.1. C.L. Dodgson him”. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  79. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: Several (2) José Rui Figueira 1 Counterexamples related to the majority rule and 1. Introduction Condorcet’s method. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Proportion Representation rule for assigning seats. 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 The idea of “the giving to each candidate the power of 3.3. P . Daunou 4. The 19th transferring to any other candidate the votes given for Century 4.1. C.L. Dodgson him”. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  80. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: Several (2) José Rui Figueira 1 Counterexamples related to the majority rule and 1. Introduction Condorcet’s method. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Proportion Representation rule for assigning seats. 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 The idea of “the giving to each candidate the power of 3.3. P . Daunou 4. The 19th transferring to any other candidate the votes given for Century 4.1. C.L. Dodgson him”. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  81. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE New concepts: Several (2) José Rui Figueira 1 Counterexamples related to the majority rule and 1. Introduction Condorcet’s method. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Proportion Representation rule for assigning seats. 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3 The idea of “the giving to each candidate the power of 3.3. P . Daunou 4. The 19th transferring to any other candidate the votes given for Century 4.1. C.L. Dodgson him”. 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  82. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira New concepts: Several (3) 1. Introduction 2. “Pioneers” 1 The apportionment problem. 2.1. J. Charles 2.2. M.J. de Caritat 2 Dodgson and its works on Tennis Tournaments. 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  83. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira New concepts: Several (3) 1. Introduction 2. “Pioneers” 1 The apportionment problem. 2.1. J. Charles 2.2. M.J. de Caritat 2 Dodgson and its works on Tennis Tournaments. 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  84. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira New concepts: Several (3) 1. Introduction 2. “Pioneers” 1 The apportionment problem. 2.1. J. Charles 2.2. M.J. de Caritat 2 Dodgson and its works on Tennis Tournaments. 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  85. 4. The Nineteenth Century 4.1. Charles Lutwidge Dodgson (1832 - 1898) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira New concepts: Several (3) 1. Introduction 2. “Pioneers” 1 The apportionment problem. 2.1. J. Charles 2.2. M.J. de Caritat 2 Dodgson and its works on Tennis Tournaments. 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  86. 4. The Nineteenth Century 4.2. Edward John Nanson (1850 - 1936) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: English mathematician. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: England, Australia, . . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: Voting theory, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

  87. 4. The Nineteenth Century 4.2. Edward John Nanson (1850 - 1936) A B RIEF H ISTORY OF S OCIAL C HOICE José Rui Figueira Short Biography 1. Introduction 1 Background: English mathematician. 2. “Pioneers” 2.1. J. Charles 2.2. M.J. de Caritat 2 Living places: England, Australia, . . . . 3. “But...” 3.1. S. L ’Huilier 3.2. J. Rodríguez 3.3. P . Daunou 3 Interested in: Voting theory, . . . 4. The 19th Century 4.1. C.L. Dodgson 4.2. E.J. Nanson 5. Before?! 5.2. N. von Kues 5.2. R. Llull 5.1. G.P . Secundus 6. Conclusions

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