×

The median procedure in cluster analysis and social choice theory. (English) Zbl 0486.62057


MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
91B14 Social choice
62P25 Applications of statistics to social sciences
91D99 Mathematical sociology (including anthropology)
91B08 Individual preferences
06Axx Ordered sets
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Abdi, H.; Barthélemy, J.P.; Luong, X., Information préordinate et analyse des préférences, ()
[2] Abelson, R.P.; Rosenberg, M.J., Symbolic psycho-logic: a model of attitudinal cognition, Behavioral sci., 3, 1-13, (1958)
[3] Adelsman, R.; Whinston, A., The equivalence of three social decision functions, Revue d’automatique, informatique et recherche opérationelle, 11, 3, 257-265, (1973) · Zbl 0364.90003
[4] Anderson, A.B., The bogart preference structures: applications, J. math. sociol., 3, 69-83, (1973) · Zbl 0289.92030
[5] Arabic, P.; Boorman, S.A., Multidimensional scaling of measures of distances between partitions, J. math. psychol., 17, 21-63, (1978)
[6] Arkhipoff, O., Reformulation du théorème d’arrow et généralisations, Annales de l’I.N.S.E.E., 18, 3-43, (1975)
[7] Arrow, K.J., Social choice and individual values, (1962), Wiley New York · Zbl 0984.91513
[8] Astie, A., Comparaisons par paires et problémes de classement: estimation et tests statistiques, Math. sci. hum., 32, 17-44, (1970)
[9] Astie, A., (), 1-50, 1, 2
[10] Avann, S.P., Metric ternary distributive semi-lattices, Proc. amer. math. soc., 12, 407-414, (1961) · Zbl 0099.02201
[11] Baker, F.B.; Hubert, L.J., Applications of combinatorial programming to data analysis: seriation using asymmetric proximity measures, Br. J. math. statist. psychol., 30, 154-164, (1977)
[12] Barbut, H.J.; Hedlikova, J., Median algebras, (1979)
[13] Barbut, M., Mediane, distributivité, eloignements, (), Math. sci. hum., 70, 5-31, (1980) · Zbl 0439.06007
[14] Barbut, M., Note sur LES ordres totaux á distance minimum d’une relation binaire donnée, Math. sci. hum., 17, 47-48, (1966)
[15] Barbut, M., Medianes, condoreet et Kendall, Math. sci. hum., 69, 5-13, (1980), note SEMA, Paris, 1967 · Zbl 0437.90010
[16] Barbut, M., Echelles a distance minimum d’une partie donnée d’un treillis distributif fini, Math. sci. hum., 18, 41-46, (1967)
[17] Barbut, M.; Monjardet, B., Ordre et classification, algébre et combinatoire, () · Zbl 0267.06001
[18] Barthélemy, J.P., Sur LES éloignements symétriques et le principe de Pareto, Math. sci. hum., 56, 97-125, (1976) · Zbl 0379.90007
[19] Barthélemy, J.P., A propos de partitions centrales sur un ensemble non nécessairement fini, Statistique e’ analyse des données, 3, 54-62, (1977)
[20] Barthélemy, J.P., Comparaison et agrégation des partitions et des préordres totaux, C.r.a.s., 285, 985-987, (1977) · Zbl 0399.05004
[21] Barthélemy, J.P., Remarques sur LES propriétés métriques des ensembles ordonnés, Math. sci. hum., 61, 39-60, (1978) · Zbl 0419.06001
[22] Barthélemy, J.P., Propriétés métriques des ensembles ordonnés, comparaison et agrégation de relations binaires, ()
[23] Barthélemy, J.P., Caractérisation axiomatiques de la distance de la différence métrique entre des relations binaires, Math. sci. hum., 67, 85-113, (1979) · Zbl 0418.06003
[24] Barthélemy, J.P., Procedures métriques d’agrégation, ()
[25] Barthélemy, J.P.; Monjardet, B., Ajustement et résumé de données relationelles: LES relations centrales, (), 645-653
[26] Benzeeri, J.P., Sur panalyse des préférences, (), 195-205
[27] Benzeeri, J.P., D’analyse des données, ()
[28] Bermond, J.C., The circuit hypergraph of a tournament, infinite and finite sets, (), 165-180
[29] Bermond, J.C., Ordres á distance minimum d’un tournoi et graphes partiels sans circuits maximaun, Math. sci. hum., 37, 5-25, (1972) · Zbl 0239.05122
[30] Bermond, J.C.; Kodratoff, Y., Une heuristique pour le calcul de l’indice de transitivité d’un tournoi, Revue d’automatique, informatique et recherche op]’erationnelle, 10, 3, 83-92, (1976)
[31] Birkhoff, G.; Kiss, S.A., A ternary operation in distributive lattices, Bull. amer. math. soc., 53, 749-752, (1947) · Zbl 0031.25002
[32] Birkhoff, G., Lattice theory, (1967), Amer. Math. Soc., Providence · Zbl 0126.03801
[33] Black, D., The theory of committees and elections, (1958), Cambridge University Press London · Zbl 0091.15706
[34] Blair, D.H.; Pollak, R.A., Collective rationality and dictatorship: the scope of the arrow theorem, J. econ. theory, 21, 1, 186-194, (1979) · Zbl 0432.90007
[35] Blau, J.H., Semiorders and collective choice, J. econ. theory, 21, 1, 195-206, (1979) · Zbl 0415.90012
[36] Blin, J.M., Preference aggregation and statistical estimation, Theory and decision, 4, 65-84, (1973) · Zbl 0284.90003
[37] Blin, J.M., A linear formulation of the multiattribute decision problem., Revue d’automatique, informatique et recherche opérationelle, 10, 6, 21-32, (1976) · Zbl 0333.90030
[38] Blin, J.M., Assignment models in voting theory, () · Zbl 0363.90011
[39] Blin, J.M.; Whinston, A.B., A note on majority rule under transitivity constraints, Manag. sci., 20, 1439-1440, (1974) · Zbl 0363.90006
[40] Blin, J.M.; Whinston, A.B., Descriminant functions and majority voting, Manag. sci., 21, 5, 1029-1041, (1975)
[41] Bogart, K.P., Preference structures I: distance between transitive preference relations, J. math. sociol., 3, 49-67, (1973) · Zbl 0303.92013
[42] Bogart, K.P., Preference structures II: distances between asymmetric relations, SIAM J. appl. math., 29, 2, 254-262, (1975) · Zbl 0326.92018
[43] Bogart, K.P.; Weeks, J.R., Consensus signed diagraph, SIAM J. appl. math., 36, 1, 1-14, (1979) · Zbl 0411.05042
[44] Boorman, S.A.; Arabie, P., Structural measures and the method of sorting, (), Theory
[45] Boorman, S.A.; Oliver, D.C., Metrics on spaces of finite trees, J. math. psychol., 10, 26-59, (1973) · Zbl 0271.92011
[46] Borda, J.C., Mémoire sur LES élections au scrutin, Histoire de l’académie royale des sciences pour 1781, (1974), English translation by A. de Grazia, Isis 44 (1953)
[47] Bordes, G., Métriques bornées définies par des valuations sur un demi-treillis, Math. sci. hum., 56, 89-95, (1976) · Zbl 0367.06007
[48] Bordes, G., Procedures d’agrégation et fonctions de choix, ()
[49] Bowman, V.J., Permutation polyhedra, SIAM J. appl. math., 22, 4, 580-589, (1972) · Zbl 0246.90030
[50] Bowman, V.J.; Colantom, C.S., Majority rule under transitivity constraints, Manag. sci., 19, 1029-1041, (1973) · Zbl 0285.90003
[51] Bowman, V.J.; Colantoni, C.S., Further comments on majority rule under transivity constraints, Manag. sci., 20, 1441, (1974) · Zbl 0363.90007
[52] Brualdi, R.A.; Gibson, P.M.; Brualdi, R.A.; Gibson, P.M.; Brualdi, R.A.; Gibson, P.M., Convex polyhedra of doubly stochastic matrices, J. combinatorial theory ser. A, J. combinatorial theory ser. A, J. combinatorial theory ser. A, 22, 338-351, (1977) · Zbl 0368.15010
[53] Brunk, H.O., Mathematical models for ranking from paired comparisons, J. amer. statist. assoc., 55, 503-520, (1960) · Zbl 0101.11902
[54] Burkov, V.N.; Groppen, V.O., Branch cuts in strongly connected graphs and permutation potentials, Automation and remote control, 6, 111-119, (1972) · Zbl 0252.90055
[55] Cailliez, F.; Pages, J.P., Introduction á l’analyse des donnees, (1976), SMASH Paris
[56] Chandon, J.L.; Lemaire, J., Agrégation typologique de quasi-ordres: an nouvel algorithme, (), 63-75
[57] Marquis de Condorcet, M.I.A., Essai sur l’application de l’analyse á la probabilité des décisions rendues á la pluralité des voix, (1974), Chelsea Publ. 6 New York, Paris
[58] Comyn, G.; Van Dorpe, J.Cl., Valuation et semi-modularité dans LES demi-treillis, Math. sci. hum., 56, 63-73, (1976) · Zbl 0367.06009
[59] Cook, W.D.; Saipe, A.L., Committee approach to priority planning: the Median ranking method, Cahiers du centre d’etudes et de recherche opérationnelle, 18, 3, 337-352, (1976) · Zbl 0348.90088
[60] Cook, W.D.; Seiford, L.M., Priority ranking and consensus formation, Manag. sci., 24, 16, 1721-1732, (1978) · Zbl 0491.90006
[61] Coombs, C.H., A theory of data, (1964), Wiley New York · Zbl 0217.27902
[62] Coxeter, H.S.M.; Moser, W.O., Generators and relations for discrete groups, (1972), Springer Berlin · Zbl 0239.20040
[63] David, H.A., The method of paired comparisons, (1963), Griffin London · Zbl 0665.62075
[64] Davidson, R.R.; Odeh, R.E., Some inconsistencies in judging problems, J. combinatorial theory, 13, 162-169, (1972) · Zbl 0242.62014
[65] De Cani, J.S., Maximum likelihood paired comparison ranking by linear programming, Biometrika, 56, 3, 537-545, (1969) · Zbl 0188.50101
[66] De Cani, J.S., A branch and bound algorithm for maximum likelihood paired comparison ranking, Biometrika, 59, 1, 131-135, (1972) · Zbl 0245.62037
[67] Defays, D., Recherche des ultramétriques á distance minimum d’une similarité donnée, Bull. soc. sci. liege, 5, 6, 330-343, (1975) · Zbl 0332.62044
[68] Degeane, A., Techniques ordinales en analyse des données: statistique, (1972), Hachette Paris
[69] Diday, E., One nouvelle méthode en classification automatique et reconnaissance des formes, Revue de statist. appl., 19, 2, 19-34, (1971)
[70] Dridi, T., Sur LES distributions binaires associées á des distributions ordinales, Math. sci. hum., 69, 15-31, (1980) · Zbl 0437.90003
[71] Ehrenberg, A.S.C., On sampling from a population of rankers, Biometrika, 39, 82-87, (1952) · Zbl 0046.35901
[72] Feldman-Hogaasen, J., Ordres partiels et permutoédre, Math. sci. hum., 28, 27-38, (1969) · Zbl 0218.06001
[73] Feldman-Hogaasen, J., Description du permutoédre á d’aide des permutations voisines, (), 109-114
[74] Feldman, J., Póles, intermédiaires et centres dans un groupe d’opinion, Math. sci. hum., 43, 39-54, (1973) · Zbl 0268.92016
[75] Fishburn, P.C., Mathematics of decision theory, (1972), The Hauge Mouton · Zbl 0276.62012
[76] Fishburn, P.C., The theory of social choice, (1973), Princeton University Press NJ · Zbl 0253.92006
[77] Fishburn, P.C., On the sum-of-rank winners when losers are removed, Discr. math., 8, 25-30, (1974) · Zbl 0279.90002
[78] Fishburn, P.C., Condorcet social choice function, SIAM J. appl. math., 33, 3, 469-489, (1977) · Zbl 0369.90002
[79] Flament, Cl., Applications of graph theory to group structure, (1963), Prentice Hall New York · Zbl 0141.36301
[80] Flueck, J.A.; Korsh, J.F., A branch search algorithm for maximum likelihood paired comparison ranking, Biometrika, 61, 3, 621-626, (1974) · Zbl 0295.62078
[81] Frey, C., Technique ordinale en analyse des données, ()
[82] Gaertner, W.; Salies, M., Procédures d’agrégation avec domaines restreints et théorèmes d’existence, ()
[83] Glower, P.; Klastorin, T.; Klingman, D., Optimal weighted ancestry relationships, Manag. sci., 20, 1190-1193, (1974) · Zbl 0303.90055
[84] Grimonprez, G.; Van Dorpe, J.Cl., Distance définie par une application monotone sur un treillis, Math. sci. hum., 56, 47-62, (1976) · Zbl 0367.06008
[85] Guenoche, A., Un algorithme pour pallier l’effet Condorcet, Revue d’automatique, informatique et recherche opérationnelle, 11, 1, 77-83, (1977), Informatique et Recherche Opérationnelle · Zbl 0356.90068
[86] Th. Guilbaud, G., LES théories de l’intérét général et le probléme logique de l’agrégation, (), 5, 4, 262-307, (1968), Dunod Paris, English Transl. in
[87] Th. Guilbaud, G., Préférences stochastiques, Math. sci. hum., 32, 45-56, (1970)
[88] Th. Guilbaud, G.; Rosenstiehl, P., Analyse algébrique d’un scrutin, Math. sci. hum., 4, 9-33, (1963)
[89] Halmos, P.R., Measure theory, (1950), Van Nostrand New York · Zbl 0117.10502
[90] Harary, F.; Norman, R.Z.; Cartwright, D., Structural models, an introduction to the theory of directed graph, (1965), Wiley New York · Zbl 0139.41503
[91] du Parc, J.Hardouin, Quelques résultats sur ‘l’indice de transitivité’ de certains tournois, Math. sci. hum., 51, 35-41, (1975) · Zbl 0319.05111
[92] Haskins, L.; Gudder, S., Height on posets and graphs, Discrete math., 2, 357-382, (1972) · Zbl 0238.06002
[93] Hausmann, D.; Korte, B., Adjacency on 0-1 polyhedra, (), 106-127
[94] D. Hausmann, Adjacency on polytopes in combinatorial optimization, in: Oelgeschlager, Gunn and Hain, eds., Mathematical Systems in Economics (Cambridge, MA). · Zbl 0439.90050
[95] Hays, W.L., A note on average τ as a measure of concordance, J. amer. statist. assoc., 55, 290, 331-341, (1960) · Zbl 0212.22403
[96] Heuchenne, C., Un algorithme général pour trouver un sous-ensemble d’un certain type á distance minimum d’une partie donnée, Math. sci. hum., 30, 23-33, (1970) · Zbl 0219.05002
[97] Hubert, L., Some applications of graph theory to clustering, Psychometrika, 39, 283-309, (1974) · Zbl 0317.62079
[98] Hubert, L., Seriation using asymmetric proximity measures, Br. J. math. statist. psychol., 29, 32-52, (1976) · Zbl 0334.92040
[99] Hubert, L.; Schultz, J., Maximum likelihood paired-comparison ranking and quadratic assignment, Biometrika, 62, 3, 655-659, (1975) · Zbl 0321.62080
[100] Jacquet-Lagréze, E., L’agrégation des opinions individuelles, Informatique et sciences humaines, 4, 1-21, (1969)
[101] Jacquet-Lagréze, E., Analyse d’opinions valuées et graphes de préférences, Math. sci. hum., 33, 33-55, (1971) · Zbl 0224.92025
[102] Jacquet-Lagréze, E., La modélisation des préférences, préordres, quasi-ordres et relations floues, () · Zbl 0416.90004
[103] Jacquet-Lagréze, E., Analyse des préférences, (), 63-97
[104] Jacquet-Lagrèze, E., Représentation de quasi-ordres et de relations probabilistes transitives sous forme standard et méthodes dápproximation, Math. sci. hum., 63, 5-24, (1978) · Zbl 0413.06001
[105] Jardine, N.; Sibson, R., Mathematical taxonomy, (1971), Wiley London · Zbl 0322.62065
[106] Kelly, J.S., Arrow impossibility theorems, (1978), Academic Press New York · Zbl 0462.90004
[107] Kemeny, J.G., Mathematics without numbers, Daedalus, 88, 577-591, (1959)
[108] Kemeny, J.G.; Snell, J.C., Mathematical models in the social sciences, (1962), Ginand Co., New York · Zbl 0256.92003
[109] Kendall, M.G., Rank correlation methods, (1962), Hafner New York · Zbl 0032.17602
[110] Kendall, M.G.; Babington Smith, B., The problem of m rankings, Ann. math. statist., 10, 275-287, (1939) · Zbl 0023.24201
[111] Kendall, M.G.; Babington Smith, B., On the method of paired comparisons, Biometrika, 33, 239-251, (1940) · JFM 66.0651.01
[112] Kreweras, G., Représentation polyedrique des préordres complets finis., (), 101-108 · Zbl 0221.90002
[113] Lawler, E.L., A comment on minimum feedback are sets, I.E.E.E. trans. circuit theory, 11, 296-297, (1954)
[114] Lemaire, J., Agrégation typologigue des préférences, ()
[115] Lemaire, J., Agrégation typologique de données de préférences, Math. sci. hum., 58, 31-50, (1977) · Zbl 0385.90006
[116] Lemaire, J., Agrégation typologique de données, () · Zbl 0385.90006
[117] Lempel, A.; Cederbaum, I., Minimum feedback are and vertex sets of a directed graph, I.E.E.E. trans. circuit theory, 13, 399-403, (1966)
[118] Lerman, I.C., LES bases de la classification automatique, (1970), Gauthier-Villars Paris · Zbl 0199.51402
[119] Ievenglick, A., Characterizations of social decision function, ()
[120] Marcotorchino, J.P.; Michaud, P., (), Technical Report
[121] Marcotorchino, J.P.; Michaud, P., Optimisation en analyse ordinale des données, (1979), Masson Paris
[122] Matula, D.W., Graphs theoretic techniques for cluster analysis algorithms, (), 96-129
[123] Meggido, N., Mixtures of order matrices and generalized order matrices, Discrete math., 19, 177-181, (1977)
[124] Merchant, D.K.; Rao, M.R., Majority decisions and transitivity: some special cases, Manag. sci., 23, 2, 125-130, (1976) · Zbl 0349.90002
[125] Michaud, F.; Marcotorchino, J.P., Modéles d’optimisation en analyse des données relationnelles, Math. sci. hum., 67, 7-38, (1979) · Zbl 0446.62058
[126] Mirkin, B.G., The problems of approximation in space of relations and qualitative data analysis, Automatika i telemechanika, 35, 9, 1424-1431, (1974), translated in Automation and Remote Control
[127] Mirkin, B.G., On the problem of reconciling partition, () · Zbl 0727.62106
[128] Mirkin, B.G., Geometrical conceptions in the analysis of qualitative variables, Quality and quantity, 9, 317-322, (1975)
[129] Mirkin, B.G., Qualitative factor analysis, (1976), Statistika Edit., Moscow, in Russian. · Zbl 0371.62086
[130] Mirkin, B.G., On a criterion of classification and analysis of structure, () · Zbl 1008.91101
[131] Mirkin, B.G., (), Russian edit.
[132] Mirkin, B.G.; Cherny, L.B., On measurement of distance between partitions of a finite set of units, Automatika i telemechanika, 31, 5, 786-792, (1970), transl. in Automation and Remote Control · Zbl 0221.05029
[133] Monjardet, B., Tournois et ordres médians pour une opinion, Math. sci. hum., 43, 55-70, (1973) · Zbl 0271.05114
[134] Monjardet, B., Caractérisations métriques des ensembles ordonnés semi-modulaires, Math. sci. hum., 56, 77-87, (1976) · Zbl 0367.06010
[135] Monjardet, B., An axiomatic theory of tournament aggregation, Math. oper. research, 3, 4, 334-351, (1978) · Zbl 0395.90002
[136] Monjardet, B., Relations á éloignement minimum de relations binaires, Math. sci. hum., 67, 115-122, (1979), note bibliographique · Zbl 0413.62045
[137] Monjardet, B., Théorie et applications de la médiane dans LES treillis distributifs finis, Annals of discrete math., (1980) · Zbl 0451.06012
[138] Monjardet, B., Dispersion d’un nuage sphérique. applcations aux coefficients d’homogénéité de relations de préferences, (1981)
[139] Moon, J.W., A note on approximating symmetric relations by equivalence relations, SIAM J. appl. math., 14, 2, (1966) · Zbl 0166.00802
[140] Moon, J.W., Topics on tournaments, (1968), Holt New York · Zbl 0191.22701
[141] Moon, J.W., Four combinatorial problems, () · Zbl 0215.33201
[142] Moon, J.W.; Pullman, N.J., On generalized tournament matrices, SIAM rev., 12, 384-399, (1970) · Zbl 0198.03804
[143] Mulder, H.M.; Schrijver, A., Median graphs and Helly hypergraphs, Discrete math., 25, 41-50, (1979) · Zbl 0395.05058
[144] Murakami, V., Logic and social choice, (1968), Dover New York
[145] Nitzan, S.; Rubinstein, A., A further characterization of Borda ranking method, ()
[146] Ore, O., Theory of equivalence, Duke math. J., 9, 573-627, (1942) · Zbl 0060.06201
[147] Peyroux, C., Aggégation d’opinions individuelles, ()
[148] Philips, J.P.N., On an algorithm of Smith and payne for determining Slater’s i and all nearest adjoining orders, Br. J. math. stat. psychol., 29, 126-127, (1976)
[149] Ranyard, R.H., An algorithm for maximum likelihood ranking and Slater’s i from paired comparisons, Br. J. math. stat. psychol., 29, 2, 242-248, (1976) · Zbl 0351.62054
[150] Regnier, S., Sur quelques aspects mathématiques des problèmes de classification automatique, I.C.C. bulletin, 4, (1965), Rome · Zbl 0548.62040
[151] Regnier, S., Stabilité d’un opérateur de classification, Math. sci. hum., 60, 21-30, (1977) · Zbl 0415.62039
[152] Regnier, S.; De La Vega, W., Préhension et interprétation de plusieurs classifications d’un même ensemble de données, ()
[153] Reingold, E.M.; Nievergelt, J.; Deo, N., Combinatorial algorithms. theory and practice, (1977), Prentice-Hall Englewood Cliffs · Zbl 0367.68032
[154] Remage, R.; Thompson, W.A., Maximum likelihood paired comparison rankings, Biometrika, 53, 143-149, (1966) · Zbl 0138.13207
[155] Restle, F., A metric and an ordering on sets, Psychometrika, 24, 207-220, (1959) · Zbl 0087.15903
[156] Roberts, F.S., Discrete mathematical models, (1976), Prentice-Hall Englewood Cliffs
[157] Romero, D., Variations sur l’effet condoreet, (), Grenoble
[158] Schader, M., Distance minimale entre partitions et préordonnances dans un ensemble fini, Math. sci. hum., 67, 39-47, (1979) · Zbl 0419.04001
[159] Schader, M., Hierarchical analysis: classification with ordinal object dissimilarities, Metrika, 27, 127-132, (1980) · Zbl 0438.62046
[160] Sen, A.K., Collective choice and social welfare, (1970), Oliver and Boyd London · Zbl 0227.90011
[161] Sen, A.K., Social choice theory: a re-examination, Econometrica, 45, 1, 53-89, (1977) · Zbl 0353.90001
[162] Seshu, S.; Reed, M.B., Linear graphs and electrical networks, (1961), Addison-Wesley Reading · Zbl 0102.34001
[163] Slater, P., Inconsistencies in a schedule of paired comparisons, Biometrika, 48, 303-312, (1961)
[164] Slater, P., Centers to centroids in graphs, J. graph theory, 2, 209-222, (1978) · Zbl 0425.05021
[165] Smith, G.W.; Walford, R.B., The identification of a minimal feedback vertex set of a directed graph, IEEE trans. circuits and systems, 22, 9-14, (1975)
[166] Sokal, R.R.; Michener, C.D., A statistical method for evaluating systematic relationships, Univ. kansas sci. bull., 38, 1409-1438, (1958)
[167] Sokal, R.R.; Sneath, P.H.A., Principles of numerical taxonomy, (1963), Freeman San Francisco
[168] Terrier, E., Permutoédre, visualisation et agrégation des préférences, 3rd cycle thesis, (1980), Grenoble
[169] Thompson, W.A.; Remage, R., Rankings from paired comparisons, Ann. math. statist., 35, 739-747, (1964) · Zbl 0138.13206
[170] Tomescu, I., Une caractérisation des graphes dont le degré de déséquilibre est maximal, Math. sci. hum., 42, 37-40, (1973) · Zbl 0266.05115
[171] Tomescu, I., La réduction minimale d’un graphe á une réunion de cliques, Discrete math., 10, 173-179, (1974) · Zbl 0288.05127
[172] Vincke, Ph., Ordres et préordres totaux à distance minimum d’un quasi-ordre, Cashiers du C.E.R.O., 20, 3, 4, 453-461, (1978) · Zbl 0415.06001
[173] Young, H.P., An axiomatization of Borda’s rule, J. econ. theory, 9, 43-52, (1974)
[174] Young, H.P., On permutations and permutation polytopes, (), 128-140 · Zbl 0424.05001
[175] Young, H.P.; Levenglick, A., A consistent extension of Condorcet’s election principle, SIAM J. appl. math., 35, 2, 285-300, (1978) · Zbl 0385.90010
[176] Younger, D.H., Minimum feedback are sets for a directed graph, IEEE trans. circuit theory, 10, 238-245, (1963)
[177] Zahn, C.T., Approximating symmetric relations by equivalence relations, SIAM J. appl. math., 12, 840-847, (1964) · Zbl 0129.16003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.