Semiorder (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Semiorder" in English language version.

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Luce (1956), p. 179. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
Luce (1956), Theorem 3 describes a more general situation in which the threshold for comparability between two utilities is a function of the utility rather than being identically 1; however, this does not lead to a different class of orderings. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
This result is typically credited to Scott & Suppes (1958); see, e.g., Rabinovitch (1977). Scott, Dana; Suppes, Patrick (1958), "Foundational aspects of theories of measurement", The Journal of Symbolic Logic, 23 (2): 113–128, doi:10.2307/2964389, JSTOR 2964389, MR 0115919. Rabinovitch, Issie (1977), "The Scott-Suppes theorem on semiorders", Journal of Mathematical Psychology, 15 (2): 209–212, doi:10.1016/0022-2496(77)90030-x, MR 0437404.
Luce (1956, p. 181) used four axioms, the first two of which combine asymmetry and the definition of incomparability, while each of the remaining two is equivalent to one of the above prohibition properties. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
Fishburn (1973). Fishburn, Peter C. (1973), "Interval representations for interval orders and semiorders", Journal of Mathematical Psychology, 10: 91–105, doi:10.1016/0022-2496(73)90007-2, MR 0316322.
Fishburn (1970). Fishburn, Peter C. (1970), "Intransitive indifference with unequal indifference intervals", Journal of Mathematical Psychology, 7: 144–149, doi:10.1016/0022-2496(70)90062-3, MR 0253942.
Dean & Keller (1968); Kim & Roush (1978) Dean, R. A.; Keller, Gordon (1968), "Natural partial orders", Canadian Journal of Mathematics, 20: 535–554, doi:10.4153/CJM-1968-055-7, MR 0225686. Kim, K. H.; Roush, F. W. (1978), "Enumeration of isomorphism classes of semiorders", Journal of Combinatorics, Information &System Sciences, 3 (2): 58–61, MR 0538212.
Chandon, Lemaire & Pouget (1978). Chandon, J.-L.; Lemaire, J.; Pouget, J. (1978), "Dénombrement des quasi-ordres sur un ensemble fini", Centre de Mathématique Sociale. École Pratique des Hautes Études. Mathématiques et Sciences Humaines (62): 61–80, 83, MR 0517680.
Rabinovitch (1978). Rabinovitch, Issie (1978), "The dimension of semiorders", Journal of Combinatorial Theory, Series A, 25 (1): 50–61, doi:10.1016/0097-3165(78)90030-4, MR 0498294.
Fishburn & Trotter (1992). Fishburn, Peter C.; Trotter, W. T. (1992), "Linear extensions of semiorders: a maximization problem", Discrete Mathematics, 103 (1): 25–40, doi:10.1016/0012-365X(92)90036-F, MR 1171114.
Doignon & Falmagne (1997). Doignon, Jean-Paul; Falmagne, Jean-Claude (1997), "Well-graded families of relations", Discrete Mathematics, 173 (1–3): 35–44, doi:10.1016/S0012-365X(96)00095-7, MR 1468838.
Roberts (1969). Roberts, Fred S. (1969), "Indifference graphs", Proof Techniques in Graph Theory (Proc. Second Ann Arbor Graph Theory Conf., Ann Arbor, Mich., 1968), Academic Press, New York, pp. 139–146, MR 0252267.

doi.org

Luce (1956), p. 179. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
Luce (1956), Theorem 3 describes a more general situation in which the threshold for comparability between two utilities is a function of the utility rather than being identically 1; however, this does not lead to a different class of orderings. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
Brightwell (1989). Brightwell, Graham R. (1989), "Semiorders and the 1/3–2/3 conjecture", Order, 5 (4): 369–380, doi:10.1007/BF00353656, S2CID 86860160.
This result is typically credited to Scott & Suppes (1958); see, e.g., Rabinovitch (1977). Scott, Dana; Suppes, Patrick (1958), "Foundational aspects of theories of measurement", The Journal of Symbolic Logic, 23 (2): 113–128, doi:10.2307/2964389, JSTOR 2964389, MR 0115919. Rabinovitch, Issie (1977), "The Scott-Suppes theorem on semiorders", Journal of Mathematical Psychology, 15 (2): 209–212, doi:10.1016/0022-2496(77)90030-x, MR 0437404.
Luce (1956, p. 181) used four axioms, the first two of which combine asymmetry and the definition of incomparability, while each of the remaining two is equivalent to one of the above prohibition properties. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
Fishburn (1973). Fishburn, Peter C. (1973), "Interval representations for interval orders and semiorders", Journal of Mathematical Psychology, 10: 91–105, doi:10.1016/0022-2496(73)90007-2, MR 0316322.
Fishburn (1970). Fishburn, Peter C. (1970), "Intransitive indifference with unequal indifference intervals", Journal of Mathematical Psychology, 7: 144–149, doi:10.1016/0022-2496(70)90062-3, MR 0253942.
Sen (1971, Section 10, p. 314) Since Luce modelled indifference between x and y as "neither xRy nor yRx", while Sen modelled it as "both xRy and yRx", Sen's remark on p.314 is likely to mean the latter property. Sen, Amartya K. (July 1971), "Choice Functions and Revealed Preference" (PDF), The Review of Economic Studies, 38 (3): 307–317, doi:10.2307/2296384, JSTOR 2296384.
Dean & Keller (1968); Kim & Roush (1978) Dean, R. A.; Keller, Gordon (1968), "Natural partial orders", Canadian Journal of Mathematics, 20: 535–554, doi:10.4153/CJM-1968-055-7, MR 0225686. Kim, K. H.; Roush, F. W. (1978), "Enumeration of isomorphism classes of semiorders", Journal of Combinatorics, Information &System Sciences, 3 (2): 58–61, MR 0538212.
Rabinovitch (1978). Rabinovitch, Issie (1978), "The dimension of semiorders", Journal of Combinatorial Theory, Series A, 25 (1): 50–61, doi:10.1016/0097-3165(78)90030-4, MR 0498294.
Fishburn & Trotter (1992). Fishburn, Peter C.; Trotter, W. T. (1992), "Linear extensions of semiorders: a maximization problem", Discrete Mathematics, 103 (1): 25–40, doi:10.1016/0012-365X(92)90036-F, MR 1171114.
Doignon & Falmagne (1997). Doignon, Jean-Paul; Falmagne, Jean-Claude (1997), "Well-graded families of relations", Discrete Mathematics, 173 (1–3): 35–44, doi:10.1016/S0012-365X(96)00095-7, MR 1468838.

ihs.ac.at

Sen (1971, Section 10, p. 314) Since Luce modelled indifference between x and y as "neither xRy nor yRx", while Sen modelled it as "both xRy and yRx", Sen's remark on p.314 is likely to mean the latter property. Sen, Amartya K. (July 1971), "Choice Functions and Revealed Preference" (PDF), The Review of Economic Studies, 38 (3): 307–317, doi:10.2307/2296384, JSTOR 2296384.

jstor.org

Luce (1956), p. 179. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
Luce (1956), Theorem 3 describes a more general situation in which the threshold for comparability between two utilities is a function of the utility rather than being identically 1; however, this does not lead to a different class of orderings. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
This result is typically credited to Scott & Suppes (1958); see, e.g., Rabinovitch (1977). Scott, Dana; Suppes, Patrick (1958), "Foundational aspects of theories of measurement", The Journal of Symbolic Logic, 23 (2): 113–128, doi:10.2307/2964389, JSTOR 2964389, MR 0115919. Rabinovitch, Issie (1977), "The Scott-Suppes theorem on semiorders", Journal of Mathematical Psychology, 15 (2): 209–212, doi:10.1016/0022-2496(77)90030-x, MR 0437404.
Luce (1956, p. 181) used four axioms, the first two of which combine asymmetry and the definition of incomparability, while each of the remaining two is equivalent to one of the above prohibition properties. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
Sen (1971, Section 10, p. 314) Since Luce modelled indifference between x and y as "neither xRy nor yRx", while Sen modelled it as "both xRy and yRx", Sen's remark on p.314 is likely to mean the latter property. Sen, Amartya K. (July 1971), "Choice Functions and Revealed Preference" (PDF), The Review of Economic Studies, 38 (3): 307–317, doi:10.2307/2296384, JSTOR 2296384.

semanticscholar.org

api.semanticscholar.org

Brightwell (1989). Brightwell, Graham R. (1989), "Semiorders and the 1/3–2/3 conjecture", Order, 5 (4): 369–380, doi:10.1007/BF00353656, S2CID 86860160.

uci.edu

imbs.uci.edu

Luce (1956), p. 179. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
Luce (1956), Theorem 3 describes a more general situation in which the threshold for comparability between two utilities is a function of the utility rather than being identically 1; however, this does not lead to a different class of orderings. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.
Luce (1956, p. 181) used four axioms, the first two of which combine asymmetry and the definition of incomparability, while each of the remaining two is equivalent to one of the above prohibition properties. Luce, R. Duncan (1956), "Semiorders and a theory of utility discrimination" (PDF), Econometrica, 24 (2): 178–191, doi:10.2307/1905751, JSTOR 1905751, MR 0078632.