| bibtype |
J -
Journal Article
|
| ARLID |
0491011 |
| utime |
20240103220220.5 |
| mtime |
20180712235959.9 |
| SCOPUS |
85049434709 |
| WOS |
000442713800007 |
| DOI |
10.1016/j.jmateco.2018.06.005 |
| title
(primary) (eng) |
Continuous SSB representation of preferences |
| specification |
| page_count |
7 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0257019 |
| ISSN |
0304-4068 |
| title
|
Journal of Mathematical Economics |
| volume_id |
77 |
| volume |
1 (2018) |
| page_num |
59-65 |
| publisher |
|
|
| keyword |
SSB representation |
| keyword |
Fishburn preference relation |
| keyword |
Maximal preferred element |
| keyword |
Non-transitive preferences |
| author
(primary) |
| ARLID |
cav_un_auth*0234872 |
| name1 |
Pištěk |
| name2 |
Miroslav |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept (eng) |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department (eng) |
MTR |
| institution |
UTIA-B |
| full_dept |
Department of Decision Making Theory |
| country |
CZ |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| source |
|
| cas_special |
| project |
| ARLID |
cav_un_auth*0348851 |
| project_id |
GA17-08182S |
| agency |
GA ČR |
|
| abstract
(eng) |
We propose a topological variant of skew-symmetric bilinear (SSB) representation of preferences. First, semi-Fishburn relations are defined by assuming convexity and coherence, a newly considered topological property. We show that lower and upper semi-Fishburn relations admit the existence of a minimal element and a maximal element, respectively. Then axiom of ‘‘balance’’ is stated and we prove that a binary relation has a continuous SSB representation if and only if it is a balanced (lower and upper semi-)Fishburn relation. The relationship between the above definitions and the original axioms of (algebraic) SSB representation is fully discussed. Finally, by applying this theory to probability measures, we show the existence of a maximal preferred measure for an infinite set of pure outcomes, thus generalizing all available existence theorems of (algebraic) SSB representation. Note that by using this framework to, e.g., finitely additive measures, one may develop a non-probabilistic variant of SSB representation as well. |
| RIV |
AH |
| FORD0 |
50000 |
| FORD1 |
50200 |
| FORD2 |
50201 |
| reportyear |
2019 |
| num_of_auth |
1 |
| inst_support |
RVO:67985556 |
| permalink |
http://hdl.handle.net/11104/0285098 |
| confidential |
S |
| mrcbC86 |
3+4 Article Economics|Mathematics Interdisciplinary Applications|Social Sciences Mathematical Methods |
| mrcbT16-e |
ECONOMICS|MATHEMATICSINTERDISCIPLINARYAPPLICATIONS|SOCIALSCIENCESMATHEMATICALMETHODS |
| mrcbT16-j |
0.667 |
| mrcbT16-s |
1.081 |
| mrcbT16-B |
45.704 |
| mrcbT16-D |
Q3 |
| mrcbT16-E |
Q2 |
| arlyear |
2018 |
| mrcbU14 |
85049434709 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
000442713800007 WOS |
| mrcbU63 |
cav_un_epca*0257019 Journal of Mathematical Economics 0304-4068 1873-1538 Roč. 77 č. 1 2018 59 65 Elsevier |
|