Technical note on the joint receipt of quantities of a single good

✍ Scribed by Thierry Marchant; R.Duncan Luce

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 179 KB
• Volume: 47
• Category: Article
• ISSN: 0022-2496
• DOI: 10.1016/s0022-2496(02)00020-2

✦ Synopsis

The joint receipt of x and y is the fact of receiving them both. If x and y are objects that are valued, their joint receipt is valued as well. Assumming joint receipt is a binary operation that satisfies the conditions of extensive measurement, there is a numerical representation that is additive over joint receipt. We consider the case where x and y are quantities of the same infinitely divisible good. Different sets of assumptions are explored. Invariance with respect to multiplication proves to be interesting. Invariance with respect to addition yields a linear form. A relaxation of the latter yields an approximately linear form. Finally, we consider a noncommutative but bisymmetric joint-receipt operation with a representation arising from preferences over gambles.