Technical Note on the Joint Receipt of Quantities of a Single Good

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. Assuming 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 non-commutative but bisymmetric joint receipt operation with a representation arising from preferences over gambles.