In the axiomatic theory of n-person bargaining, we show that there is a unique solution possessing properties: efficiency, symmetry, invariance under utility transformations, independence of irrelevant alternatives other than ideal point, and individual monotonicity on comparable domains. The solution obtained both extends and modifies the solution characterized by Kalai and Smorodinsky which is also known as Raiffa's solution, and is given a characterization as the lexicographic maxmin solution up to a normalization of utilities. The result can be translated to provide an axiomatic derivation of the Rawlsian lexmin choice function with a suitable redressing.