The matrix organization assumes that folks have some degree of tolerance for multiple bosses and that the source of authority can be split.
Perhaps the matrix can work well in some cultures; it surely cannot be implemented successfully in all cultures.
Luckily, “make the matrix work” in places like Taiwan, Israel, China and Spain is a great source of revenue for an OD consultant, even in bad times. Here are 3 examples where culture inhibits successful implementation of the matrix.
1-One tiger on the hill
There is a Chinese expression which says: 2 tigers cannot share a hill. In other words, one leader creates stability, many leaders create chaos. In cultures where this is the cultural belief system, matrix organizations (often imposed by a US or European HQ) are cess pools of manipulation. Many Asian cultures come to mind.
2-I win if you lose
Many cultures which see win win as a manifestation of imperial opulence and a manipulative game of the gentry; in such cultures, organizational life is hard ball, or a boxing match. The matrix brings out the very worst of these cultures. Survivalist cultures (Israel, S’pore) come to mind.
3-Cultures where problems are delegated up, not down
There are cultures where people actually believe that problems need to shifted up, not downloaded. These cultures see the boss as having privileges, and duties as well. These duties include making decisions about conflicting demands, not “tossing them down to the man in the trench”. Many African cultures come to mind.
In all of the above examples, implementing the matrix is, as another Chinese expression goes, playing the piano for the cow.