Imagine there is a cause but several effects. Of course determinism is not held, but my question is about causality. If cause C has two mutually exclusive effects Y and Z, then at each given time either Y or Z are the effects (outcome, if you wish). Now, at one specific time T, let's say, Y is the outcome. WHY wasn't Z the outcome? In other words, why at T, it wasn't the other way around? My assumption is that there is no other cause that I don't know (i.e. hidden variable). In this scenario, is causality held? If yes, what is the cause of Y to be the outcome but not Z? If no, does it imply that QM is acausal at orthodox viewpoint, where no hidden variable is allowed?
Long comment (too long for a comment) regarding my preceding comment's link to
I think that might be analogous to what you're trying to think about in the following way, which is analogous in some ways, but very different in other ways...
You introduce C as a "cause" with mutually exclusive possible effects Y and Z. Instead, think of that cause C as a preparation procedure that prepares an entangled system (see that paper's title) with components Y and Z. And let's use the usual example that Y and Z are electrons, prepared by C such that the total system has spin-0, with one component spin +1/2 and the other -1/2.
Then these two "effects" are indeed mutually exclusive, but C has prepared them both. And that's what leads to some very weird causality issues.
Subsequent measurements of Y or Z's spin are non-deterministic: measurement of either gives you a 50-50 chance of a +1/2 outcome (and ditto for a -1/2 outcome). However, once you've measured either one of them, the outcome of a >>subsequent<< measurement of the other is guaranteed. If the first outcome is, say, +1/2, then the second outcome is always -1/2. So you might be tempted to say that the first "caused" the second.
But note how I emphasized >>subsequent<<. That implies you can know that one measurement occurred before the other. However, before performing either measurement, you can separate the two Y and Z electrons by a large distance d, and then perform both measurements almost simultaneously, by a time difference t such that d>ct (c the speed of light).
That's called a space-like separation, and means there's no possible communication between the two measurement events. So one cannot cause the other. People who don't want to believe that suggest faster-than-light communication. But that's not even the worst of their troubles.
What's really worst is that for space-like separated events, one observer can see one event occurring before the other, whereas another observer can see it the other-way-round. There's no such thing as my previously-emphasized >>subsequent<<. So you can't possibly say one event caused the other, because you can't even say which one came first. And this little conundrum isn't just theoretical; it's been experimentally verified time-after-time (starting in the early 1980's with Alain Aspect's famous experiments).
So what can you say??? The only thing that caused anything is the original C preparation event (it's in the unambiguous past, aka past light cone, of both Y and Z). But what did C "cause"?... the subsequent Y- and Z-measurement outcomes are non-deterministic, so C can't possibly have caused them. What C did cause is the correlation between them.
So how can you cause a correlation without causing the correlated events??? That remains an unanswered question. This space-time order-of-events confusion gives an entirely more subtle connotation to the idea of causality, with mathematical correlations themselves as "things" that can be "caused". So, rather than your contrived situation, I'd suggest you instead try focusing on the interpretation of these very concrete experimentally verified phenomena. Reality's a whole lot more mysterious and fascinating than fantasy.
If C is a cause in a non-deterministic system leading to mutually exclusive and jointly exhaustive outcomes Y and Z, and at time T, C causes Y, to answer the question why Y and not Z will inevitably be a function of the context. That is to say, your example of a causal system is an abstraction, and the only answer in the abstract sense is that by definition you established that the system was non-deterministic. Why Y and not Z at T is simply a result of the fact that you defined the system's effects Y and Z as mutually exclusive and non-deterministic, and therefore it would be a contradiction for Y and Z to happen simultaneously since you presume Y happened.
That being said, return from the abstraction to a concrete example.
Flipping a fair coin and letting it land on a face will yield a mutually exclusive and jointly exhaustive outcome when it is either heads or tails. C is defined as 'flipping a fair coin and letting it land on a face' and Y and Z are defined as 'It lands heads up' and 'It lands tails up'. In this context, your question is why is it at time T (which is some value over which the variable of time ranges) is the outcome heads and not tails. In this case, you need to differentiate between the physics of the coin toss from the logical events of the coin toss, which is yet another level moving from an abstract state of mental events like coin tosses and considering the material states of the coin toss itself, that is to say, the atoms, and friction, and gravity at play. In the case of a coin toss, how come a heads and not tails is because the material system is not a deterministic system and instead stochastic. The factors at play for predicting a coin toss would include the actual distribution of mass in a coin, the application of force, the results of forces on and in the rigid body including wind resistance, the normal force, tension, compression, and so on. All told, to predict this is computationally impossible because of phenomena such as sensitive dependence of initial conditions and permutational explosion. But, experience shows that either a head or a tail lands, and so in this regard it is empircal fact, rather than a logical argument.
To understand it from a rational way, one need look at the nature of the coin, that is to understand that the properties of the coin are such that the two faces of the coin are visible one at a time because of the configuration of the lump of metal that is the coin. Both the heads and the tails are surfaces that are facing opposite of each other in space, and the paths the light may take to the eye are such that they reflect in opposite directions. In addition, one can understand how the results are disjoint and exhaustive by the way gravity and mass works such that the center of mass seeks the lowest level and the edge of the coin rarely stands as seen by trial and error.