Why is the conditional operator right associative?

If it evaluated from left to right, it'd look like this:

z = ((a == b ? a : b) ? c : d);

That is, it would use the result of the first conditional (a or b) as the boolean condition of the second conditional. That doesn't make much sense: that's like saying:

int z, tmp;/* first conditional */if(a == b) tmp = a;else       tmp = b;/* second conditional */if(tmp) z = c;else    z = d;

While perhaps one day you'll want to do exactly this, it's far more likely that each ?: that follows is meant to add more conditions, like if / else if / else if / else, which is what the right-associative binding yields:

int z;/* first conditional */if(a == b)                          z = a;else /* second conditional */ if(b) z = c;else                                z = d;

In any language with a right associative ternary operator, you can stack them and build an if-elseif-elseif-else expression, like this:

val = a == 0 ? 1:      a == 1 ? 2:               4;

On the contrary, in languages with a left associative ternary operator (such as PHP, thanks @user786653) you need to explicitly enforce the aforementioned intent with parentheses:

<?php// This will output 't', not 'true'.echo (true ? 'true' : false ? 't' : 'f');// the following is a more obvious version of the same code as aboveecho ((true ? 'true' : false) ? 't' : 'f');// here, you can see that the first expression is evaluated to 'true', which// in turn evaluates to (bool)true, thus returning the true branch of the// second ternary expression.?>

You got the concept of associativity wrong.

When operator + is said to be left-associative, this means that a + b + c is equivalent to (a + b) + c, as opposed to a + (b + c).

The operator = is right-associative, which means that a = b = c is equivalent to a = (b = c), as opposed to (a = b) = c.

Associativity has nothing to do with the order of evaluation.