In C++, an expression like 1 is a perfectly valid statement with no side effects. You could very feasibly write this function:
void f() {
    1;
}
In fact, even this is correct.
void f() {
    ;;;;
}
A literal statement evaluates its arguments but does nothing more. The system views 1; as being just like func();. The only difference is that while func(); would logically have some side effects, 1; does not so it ends up being a no-op. The ternary operator evaluates like an if-statement, so the second form is only evaluated if the operand is true. Thus:
(i > 0) ? i-- : 1;
If i is greater than 0, the second form is evaluated. When it is evaluated, it carries its side effect, which decrements i by 1. Otherwise, the third form is evaluated, which does nothing. Although this block of code works, it is not incredibly readable, so while it's nice toy code a real if-statement is ideal for situations like this. For the same reason, this line would have the same effect but be frowned upon for being equally unreadable.
((i > 0) && (i--)) || 1;
Assuming you didn't overwrite the boolean operators, this code will short-circuit and behave like the ternary operator. If i is not greater than 0, then the && need not evaluate its second operand since the && is false, but the || must since it might be true. Inversely, if i is greater than 0, the && needs to evaluate but the || already knows it's true.