Why are JavaScript negative numbers not always true or false?

In most systems, non-zero values are considered a true value, but that doesn't necessarily mean that they are the same true value as true. Thus, -1 == true doesn't necessarily hold, but -1 can still be considered a true value since it is non-zero.

Really, though, you shouldn't be comparing integers to booleans if you can avoid it.

In the first two cases, the boolean is cast to a number - 1 for true and 0 for false. In the final case, it is a number that is cast to a boolean and any number except for 0 and NaN will cast to true. So your test cases are really more like this:

-1 == 1; // false
-1 == 0; // false
true ? true : false; // true

The same would be true of any number that isn't 0 or 1.

For more detail, read the ECMAScript documentation. From the 3rd edition [PDF], section 11.9.3 The Abstract Equality Comparison Algorithm:

19. If Type(y) is Boolean, return the result of the comparison x == ToNumber(y).

It's worth giving the full algorithm a read because other types can cause worse gotchas.