But this only makes any sense if you accept that, if you could somehow quantify happiness, that it is a quantity on which the operation of summation has meaning.

But happiness is not even a quantity, it is a direction. It is not a destination, it is a journey. Those who arrive at a destination where they think they will find happiness, without having a new destination to seek, inevitably become stagnant and miserable. You can't define a linear sum on such a phenomenon.