When the cambist showed that a prisoner was valued more than the king, he was essentially using happiness to compare value. The king valued his happiness more than his life. The jailers valued the life of the prisoner more than his happiness. By using that, he implicitly assumed that the king values his own happiness the same as the jailers value the happiness of the prisoner. This couldn't be more wrong. The king wants to be happy, but the jailers want the prisoner to be unhappy. The values weren't just different. They had opposite signs.
- I find the argument in that case unconvincing as well, but for different reasons. If I am understanding the argument correctly, Olaf's thought was that the king being more spendthrift with his lifespan than the prisoner implies that he values it less — that he would pay twenty-four hours of lifespan for an indulgence which the prisoner would only be willing to pay nineteen-and-three-quarters hours. What seems more likely to be the case, however, is that the price in lifespan of the pleasures which the king buys is inflated for the prisoner by the threat of punishment, making many of the pleasures that the king sacrifices his allotted share of days to enjoy too expensive for the prisoner to be willing to do the same.