alyssavance comments on Expected utility without the independence axiom - Less Wrong

9 Post author: Stuart_Armstrong 28 October 2009 02:40PM

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Comment author: alyssavance 28 October 2009 09:25:59PM *  2 points [-]

"When you buy a chocolate bar for a dollar, that "preference of a chocolate bar to a dollar" does not somehow mean that you are willing to trade every dollar you have for a chocolate bar, nor have you legally obligated yourself to redeem chocolate bars for dollars on demand (as a money pump would require), nor does anyone expect that you will trade the rest of your dollars this way."

Under normal circumstances, this is true, because the situation has changed after I bought the chocolate bar: I now have an additional chocolate bar, or (more likely) an additional bar's worth of chocolate in my stomach. My preferences change, because the situation has changed.

However, after you have bought A, and swapped A for B, and sold B, you have not gained anything (such as a chocolate bar, or a full stomach), and you have not lost anything (such as a dollar); you are in precisely the same position that you were before. Hence, consistency dictates that you should make the same decision as you did before. If, after buying the chocolate bar, it fell down a well, and another dollar was added to my bank account because of the chocolate bar insurance I bought, then yes, I should keep buying chocolate bars forever if I want to be consistent (assuming that there is no cost to my time, which there essentially isn't in this case).