qwertyasdef

How do bounded utility functions work if you are uncertain how close to the bound your utility is?

I think you're right that your pennies become more valuable the less you have. Suppose you start with money and your utility function is . Assuming the original lottery was not worth playing, then , which rearranges to . This can be though of as saying the average slope of the utility function from to is greater than some constant .

For the second lottery, each ticket you buy means you have less money. Then the utility cost of the first lottery ticket is , the second , the third, and so on. If the first ticket is worth buying, then so . This means the average slope of the utility function from to is less than the average slope from to , so if the utility function is continuous, there must be some other point in the interval where the slope is greater than average. This corresponds to a ticket that is no longer worth buying because it's an even worse deal than the single ticket from the original lottery.

Also note that the value of is completely arbitrary and irrelevant to the argument, so I think this should still avoid the Egyptology objection.

If human behaviour is fully determined by the laws of the universe, then you have no choice in whether you assign moral blame or not so it doesn't make sense to discuss whether we should or shouldn't do that.