It is possible for a lottery to be +EV in dollars and -EV in utility due to the fact of diminishing marginal utility . As you get more of something, the value of gaining another of that thing goes down. The difference between owning 0 homes and owning your first home is substantial, but the difference between owning 99 homes and 100 homes is barely noticeable despite costing just as much money. This is as true of money as it is of everything else since the value of money is in its ability to purchase things (all of which have diminishing marginal utility).
The diminishing value of money is borne out in studies that look for the link between happiness/life satisfaction and income. Additional income almost always improves your life, but the rate of that improvement is approximately at the log scale (i.e. multiplying your income by 10 gives you +1 happiness, regardless of what your income was).
What does this all have to do with a lottery? Well, a lottery gives you a small probability of a massive number of dollars at a fixed cost. Since the hundred millionth dollar is worth much less to you than the first dollar, this can be a bet that has negative expected utility even when you would make money on average.
I agree that both DMV/DMU of money units is true and worth considering. However, I think it might be a bit more complex than that since I think one can make a case for network effects/economies of scale type aspects.
For example, the marginal value of the next dollar I add to my wealth today is pretty small. Clearly if I had 300 million additional dollars the MV of the next dollar absolutely will be smaller. But the MV/MU of having 50 million to put into my “this pays for my day to day life” and this other 100 million goes into some research projects I would like to see done but in no way could pursue that effectively now, and this other 100 million can go to some other useful (in my assessment) efforts that I might want to support and the remaining could be “wasted” on gifts and assistance to those I think deserve more than life has given them. So I think understanding just what the margin is matter a lot in this type of view.
It is possible for a lottery to be +EV in dollars and -EV in utility due to the fact of diminishing marginal utility . As you get more of something, the value of gaining another of that thing goes down. The difference between owning 0 homes and owning your first home is substantial, but the difference between owning 99 homes and 100 homes is barely noticeable despite costing just as much money. This is as true of money as it is of everything else since the value of money is in its ability to purchase things (all of which have diminishing marginal utility).
The diminishing value of money is borne out in studies that look for the link between happiness/life satisfaction and income. Additional income almost always improves your life, but the rate of that improvement is approximately at the log scale (i.e. multiplying your income by 10 gives you +1 happiness, regardless of what your income was).
What does this all have to do with a lottery? Well, a lottery gives you a small probability of a massive number of dollars at a fixed cost. Since the hundred millionth dollar is worth much less to you than the first dollar, this can be a bet that has negative expected utility even when you would make money on average.
I agree that both DMV/DMU of money units is true and worth considering. However, I think it might be a bit more complex than that since I think one can make a case for network effects/economies of scale type aspects.
For example, the marginal value of the next dollar I add to my wealth today is pretty small. Clearly if I had 300 million additional dollars the MV of the next dollar absolutely will be smaller. But the MV/MU of having 50 million to put into my “this pays for my day to day life” and this other 100 million goes into some research projects I would like to see done but in no way could pursue that effectively now, and this other 100 million can go to some other useful (in my assessment) efforts that I might want to support and the remaining could be “wasted” on gifts and assistance to those I think deserve more than life has given them. So I think understanding just what the margin is matter a lot in this type of view.