Could that domain not just be really small, such that the ratio of outcomes you’d accept the bet at get closer and closer to 1? It seems like the premise that the discounting rate stays constant over a large interval (so we get the extreme effects from exponential discounting) is doing the work in your argument, but I don’t see how it’s substantiated.
Yeah, this is a good point. In the mathematical argument it simply has to be assumed as an input that the response is the same over at least a several-thousand-dollar span. But does that seem to bear out in the data about real humans? I think so. If you have a bunch of people who exhibit similar apparent risk aversion, spread out over a variety of wealths and dispositions, it seems like it would be a miracle for them to all be just below the level of wealth where they’d change their minds.
Could that domain not just be really small, such that the ratio of outcomes you’d accept the bet at get closer and closer to 1? It seems like the premise that the discounting rate stays constant over a large interval (so we get the extreme effects from exponential discounting) is doing the work in your argument, but I don’t see how it’s substantiated.
Yeah, this is a good point. In the mathematical argument it simply has to be assumed as an input that the response is the same over at least a several-thousand-dollar span. But does that seem to bear out in the data about real humans? I think so. If you have a bunch of people who exhibit similar apparent risk aversion, spread out over a variety of wealths and dispositions, it seems like it would be a miracle for them to all be just below the level of wealth where they’d change their minds.