If you truncate the second lottery so that the outcome that you got from the first one doesn’t appear then you would not want to switch.
I am a little confused as I read this setup multiple times as “We draw a an outcome ‘jackpot’ from St. Petersburg. Then you get to choose between ‘jackpot’ and ‘heads goat, tails jackpot’”. If goat were just an arbitrary condolence price then it might happen that jackpot<goat and it might happen that jackpot>goat. But goat is not an unconnected outcome but the shittiest thing that St Petersburg can spit out. So jackpot>=goat and I am fine staying with jackpot. And I think the setup intends that the lotteries are drawn “separately”, that you can get a diffrent thing out. But in that case it escapes me how rolling one die would make me update in any direction about disconnected dice even if they have the same makeup. That somebody wins the lottery doesn’t make me update the value of lottery tickets upwards.
To my mind “half St. Petersburg” has a transfinite expectation value which is smaller than St. Petersburg. The main gist how the argument goes forward is imply that transfinite values breaking things sufficiently mean they need to have equal value. If you can’t say > and can’t say < one option is that the things are equal but another option is that they are incoparable or can’t be compared by those methods one wishes to use.
If you truncate the second lottery so that the outcome that you got from the first one doesn’t appear then you would not want to switch.
I am a little confused as I read this setup multiple times as “We draw a an outcome ‘jackpot’ from St. Petersburg. Then you get to choose between ‘jackpot’ and ‘heads goat, tails jackpot’”. If goat were just an arbitrary condolence price then it might happen that jackpot<goat and it might happen that jackpot>goat. But goat is not an unconnected outcome but the shittiest thing that St Petersburg can spit out. So jackpot>=goat and I am fine staying with jackpot. And I think the setup intends that the lotteries are drawn “separately”, that you can get a diffrent thing out. But in that case it escapes me how rolling one die would make me update in any direction about disconnected dice even if they have the same makeup. That somebody wins the lottery doesn’t make me update the value of lottery tickets upwards.
To my mind “half St. Petersburg” has a transfinite expectation value which is smaller than St. Petersburg. The main gist how the argument goes forward is imply that transfinite values breaking things sufficiently mean they need to have equal value. If you can’t say > and can’t say < one option is that the things are equal but another option is that they are incoparable or can’t be compared by those methods one wishes to use.