04-09-2004, 08:55 PM
If you plug everything in, you'll get that switching gets you the prize 2/3 of the time.
Isn't this the wrong conclusion? Or at least poorly worded? 2/3 seems to be your total probability of getting what you want by making the logical choices. Whether to switch or not depends on what you see the first time. If door number 2 is "bad", the choice of whether to stay with door number 1 or switch to door number 3 is random: 50% chance to win if you stay, 50% chance to win if you switch. If door number 2 is "good", the chance to win is 100% if you switch to door number 2, 0% if you stay on door number 1, and 0% if you switch to door number 3.
So, there is a 1/3 chance that the first door revealed to you is good, in which case you will take it and guarantee a win. There is a 2/3 chance that the first door revealed to you is bad, in which case you will randomly take one of the other two doors which will then each have a 1/2 chance of being good. Thus your total chance of getting the prize by this method is (2/3)*(1/2) + (1/3)*(1) = 2/3.
I'm not quite sure how this concept applies to the society discussion, and I have absolutely no background knowledge on any of this. It seems to me that a person would only be guaranteed to pick the more egalitarian system if they would consider the enhanced minimum place in that society to be a "good" result. Otherwise, the person would consider risking a system in which he could end up far worse off, if it gives a greater probability of him reaching the lifestyle he would be happy with. For an example with maybe less variables than an entire society, if a person was given the choice: either live in a slum or have a 50/50 chance between a ranch house or a cardboard box, the choice is not an automatic one. It is only an automatic choice under the assumption that living in the slum is considered a good outcome. If we improve the first case to 80% chance of living in a slum and 20% chance of living in a ranch house, it's still not an automatic choice.
Isn't this the wrong conclusion? Or at least poorly worded? 2/3 seems to be your total probability of getting what you want by making the logical choices. Whether to switch or not depends on what you see the first time. If door number 2 is "bad", the choice of whether to stay with door number 1 or switch to door number 3 is random: 50% chance to win if you stay, 50% chance to win if you switch. If door number 2 is "good", the chance to win is 100% if you switch to door number 2, 0% if you stay on door number 1, and 0% if you switch to door number 3.
So, there is a 1/3 chance that the first door revealed to you is good, in which case you will take it and guarantee a win. There is a 2/3 chance that the first door revealed to you is bad, in which case you will randomly take one of the other two doors which will then each have a 1/2 chance of being good. Thus your total chance of getting the prize by this method is (2/3)*(1/2) + (1/3)*(1) = 2/3.
I'm not quite sure how this concept applies to the society discussion, and I have absolutely no background knowledge on any of this. It seems to me that a person would only be guaranteed to pick the more egalitarian system if they would consider the enhanced minimum place in that society to be a "good" result. Otherwise, the person would consider risking a system in which he could end up far worse off, if it gives a greater probability of him reaching the lifestyle he would be happy with. For an example with maybe less variables than an entire society, if a person was given the choice: either live in a slum or have a 50/50 chance between a ranch house or a cardboard box, the choice is not an automatic one. It is only an automatic choice under the assumption that living in the slum is considered a good outcome. If we improve the first case to 80% chance of living in a slum and 20% chance of living in a ranch house, it's still not an automatic choice.