Parfait
peace.
I had a story of private providence (I believe it…) I have a very brilliant friend, just last week I argued with him about whether there is any point in going to vote in elections and in any activity whose benefit is contingent on collectivity. He actually argued the argument of Parfit that his honor brought in column 252, and only now did I see that his honor extended it with good taste. I have a few questions, mainly the argument and his honor’s argument.
A. Parfitt assumes that the greater statistical benefit is worth the lesser expense of the election. My friend proved it this way: If it is certain that someone will win the election, it is worth the expense of 100,000 people (for example), and everyone understands this (that if everyone votes, it is equal), then a chance of one in 100,000 is worth the expense of one person. I argued: Just as I would not buy a lottery ticket that had a one in a million chance that I would win $2,000,000, even if the price was $1, even though I would buy the ticket that would surely win $1,900,000 or more. He argued that the very doubt reduces the value of money, and that apart from the statistical probability that it is one in a million, this statistical money is actually worth less, because for example, I cannot buy anything with this money because it is doubtful, I cannot go to a restaurant now on the basis that I will pay for it when I win. So the very doubt reduces the value of money. (I thought this was an answer to the St. Petersburg paradox, but no, because if the money I could win is infinite, that doesn’t excuse anything.) And if so, can I also claim this in elections? So he answered that depending on whether my candidate doesn’t win, I don’t lose anything, but rather, I don’t gain anything, so I’m right. However, if I lose to the other side (let’s say the amount I won’t gain), then that’s not a correct consideration because the provided benefit is certainly worth less than the certain benefit, but there is a provided loss against it. Is all of this true? And if not, what was he wrong about?
on. Is this very argument of Parfitt’s (and Pascal’s) correct? When I have two options, either to save one person for sure or to save two people 50%, are both exactly equal? Or does certainty also have value?
third. According to his honor, if the chance is zero and the benefit is not expected, then there is no need to think about the distribution anymore (I understand: when the person does not really think that he will win). Is there a clear definition for this? And is there a sharp limit that is difficult to place, or does it go gradually, for example, a 20% chance, the person thinks that he will probably not win, but of course the benefit is still expected. Is it worth investing 20% of what is definitely worth investing, or does it decrease gradually (for example, for 20%, 15% investment, for 10%, 5% investment)? I would be very happy if his honor would address my desolating creative arguments.
First, why don’t you post this as a talkback to that column? And here are the references of my honor (full of worlds):
A. I don’t understand his argument and your question. In elections, it’s not about a small impact, but about a tiny chance of having an impact. Therefore, St. Petersburg applies here as well.
B. I don’t know the answer to that. On the surface, it looks the same.
C. Of course there is no sharp boundary.
A. I didn't post it because I thought that column was already out of date because it was written a few years ago (I didn't really know that his honor was all over the world and his hands wandered everywhere and he bothered to reply to everyone on Talkback)
B. What he wrote on the surface seems to be the same. I didn't ask if it was the same thing or not. I want to know if the argument that the investment is equal to the sextist distribution from which Pascal and Parfitt proceed from this assumption should be questioned (as I apparently saw in that column that you were hinting at it but I couldn't find it now)
C. At the beginning of my words, what you wrote about St. Petersburg also applies to this, of course. I ask if we don't accept your words and assume, as Pascal and Parfitt said, that they don't distinguish between expected benefit or not, that in any case statistical probability is not the whole picture, since in the end the actual money provided is actually worth less than the certain money, and therefore, in addition to probability, another consideration must be taken into account.
In any case, thank you very much for taking the time to reply to me.
B. I didn't understand. I answered you. Besides, isn't that what I showed from St. Petersburg? That expectancy is not necessarily a good criterion. Maybe you could explain the question better.
C. I don't see any logic in this except for St. Petersburg. That could be another explanation why expectancy is not a criterion. So what's new?
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