tag:blogger.com,1999:blog-264226589944705290.post2471563540517045021..comments2023-03-24T08:16:45.600-07:00Comments on God Plays Dice: Hyperbolic discountingMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-264226589944705290.post-87311777451768051232009-04-09T15:33:00.000-07:002009-04-09T15:33:00.000-07:00I came across picoeconomics.com, and this article ...I came across picoeconomics.com, and this article recently:<BR/><BR/>Uncertainty as Wealth<BR/>http://www.picoeconomics.com/articles.htm<BR/><BR/>Nice little graph on the site illustrating the difference in discount curves.Evelynnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-80472303604621913372008-02-26T19:46:00.000-08:002008-02-26T19:46:00.000-08:00johann richter made exactly the point I should hav...johann richter made exactly the point I should have liked to make: given that the risk of not surviving to realize the gain increases with length of time, it sounds like this "discounting" is just about right.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-43073019721010076312008-02-26T10:09:00.000-08:002008-02-26T10:09:00.000-08:00The "correct" discount rate depends on far more th...The "correct" discount rate depends on far more than inflation. It should depend on "risk", eg of dying and not getting any use of the money, and of what economists call the pure rate of time reference.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-53347448525669504752008-02-26T10:06:00.000-08:002008-02-26T10:06:00.000-08:00That's a great point, Greg. Is there a "big numbe...That's a great point, Greg. Is there a "big number" effect in play? That is, would people make more of a mistake when they choose between 16 and 24 weeks, or between 4 and 6 months? Between 50 and 100 weeks or between 1 and 2 years?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-47261812473455026592008-02-26T07:30:00.000-08:002008-02-26T07:30:00.000-08:00Good to see this worked out. However, I disagree ...Good to see this worked out. However, I disagree that the way to equate the two models is to have them agree to first order at time zero. <BR/><BR/>In that case, the person would never over-value nearer options; instead they would always over-value the further of the two options, at an amount proportional to the distance of the choice.<BR/><BR/>I think its more realistic to have the hyperbola dip below the exponential for awhile (the 'immediate gratification' zone), and then cross it at some reasonably far away point (the 'correct value' distance). The value of this point is probably extremely variable, and might even have to do with pesky things like whether the question is phrased in 'weeks' versus 'years'.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-16888797851436492062008-02-25T15:54:00.000-08:002008-02-25T15:54:00.000-08:00And information too. Assume we have 2 independent ...And information too. Assume we have 2 independent events, one has probability p and the other q. When we learn that the first event happened, we are surprised by the amount s(p), and when we learn that the other happened, we are surprised by s(q), so the total surprise is s(p)+s(q) and this should be the surprise of the combined event that is s(pq), so the surprise is (up to a costant factor) a logarithm of probability, and the expected value of surprise of a finite probability space is its entropy!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-52922359053383770582008-02-25T15:28:00.000-08:002008-02-25T15:28:00.000-08:00Sounds are certainly perceived logarithmically, bo...Sounds are certainly perceived logarithmically, both the tone scale (the even tuning) and loudness (decibels) are logarithmic scales.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-68720287186116898632008-02-25T14:21:00.000-08:002008-02-25T14:21:00.000-08:00That's a great point: people think logarithmically...That's a great point: people think logarithmically. I'd even go farther and say that people <I>perceive</I> logarithmically.<BR/><BR/>We know it's true for sound, for not just on instance, but two! A constant increase in (perceived) loudness is a constant <I>multiple</I> in power, and a constant increase in (perceived) pitch is a constant multiple in frequency.Anonymousnoreply@blogger.com