Is your first objection that, in my scenario, the decrease in lambda occurs in the present year, while Leslie assumes that the decrease in lambda will not occur until 150 years from now? That’s a fair issue to raise. In my book, I work through numerical examples in detail (using Poisson processes instead of binomial processes), including an example using plausible numbers based on Leslie’s own scenario, and I also identify more general mathematical formulas. But I will try to defend the basic ideas here.
Suppose I amend my scenario as follows: the asteroid destroyer will not be completed until 150 years from now.
Recall that the Doomsday Argument (DA) invokes the Self-Sampling Assumption... (read 459 more words →)
Your use of the Jeffreys prior--P(T=n) ∝ 1/n--is the exception I mention: Gott (1994, 108) uses the Jeffreys prior.
I do not know how to get nice formatting into a comment, so I will try to address your question in an addendum to my original post.
Since the Doomsday Argument still is discussed often on Less Wrong, I would like to call attention to my new, short, self-published e-book, The Longevity Argument, which is a much-revised and much-expanded work that began with my paper, “Past Longevity as Evidence for the Future,” in the January 2009 issue of Philosophy of Science. In my judgment, my work provides a definitive refutation of the Doomsday Argument, identifying two elementary errors in the argument.
The first elementary error is that the Doomsday Argument conflates total duration and future duration. Although the Doomsday Argument’s Bayesian formalism is stated in terms of total
... (read 1355 more words →)I came to Less Wrong in 2009 because of posts I noticed on the Doomsday Argument, which I have written about in the peer-reviewed literature. Recently, I self-published a short e-book which addresses the subject along with other subjects that I think would be of interest to this community. But the book is not free—the price is $4—and I am concerned that I might be violating etiquette if I self-promote it in a Discussion post. (I do have four karma points.)
In a post I have drafted (but not submitted) for Less Wrong, I summarize part of my book; I also invite professional scholars and educators to email me to request a... (read more)
My paper, Past Longevity as Evidence for the Future, in the January 2009 issue of Philosophy of Science, contains a new refutation to the Doomsday Argument, without resort to SIA.
The paper argues that the Carter-Leslie Doomsday Argument conflates future longevity and total longevity. For example, the Doomsday Argument’s Bayesian formalism is stated in terms of total longevity, but plugs in prior probabilities for future longevity. My argument has some similarities to that in Dieks 2007, but does not rely on the Self-Sampling Assumption.
Your comment touches on the crux of the matter.
Of course, what is moving and what is fixed depends on the point of reference. In my analysis, I take the present as the fixed point of reference. When I vary the unknown Y, I am varying the unknown number of years ago when the last asteroid strike occurred. The time when the asteroid destroyer is built remains fixed at 150 years after the present.
Keep in mind the first error I noted in my post. Leslie starts with prior information and prior probabilities about future births, not total births. Leslie assumes that mankind will be able to colonize the galaxy 150 years--equivalently, roughly 20... (read more)