The following post aims to explain why the diagram below is a proof without words that the Kaldor-Hicks criterion for an improvement in the economy can be non-transitive. This is in response to a request for help from a student of mine who made the request on the Facebook group...
Edit: Pre-print available here https://arxiv.org/abs/2005.01563 Also link to earlier post here https://www.alignmentforum.org/posts/5bd75cc58225bf06703753a9/formal-open-problem-in-decision-theory?fbclid=IwAR2u-8RVfnfRtEo51vag5vYWAcfkoHDJAr6aydVGqYVmEq0oxnjwR0Ee34E Scott Garrabrant has raised the question of whether there is any topological space A for which the exponential topology on [0,1]A exists and such that there is a continuous surjection g:A→[0,1]A. In cited pre-print above I claim to...
The goal of this blog-post is to explore the intuition that drives the feeling that the agent who arrives at the conclusion that they should pay Pascal's mugger is being unreasonable, and whether this can be tied in with the analysis of a logical inductor as an algorithm not exploitable...
Point C is a particular combination of utilities. The particular combination of utilities is not attainable via re-distribution while the economy is in state a. If a change took place so that the economy was now in state c, then point C would be attainable by re-distribution.
(And there is a point common to both the curves a and c, but just from knowing that the utilities of Citizens 1 and 2 were at that particular point wouldn't allow you to know whether the economy is in state a or c, that would be extra information, and this extra information would be necessary in order to know which other points you could get to via re-distribution from your current situation.)
A Kaldor-Hicks improvement is a change of state of the economy from A to B such that B can be converted into a Pareto improvement by re-distribution, and such that A cannot be converted into a Pareto improvement of B by re-distribution.
Every labelled point on that diagram permits re-distribution (because it lies on a curve).
Each curve corresponds to a "state of the economy". To get to a state where you could start re-distributing by moving along a different curve to the one you were originally moving along would require a change of state. When re-distributing, you can only move along one curve corresponding to the current state of the economy.
Oh yes, and when the economy is in a given state you are only allowed to move along one curve. The curves are allowed to intersect, but you can't change which curve you are moving along when doing re-distribution. The explanation I just added of why the curves are allowed to intersect may help.
All of the curves represent states of the economy such that a re-distribution of resources will correspond to a movement along that curve. A change in state of the economy can be explained by a change in technological knowledge, a change in climate, the discovery of a deposit of a particular resource, stuff like that. "Re-allocation of resources" can correspond to re-allocation of quite a complex bundle of goods. The projections of the points on the co-ordinate axes merely represent the utilities of each of the two citizens, where only the order relations between utilities matters.
The following post aims to explain why the diagram below is a proof without words that the Kaldor-Hicks criterion for an improvement in the economy can be non-transitive. This is in response to a request for help from a student of mine who made the request on the Facebook group Bountied Rationality, and hoped that a LessWrong post could be drawn up explaining the matter in detail.
Let me briefly explain the meaning of the terms. A Pareto improvement in an economy is a change in the state of the economy where every individual in the economy is at least as well off as before, and some individuals are strictly better off. A... (read 331 more words →)
Let me be sure I understand what you're saying? If someone wants to argue on the internet that abortion should be prohibited by the criminal law, or that there isn't any moral obligation to be vegan, then I shouldn't moralize about the fact that I disagree with them? I mean, I can think of ways that you could maybe argue that point, I just want to make sure I understand you though.
My main thought would be that you consider the risk factors of physical intimacy but possibly ought to look a bit more closely at whether there are risk factors associated with avoiding physical intimacy (are you sure that that's not harmful as well if taken to sufficient lengths?)
My main thought would be that you consider the risk factors of physical intimacy but possibly ought to look a bit more closely at whether there are risk factors associated with avoiding physical intimacy (are you sure that that's not harmful as well if taken to sufficient lengths?)
My main thought would be that you consider the risk factors of physical intimacy but possibly ought to look a bit more closely at whether there are risk factors associated with avoiding physical intimacy (are you sure that that's not harmful as well if taken to sufficient lengths?)
Edit: Pre-print available here https://arxiv.org/abs/2005.01563
Also link to earlier post here https://www.alignmentforum.org/posts/5bd75cc58225bf06703753a9/formal-open-problem-in-decision-theory?fbclid=IwAR2u-8RVfnfRtEo51vag5vYWAcfkoHDJAr6aydVGqYVmEq0oxnjwR0Ee34E
Scott Garrabrant has raised the question of whether there is any topological space for which the exponential topology on exists and such that there is a continuous surjection . In cited pre-print above I claim to resolve this question negatively in ZFC (using techniques of inner model theory, Skolem hull arguments, and some Reverse Mathematics results presented by Stephen Simpson in "Subsystems of Second Order Arithmetic") but also to give an example of a pair of spaces with the same carrier set, topology on finer than that on , and a continuous surjection... (read 368 more words →)
The goal of this blog-post is to explore the intuition that drives the feeling that the agent who arrives at the conclusion that they should pay Pascal's mugger is being unreasonable, and whether this can be tied in with the analysis of a logical inductor as an algorithm not exploitable by an efficiently computable trader. An analysis of this intuition may help us to design the decision theory of a future Friendly AI so that it is not vulnerable to being Pascal-mugged, which is plausibly a desirable goal from the point of view of obtaining behaviour in alignment with our values.
So, then, consider the following conversation that I recently had with... (read 466 more words →)
I made the following observation to Chris on Facebook which he encouraged me to post here.
My point was basically just that, in reply to the statement "If we don't have such a model to reject, the statement will be tautological", it is in fact true relative to the standard semantics for first-order languages with equality that there is indeed no model-combined-with-an-interpretation-of-the-free-variables for which "x=x" comes out false. That is to say, relative to the standard semantics the formula is indeed a "logical truth" in that sense, although we usually only say "tautology" for formulas that are tautologies in propositional logic (that is, true under every Boolean valuation, a truth-valuation of all subformulas... (read more)