Karsten wrote: > Ben_Tilly@trepp.com wrote: > > > > Stephen Turnbull wrote: > [...] > > Keep this in mind the next time you cannot figure out how a group > > organization (eg a company) does not seem to make much > > sense. That *might* just be a reflection of the reality of how > > people behave in groups! > > First: wrong problem domain. Stephen was, AFAICT, speaking of > individual preferences. You are alluding to group or voting > preferences. Old hat. Arrow's Impossibility Theorem: > Many areas of software are priced by groups. To the extent that this is true, the usual mental models we have of individuals is not accurate. And yes, this is old hat, and yes, I knew that fact. To some extent I am being catankerous, and yes, I knew that as well. [...] > > > (1) "continuity", which implies that given two goods it's always > > > possible to make up for a loss of one by a sufficiently large gain > > > in the other. > > > > > Uh, please explain this? I thought I knew what continuity was > > inside out and backwards, and I certainly DO NOT see how the > > above statement is derivable from any of the several definitions > > that I am familiar with. > > Buy the econ book I mentioned before, Ben. Varian "Intermediate > Microeconomics". If you really want to practice some cranial > self-indulgence, you could graduate to Georgescu-Roegen.... > Thereby demonstrating that your understanding of mathematics is strongly biased by how it is applied in economics, and therefore you make several implicit assumptions without knowing that you are making those assumptions. > Substitution preferences for two goods. Say, for the benefit of the > current crowd, hacking and sex. > Yada, yada, yada. All of which requires continutity PLUS monotonicity. A *far* stronger hypothesis that fails at every local max or min. Plus to be able to assert that an arbitrary loss of one can be made up by a sufficiently large gain in the other, you must assume global conditions that are both unreasonable and false. Unless you are capable of replacing your need for sufficient oxygen to live with sufficiently large amounts of granite? I did not think so! Karsten, FYI, when I left graduate school I was only a few months away from my PhD in mathematics. Were it not for the fact that I am supporting my wife through medical school, I would have that degree, as useless as I feel it is. Therefore when it comes to a question of mathematical definitions, think twice about what I say before jumping to the conclusion that I do not understand a concept that comes up in first year calculus... [,..] > Plotted, you have a curve asymptotically approaching the sex axis where > hack approaches zero, and asymptotically approaching the hack axis where > sex approaches zero. If that is your graph, then you have far more stamina than I do! :-P Ben