4 ms·

Single dimension fallacy might be a good alternative name. I'd add that often things don't have a single ordering of goodness at all. Like a tomato sauce: some

by dmos62 7y ago

Single dimension fallacy might be a good alternative name. I'd add that often things don't have a single ordering of goodness at all. Like a tomato sauce: some people like it thick, others watery, others chunky; so it actually has at least 3 orderings.

moron4hire 7y ago
A scalar is a single dimension
- andrewprock 7y ago
  I love that this is both technically correct, and at the same time is a "move" in the "status game".
  - CuriouslyC 7y ago
    Everything is a move in the status game, including your comment and this one.
jonathanstrange 7y ago
Well, the general solution of economists is to assume that every person has their own ordering. This doesn't work for Spectrum Arguments by Larry Temkin, though. A typical argument goes like this: Suppose alternative A gives you an extremely high level of well-being for a month. B brings a little bit less well-being than A for two months. C a little bit less well-being for four months, and so forth. In pairwise comparisons you judge that B is better than A, C is better than B, and so on. Yet at some point, say, Z you will consider A better than Z if you compare A to Z, but you will continue to consider Z better than Y. Therefore, "better than" is not transitive. People have written a lot of articles on how to solve these types of puzzles, which can be formulated many different evaluative domains. They always involve two or more criteria.
- stared 7y ago
  Once you go to multidimensional vector spaces, you don't need order. For example, the classic rock-paper-scissors can be modeled with 3 points in 2d. This has fundamental implications, as many activities do have this cyclical parts (see also such decomposition for vector fields, https://en.wikipedia.org/wiki/Helmholtz_decomposition https://en.wikipedia.org/wiki/Helmholtz_decomposition). Vide Reinforcement Learning for StarCraft 2: https://deepmind.com/blog/article/AlphaStar-Grandmaster-level-in-StarCraft-II-using-multi-agent-reinforcement-learning https://deepmind.com/blog/article/AlphaStar-Grandmaster-leve...
  - TeMPOraL 7y ago
    Unfortunately time is one-dimensional, which creates a demand for ordering (I wouldn't be surprised if all demand for order actually came from that fact). I may not need ordering in 3D space, up until the moment I need to grab a few things - then I have to decide on an order, because grabbing is sequential.
- yboris 7y ago
  I've heard Temkin give talks attacking transitivity and I never buy it. Most of his examples involve infinity which is problematic. In the example you share, I think all it points out is that our ability to compare things (psychologically) is broken: we may think A < B < C < ... X < Z in pairwise comparisons, but something goes silly when we compare A and Z and think A > Z. I strongly think this is a bias akin to scope insensitivity. By the time we get to Z we're likely talking about HUNDREDS OF YEARS of experience, and we just are not psychologically fit to make such a comparison. So I don't think Temkin is right. PS - Derek Parfit and the "repugnant conclusion" ... not so repugnant if you think about it right ;)
  - jonathanstrange 7y ago
    That's a common reply. However, you can simply adopt these examples to fit whatever intuitions someone has, e.g. give Z a duration of thirty years and adjust the other intervals accordingly. Or give it a duration of 10 years and start with 30 minutes. Likewise, you can change the levels, replace well being with money or health or pleasure, and so on. Bear in mind that Temkin only needs one counter-example. I personally think we're psychologically fit to make these comparisons and that his arguments go through. It's not very surprising, if you take into account that in multicriteria decision making cases similar to these have been analysed and discussed since the 60s, e.g. by Peter C. Fishburn and by the French/Belgium tradition. You can solve these without giving up transitivity. Technically, even just incompleteness solves the issue. My own favorite solution is lexicographic, but apparently not many reviewers like it. :(
Psyladine 7y ago
If I don't care, it doesn't exist? And in all 3 cases you have putrid to fresh to masterfully made in terms of composition, quality of ingredients, age, etc...valuation can't be the composite of 'goodness', or we'd all become utility monsters chasing bitcoin.

by dmos62 7y ago

moron4hire 7y ago

A scalar is a single dimension

andrewprock 7y ago
I love that this is both technically correct, and at the same time is a "move" in the "status game".
- CuriouslyC 7y ago
  Everything is a move in the status game, including your comment and this one.

jonathanstrange 7y ago

Well, the general solution of economists is to assume that every person has their own ordering. This doesn't work for Spectrum Arguments by Larry Temkin, though. A typical argument goes like this: Suppose alternative A gives you an extremely high level of well-being for a month. B brings a little bit less well-being than A for two months. C a little bit less well-being for four months, and so forth. In pairwise comparisons you judge that B is better than A, C is better than B, and so on. Yet at some point, say, Z you will consider A better than Z if you compare A to Z, but you will continue to consider Z better than Y. Therefore, "better than" is not transitive. People have written a lot of articles on how to solve these types of puzzles, which can be formulated many different evaluative domains. They always involve two or more criteria.

stared 7y ago
Once you go to multidimensional vector spaces, you don't need order. For example, the classic rock-paper-scissors can be modeled with 3 points in 2d. This has fundamental implications, as many activities do have this cyclical parts (see also such decomposition for vector fields, https://en.wikipedia.org/wiki/Helmholtz_decomposition https://en.wikipedia.org/wiki/Helmholtz_decomposition). Vide Reinforcement Learning for StarCraft 2: https://deepmind.com/blog/article/AlphaStar-Grandmaster-level-in-StarCraft-II-using-multi-agent-reinforcement-learning https://deepmind.com/blog/article/AlphaStar-Grandmaster-leve...
- TeMPOraL 7y ago
  Unfortunately time is one-dimensional, which creates a demand for ordering (I wouldn't be surprised if all demand for order actually came from that fact). I may not need ordering in 3D space, up until the moment I need to grab a few things - then I have to decide on an order, because grabbing is sequential.
yboris 7y ago
I've heard Temkin give talks attacking transitivity and I never buy it. Most of his examples involve infinity which is problematic. In the example you share, I think all it points out is that our ability to compare things (psychologically) is broken: we may think A < B < C < ... X < Z in pairwise comparisons, but something goes silly when we compare A and Z and think A > Z. I strongly think this is a bias akin to scope insensitivity. By the time we get to Z we're likely talking about HUNDREDS OF YEARS of experience, and we just are not psychologically fit to make such a comparison. So I don't think Temkin is right. PS - Derek Parfit and the "repugnant conclusion" ... not so repugnant if you think about it right ;)
- jonathanstrange 7y ago
  That's a common reply. However, you can simply adopt these examples to fit whatever intuitions someone has, e.g. give Z a duration of thirty years and adjust the other intervals accordingly. Or give it a duration of 10 years and start with 30 minutes. Likewise, you can change the levels, replace well being with money or health or pleasure, and so on. Bear in mind that Temkin only needs one counter-example. I personally think we're psychologically fit to make these comparisons and that his arguments go through. It's not very surprising, if you take into account that in multicriteria decision making cases similar to these have been analysed and discussed since the 60s, e.g. by Peter C. Fishburn and by the French/Belgium tradition. You can solve these without giving up transitivity. Technically, even just incompleteness solves the issue. My own favorite solution is lexicographic, but apparently not many reviewers like it. :(

Psyladine 7y ago

If I don't care, it doesn't exist? And in all 3 cases you have putrid to fresh to masterfully made in terms of composition, quality of ingredients, age, etc...valuation can't be the composite of 'goodness', or we'd all become utility monsters chasing bitcoin.