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.

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 ;)

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. :(

Re: jonathanstrange's reply to my reply

Thanks for more comments. You're right you can re-scale things to be (A) 30 minutes VS 10 years (Z) ... at which point, why would anyone prefer A > Z ???

Part of the argument relies on this very vague definition of the eventual state of things. Temkin talks about an experience "just above 'barely worth living'" (Life-Z-1) ... and that is _so_ vague, and it means something _so_ different to different people. Given that people in concentration camps chose to continue living rather than kill themselves right away might make someone think "Life-Z-1" sucks, I would take 10 minutes of pleasure over that torture. Meanwhile I'm thinking what is just above 'barely worth living' (Life-Z-2) is just great -- the kind of basic enjoyment you have day to day without too much humor or excitement.

Philosophy is hard - I don't mean to poo-poo Temkin, I just never could grasp why transitivity was what he was attacking. As he says (something akin to) "there are several balls we're juggling in the air, and we must drop at least one to make it work" and he chooses to drop transitivity. And I don't see why he chose that 'ball'.

I can certainly see a case. Let's make it about money.

A is a single payment of $10,000.

B is two monthly payments of $5250. Or, in other words, a 5% improvement over A in total payments.

C is three monthly payments of $3675. Again, 5% better than B in sum.

I could completely see someone doing a pairwise comparison between A and B, and picking B for the 5% increase, because the time difference is not that important. Same again for B and C; it's only one more month for an extra 5%.

However, I could also see that same person comparing A and Z and deciding that instantaneous vs a period of two years is not worth the wait.

If a person is wealthy and doesn't need to spend that amount during the entire duration of Z, since they have other wealth to spend, they would likely choose Z for the higher return over the same time period.

So only a relative poverty would encourage the person to choose A.

Assuming they have unlimited life span. If not and their lifespan is uncertain, then the value of Z is reduced by the chance of not surviving long enough to profit from it.

If they can invest A and get a higher return than waiting for Z, then A is a more profitable choice.

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).

Vide Reinforcement Learning for StarCraft 2: https://deepmind.com/blog/article/AlphaStar-Grandmaster-leve...

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.

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.

A scalar is a single dimension

I love that this is both technically correct, and at the same time is a "move" in the "status game".

Everything is a move in the status game, including your comment and this one.