Hacker News Reader

Comment by yummyfajitas | Hacker News Reader

How do you scale that up? Say you implement your system. Now the output of the system is a Map[Student,List[Project]] rather than a Map[Student,Int]. How do I compare schools, determine whether a school is doing it's job, or do the same thing for students?

Ultimately all consistent objective decisionmaking processes [1] must come down to a single number - that's a simple exercise in undergrad topology. Anything else will be either subjective or inconsistent (i.e., we prefer A to B, and B to C, but prefer C to A).

So what are you proposing? A different format/syllabus for standardized tests, a subjective testing procedure, or an inconsistent one?

[1] On a countable set of choices. Things get weird on uncountable sets.

View on HN

It's very arguable that every decisionmaking process must come down to a number, as we're talking about people and not cattle.

In this perspective, having people working on projects would be an appreciation of the "multidimensional" nature of people.

After all, contemporarily, psychology started to think of multiple intelligences rather than a single one. If we assume this is true, what's the sense of assigning a single number to a person? Either it's false that multiple intelligences exist, or it's useless to single-dimensinally evaluate them. Then, let's start to assign 10 numbers instead of one.

I don't say that single-dimensional ratings are inherently wrong, but just that they're too narrow minded. "Scaling up" such procedures would mean scale up something wrong and inefficient; it's not real scaling up.

I would propose to throw standardized tests in the garbage, and try novel approaches in the evaluation processes of people; I find hard to believe that assigning a number to a person is the only possible (and practical) perspective.

It's very arguable that every decisionmaking process must come down to a number, as we're talking about people and not cattle.

It's not debatable if you believe in the axiom of induction (or the axiom of choice for countably infinite sets).

Theorem: If there is a total order (a consistent decisionmaking process) on the set of people (or any countable set), then there exists an order preserving function f: People->Real numbers.

Sketch of proof: Start with an arbitrary person A. Define the ranking function f(A)=0. Choose an arbitrary person besides A, call them B. If B > A then f(B)=1, else if B = a then f(B)=0 else f(B) = -1. Choose a third person C, different from A and B. If C > max(A,B) define F(C) = f(max(A,B))+1. If A < C < B or B < C < A define f(C)=0.5x(f(A)+f(B)). If C < min(A,B) then f(C) = f(min(A,B))-1. Continue ad nauseum.

Either it's false that multiple intelligences exist, or it's useless to single-dimensinally evaluate them.

Multiple intelligences probably don't exist. But even supposing they do, claiming that the domain of a function is multidimensional does not disagree with my claim that the range is one dimensional.

Background:

A total order is a way of saying "person A is at least as good as person B" which obeys all the obvious laws. Person B can be either a real person or a standard of achievement (e.g. "passing").

http://en.wikipedia.org/wiki/Total_order

http://www.chrisstucchio.com/blog/2013/metrics_manifesto.htm...

Holy circular reasoning, Batman! The premise of your theorem, that there is such a total order, is equivalent to the existence of such a numbering function. You're saying "A must be true because B is true", where B is just an identical version of A, disingenuously obfuscated by a thin veneer of mathematics!

http://en.wikipedia.org/wiki/Fashionable_Nonsense

This all ignoring the fact any such "total order" is going to be highly variable through time (today's top engineer is tomorrow's dementia patient is yesterday's toddler)!

A total order is a consistent objective decisionmaking function.

I'm assuming that consistency and objectivity are obvious properties that any reasonable process must have. If you want to argue against consistency and/or objectivity, go ahead and do so. It'll certainly be interesting.

The theorem is fine, but there's obviously not a total order of 'general aptitude' on the set of people since there definitely exist two people and two jobs for which the first person is better at the first job than the second person and worse at the second job than the second person.

Each job would have a different decision function.

Of course, it's irrelevant for exams - the decision function in that case is just to answer the question "is student A > minimum passing standard" or "is student A > student B at math".

>"Ultimately all consistent objective decisionmaking processes [1] must come down to a single number"

Look up Campbell's law. Here, I'll even do it for you: http://en.wikipedia.org/wiki/Campbell%27s_law

Reply on news.ycombinator.com