# Talk:Theory of conjoint measurement

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## Untitled

I'm no expert, but a few points. Firstly, there's obviously something missing in "3. Double Cancellation". Secondly, what does "f is a non-interactive, additive function (i.e. is a monotonic function ..." mean? In particular, there's no explanation of non-interactive, or of additive on general, non-structured sets. Thirdly, what does the first bullet point under "2. Single cancellation" mean? Is it "For all a,b \in A and x \in X then (a, x) \succsim (b, x) is implied whenever there exists some w \in X such that (a, w) \succsim (b, w)"? Richard Pinch (talk) 21:33, 4 July 2008 (UTC)

I'm not finished with the page yet, so hopefully your questions will be answered when it is. —Preceding unsigned comment added by Axiomguy (talkcontribs) 14:24, 9 July 2008 (UTC)

The symbol Q is overloaded at the beginning of the axiom section: Q=f(A,X) and Q=<A,X,\succsim>. Furthermore, f never appears again. What's it doing? Augustinc (talk) 22:18, 22 September 2009 (UTC)

Moreover, both \succ and \succsim are overloaded. If \succsim is a relation on A\times X, then it is not a relation on A or X, and similarly for \succ. So the axioms are very unclear. Furthermore, the definition of weak order is unusal --- I would say unique. By way of comparison, here are Luce and Tukey's axioms:

1. \succsim is a weak order on A\times X (transitive, connected and reflexive). 2. Solvability, as it appears in the article. 3. Double cancellation. 4. A different Archimedean axiom.

Essentialness is sated as a definition, not an axiom. The theorem does not require essentialness. Solvability implies that if one factor is essential, then so is the other. Suppose the second factor is essential, that is, there are x and y such that x>y. Then (a,x)\succ (a,y). Solvability implies the existence of a b such that (a,x)\sim (b,y). Since \succeq is a weak order, (b,y) \succ (a,y) and so b>a and the first factor is essential too. If essentialness fails, \phi_A and \phi_X are constant functions --- the conclusion of the theorem still holds. Finally, what is called symmetry here is implied by solvability. No doubt some of my confusion is due to the overloading of symbols, but it appears to me that this section is simply incorrect. It might be much more straightforward to use the relatively simple Luce-Tukey axioms which don't say anything about the conditional (factor) orders. Krantz's generalizations are as inaccessible as they are elegant. Augustinc (talk) 23:24, 22 September 2009 (UTC)

Hey there, I'm the guy who created the conjoint measurement page a couple of years back. I had neglected it until this week and I have spent the past couple of days revising it. I've brought it up to date a bit and taken some of the above comments into consideration. After revising the page, I saw that the WikiProject Measurement team had passed their judgment on my efforts at the top of the discussion page. After checking out what this measurement team is about, I decided to remove the conjoint measurement page from the category of measurement. I did this as the Measurement Team seems to be focussed solely on physical measurement and the page is more relevant to psychology and the behavioural sciences. I would like, if possible, for the Measurement team to remove their banner from the top of the discussion page. Thankyou Axiomguy (talk) 05:21, 18 March 2011 (UTC)

i'm a phd student in education, no expert and can't comment on the accuracy, but i can comment on the exceptional readability of the article. thank you for making this complex topic accessible to a novice. best! 69.229.153.102 (talk)

This article appears to use terms in a contradictory way, or at least, fails to define them. One important example appears in the first axiom where the "levels" of A and X are referenced, but the term "levels" is not explicitly defined. Elsewhere, articles on Conjoint Measurement refer to levels of measurement being, for example, "Nominal", "Ordinal", "Interval", etc. (total of 6 levels). Interpreted this way, it is hard to understand what one means by levels of A or even what A is meant to represent. Only what it isn't, is given (that is, not known to be a continuous quantity). Conversely, if the author meant that some measurable quantity A has, say, at least 3 outcomes from measurement, the term "levels" should be avoided, because of its special meaning within the theory. — Preceding unsigned comment added by 68.65.71.91 (talk) 18:12, 20 February 2015 (UTC)

## Proper use of TeX

$\tbinom{j}{3}$2$\Big($$\tbinom{n}{2}$$j\left(n - 2\right)$$\Big)$.

$\binom{j}{3}^2 \binom{n}{2} j \left(n - 2 \right).$

I found the first expression above in the article and changed it to the second. The first is not the right way to use TeX. The superscript "2" is outside of TeX, and repeatedly we see [/itex][itex], i.e. getting out of math mode and then back in. That prevents the software from automatically aligning things correctly. In particular, if you write \left( and \right), and don't stay in math mode throughtout the whole expression including both parentheses and everything in between, then the software can't properly adjust the sizes of the delimiters. Michael Hardy (talk) 15:13, 29 July 2008 (UTC)