# The Theory Of Conjoint Measurement

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Conjoint Measurement

BACKGROUND KNOWLEDGE

To talk about the theory of conjoint measurement, we should already understand the theory of measurement. Conjoint Measurement is an example of fundamental measurement.

If there is relationship between set A and set B, and a ∈ A and b ∈ B, we can construct a binary relation aRb. For example, suppose A is a set of squares and B is a set of rectangles. The binary relation aPb holds if and only if you judge the perimeter of a is smaller than b. We can assign a value of perimeter, f(a), to each a ∈ A and b ∈ B. Then, we can get a formula, aPb ⇔ f(a) < f(b). The relationship could also be defined as preference. If A is a set of alternatives and aPb holds on A if and only if you strictly prefer a to be, then we

To explain, Cartesian product represents n-tuple, which is a finite ordered list of elements. It includes all possible combination of elements in set A and set B. But binary relation only includes the combination of two elements which are respectively from set A and set B and fit the defined relationship.

INTRODUCTION

Conjoint Measurement basically models a representation of preference from collected data, and thus we can apply the model to make prediction of preference. When we make decisions of choosing, it is possible there are multiple attributes we can use to judge each choice. For example, when a customer want to choose a restaurant between The Cheesecake Factory and IHOP to have dinner, the customer can consider attributes, such as price, distance, etc. Price is average 20 dollars and 10 dollars. Distance is 20 miles and 10 miles. The customer could have a preference on The Cheesecake Factory or IHOP. Mathematically, each attribute could be considered as a finite set Ai (i ∈ ℕ). Each element, ai , in set Ai represents a measured value of the attribute. Set A of alternatives could be considered as a Cartesian

BACKGROUND KNOWLEDGE

To talk about the theory of conjoint measurement, we should already understand the theory of measurement. Conjoint Measurement is an example of fundamental measurement.

If there is relationship between set A and set B, and a ∈ A and b ∈ B, we can construct a binary relation aRb. For example, suppose A is a set of squares and B is a set of rectangles. The binary relation aPb holds if and only if you judge the perimeter of a is smaller than b. We can assign a value of perimeter, f(a), to each a ∈ A and b ∈ B. Then, we can get a formula, aPb ⇔ f(a) < f(b). The relationship could also be defined as preference. If A is a set of alternatives and aPb holds on A if and only if you strictly prefer a to be, then we

*…show more content…*To explain, Cartesian product represents n-tuple, which is a finite ordered list of elements. It includes all possible combination of elements in set A and set B. But binary relation only includes the combination of two elements which are respectively from set A and set B and fit the defined relationship.

INTRODUCTION

Conjoint Measurement basically models a representation of preference from collected data, and thus we can apply the model to make prediction of preference. When we make decisions of choosing, it is possible there are multiple attributes we can use to judge each choice. For example, when a customer want to choose a restaurant between The Cheesecake Factory and IHOP to have dinner, the customer can consider attributes, such as price, distance, etc. Price is average 20 dollars and 10 dollars. Distance is 20 miles and 10 miles. The customer could have a preference on The Cheesecake Factory or IHOP. Mathematically, each attribute could be considered as a finite set Ai (i ∈ ℕ). Each element, ai , in set Ai represents a measured value of the attribute. Set A of alternatives could be considered as a Cartesian