## 2 Theoretical Background
### Conjoint Analysis  
Conjoint analysis was developed by [PERSON] and [PERSON] in 1964. It was then introduced by [PERSON] and [PERSON] in 1971 into the marketing field, and became one of the important methods in the marketing studies to measure consumer preferences. The basic assumption to operate the conjoint analysis is: consumers undertake the determination of perception preferences based on a plurality of attributes and their levels, which compose the product. In other words, consumer preferences for a certain product can be decomposed as the part-worth utilities which form the attribute and levels of the product.  
The way to conduct the conjoint analysis is to use the decompositional approach to estimate the subject's preference structure under the condition that the overall assessment results of subjects for a set of samples are already known [25]. In other words, the estimated independent variables and dependent variables can be obtained via consumers' assessed values of a set of dependent variables. In addition, it is expected to minimize the difference between the original assessed values and the predicted values of the dependent variables. Therefore, the conjoint analysis is extremely effective when it is applied to the investigation of multi-attribute decision-making problems. It is only required to understand overall assessed values of the subjects on a set of samples aggregation and will be able to decompose the part-worth utilities of each attribute level. Then the relative importance weight of each attribute level can be calculated.  
When applying the conjoint analysis, the strategic purposes listed below can be developed after the part-worth utilities of each attribute level has been determined:  
1. Understand the relative importance of each attribute level during consumers' decision-making process.
2. Find products' best attribute combination for a group or an individual.
3. Market segmentation can be conducted based on the difference of attribute levels that are emphasized.
4. Discover the attribute combinations of products which do not exist on the market but are preferred by consumers.
5. Under the assumption that other conditions remain unchanged, the market share of products which are composed of different attribute levels can be estimated based on the judgment of consumer preferences.  
Based on the relationship between levels of different attributes, the preference model can also be divided into the vector model, ideal-point model, and part-worth utility model as shown in Figure 3. To determine whether the constructed preference models have the prediction capability, typically Pearson's R and [PERSON]'s tau are used as the indices, whereby both indicate that the prediction is more precise if these two values are closer to 1 [26].  
In this research, it is assumed that consumers' judgment of the forms is constructed by various types of aesthetic principles, and therefore the required attributes in the conjoint analysis are namely various types of aesthetic principle. The levels are namely aesthetic measures which are values between 0-1. The combinations of attributes and levels will form different independent variables. In addition, the dependent variables are namely the subject's preferences. For the selection of the preference  
Figure 3: Types of preferences model.  
models, since the trend of subjects' view of the aesthetic principles and their values are not known previously, each aesthetic principle value will be viewed as a class variable. Therefore, the conjoint analysis will be conducted by the selection of part-worth utility models.  
To determine whether the subjects possess the contemplated preference models for the preferred forms, the two indices of Pearson's R and [PERSON]'s tau can be utilized as the assessment basis. If these two values are provided with a certain degree of levels, it not only indicates that the preference models are accurate in terms of the predictions, but also confirms that the subjects indeed have a certain degree of tendency for their preferences.