## 4 Methodology and Data Collection  
### Designing the Research Method  
To study the effects of privacy fatigue on the privacy paradox, the following issue has to be considered. That is, if conventional empirical research methods were employed, owing to the presence of confounding variables, it would be quite difficult to observe the net effects between the independent variable and the dependent variable. Specifically, since initial conditions are not identical within the samples, selection bias is present, and the influence from privacy fatigue on the privacy paradox may be \"over-estimated\" or \"under-estimated\". Figure 1: The research model. In order to control and eliminate selection errors caused by confounding variables, this study employs propensity score matching (PSM) to study the influencing relationships by privacy fatigue on the privacy paradox, namely matching individuals with variation in core variables and similar levels in other characteristics so as to simulate the scenario of individuals with the same characteristic levels randomly receiving experimental intervention, thus effectively lowering confounding bias. Specifically, the basic thinking is to make the non-random data close to random through constructing a counterfactual framework. By dividing users into a control group and experience group by the degree of privacy fatigue, then calculating the propensity score according to demographic variables as well as using characteristic variables, followed by matching individuals in both groups with close propensity scores, endogenous issues due to individual characteristic variables can be effectively resolved. The paper considers the sample with a high level of privacy fatigue as the experience group, otherwise, the control group. Processing variable \(\mathrm{D}_{\mathrm{i}}=\{0,1\}\) indicates whether the individual is in a state of privacy fatigue. With privacy fatigue, a value of 1 will be given, without the fatigue a value of 0. protect\({}_{\mathrm{i1}}\) and protect\({}_{\mathrm{0i}}\) respectively denote the intention for privacy protection behaviors in individuals under privacy fatigue or not. The average treatment effect on the treated (ATT) on privacy fatigue is defined as:  
\[\mathrm{ATT}=\mathrm{E}\big{(}\mathrm{protect}_{\mathrm{1i}}-\mathrm{protect} _{\mathrm{0i}}\left|\mathrm{D}_{\mathrm{i}}=1\right)=\mathrm{E}\big{(} \mathrm{protect}_{\mathrm{1i}}\left|\mathrm{D}_{\mathrm{i}}=1\right)-\mathrm{ E}\big{(}\mathrm{protect}_{\mathrm{0i}}\left|\mathrm{D}_{\mathrm{i}}=1\right) \tag{1}\]  
In Equation (1), \(\mathrm{E}\big{(}\mathrm{protect}_{\mathrm{0i}}\left|\mathrm{D}_{\mathrm{i}}=1\right)\) is the non-observable outcome, since, in reality, we can only observe the intention for privacy protection behavior of an individual under one specific state. By employing PSM, for the privacy fatigue group, a close sample from the non-privacy fatigue group can be matched. The substitute value for \(\mathrm{E}\big{(}\mathrm{protect}_{\mathrm{0i}}\left|\mathrm{D}_{\mathrm{i}}=1 \right)\) can thus be constructed. Equation (1) can be changed to:  
\[\mathrm{ATT}=\mathrm{E}\big{\{}\mathrm{E}\big{(}\mathrm{protect}_{\mathrm{1i} }-\mathrm{protect}_{\mathrm{0i}}\left|\mathrm{D}_{\mathrm{i}}=1,\,\mathrm{p}( \mathrm{X}_{\mathrm{i}})\big{)}\big{\}} \tag{2}\]  
In Equation (2), \(\mathrm{p}(\mathrm{X}_{\mathrm{i}})\) represents the propensity score, indicating the conditional probability of privacy fatigue of individuals with characteristic variables fixed. It is calculated as:  
\[\mathrm{p}(\mathrm{X}_{\mathrm{i}})=\frac{\exp(\beta\mathrm{X}_{\mathrm{i}})} {1+\exp(\beta\mathrm{X}_{\mathrm{i}})} \tag{3}\]  
Upon the basis of propensity score calculation, selecting an appropriate matching method would enable conditional probabilities of the control group and the experience group to be as close to each other as possible. Selection bias can be eliminated via controlling observable characteristics.