Multidimensional Preference Game and Extreme Dispute Resolution for Optimal Compensation of House Expropriation

Abstract

Although the compensation for house expropriation has increased significantly in recent years, the conflicts persist. The subjects in the expropriation process have multiple behavioral preferences, such as self-interest, loss aversion, and inequity aversion, and the expropriation process is hampered by extreme disputes on expropriation compensation. In order to make the houseowners agree to the expropriation immediately and tackle the root of extreme disputes, this paper establishes a two-stage sequential game model involving local government and two houseowners, analyzes the different payoff situations under multidimensional preferences, and finds out the optimal compensation standard. Then, through a case analysis, the TOPSIS method is used to determine the ideal strategy when the houseowners are simultaneously considering three preferences. The optimal compensation standard’s value is discovered to be significantly influenced by the houseowners’ behavioral preferences, but the compensation cannot be raised by excessive attention to the reference point and other houseowners.

1. Introduction

In China’s practice of house expropriation, illogical tragedies involving the protection of rights continue to occur. It is still difficult to find a solution for the extreme disputes that arise during the expropriation procedure. The underlying reason for the “nail house” issue, widespread protests, and group conflicts that result in extreme behavior from homeowners is that they believe they will benefit more from holding out. However, the appearance of these extreme disputes also makes subsequent projects unable to be completed on time, missing the opportunity for economic development, which has an immensely unfavorable impact on the social order.

A large number of studies have proven that people have bounded rationality and have multidimensional behavioral preferences. In the process of house expropriation with conflicts of interest as the essence, the subject’s behavior also satisfies the hypothesis of bounded rationality; that is, the government and the houseowner’s utility will be affected by other behavioral preferences in addition to considering their own absolute benefits. The houseowners make fair judgments about their expropriation compensation by comparing it with that of other houseowners or expropriation cases in the same region. This phenomenon is the realistic manifestation of “not suffering from shortage but suffering from inequity”. The difference between the homogenized compensation standard and the houseowners’ appeal is the root cause of extreme disputes in the expropriation process. Therefore, when resolving the extreme disputes over house expropriation, we should not only analyze the perspective of rational people, but we should also take into account the multidimensional preferences of the subject.

In order to find out whether the houseowners agree to sign the contract immediately and solve the extreme disputes in the expropriation, this paper establishes a two-stage game model of house expropriation, including the government and two houseowners, and analyzes the different utilities of the houseowners under multidimensional preferences so as to explore the optimal compensation standard of house expropriation. The contribution and practical significance of this paper is mainly reflected in the following two aspects: First, the mechanism of the extreme disputes that may occur in the process of house expropriation is elaborated, and the internal reasons behind people either accepting or refusing the expropriation at the same time are also explained. Secondly, based on the utility model of the houseowners under multidimensional behavioral preferences, this paper analyzes the influence of the houseowners’ preferences on the optimal compensation standard, such as self-interest, loss aversion, and inequity aversion. Finally, through the analysis of an actual case, this paper uses the TOPSIS method to consider the three kinds of preferences at the same time, in order to provide a theoretical basis for the government to formulate expropriation compensation policy and resolve the extreme disputes that occur because of house expropriation.

Section 2 is a literature review. Section 3, respectively, considers the houseowner’s self-interest, loss avoidance, and unfair aversion preference, and finds out the optimal compensation standard. Section 4 and Section 5 make use of the TOPSIS method to study the actual case and explore the reasons for the extreme disputes over expropriation compensation. Section 6 includes the conclusion and our suggestions.

2. Literature Review

In 2011, China promulgated the Regulations on Expropriation and Compensation of Houses on State-owned Land, Decree No. 590 of the State Council, to regulate house expropriation. The new Land Administration Law, which came into effect on 1 January 2020, is another valuable law concerning house expropriation. It stipulates that fair and reasonable compensation shall be given to land owners to ensure that their living standards will not be reduced after expropriation and their long-term livelihood will be guaranteed (Land Administration Law of the People’s Republic of China, Reg. 48). This requirement of fair and reasonable compensation was not reflected in the old version of the Land Administration Law, which reflects the improvement of the law and the growing emphasis on fair and reasonable compensation. However, while the Land Administration Law states that the living standards of land owners should not be affected by expropriation, it neither specifies the measures to achieve this goal nor provides a clear and measurable definition of what a non-poor standard of living is. In the absence of clear guidelines for fair compensation, compensation to landowners tends to be arbitrary. Meanwhile, these law about expropriation only outline the broad compensation principles. Details of compensation and adjustments are to be determined by the respective governments of the province, autonomous region, and municipality directly under the Central Government. Since each authority has its own considerations and objectives when formulating standards, there is bound to be a wide disparity in their standards [1].

2.1. The Method of House Expropriation Compensation

Expropriation conflict is essentially a value-added distribution problem involving the expropriated, the developers, and the government. China’s current expropriation compensation measures include a program that builds affordable houses for displaced families, offers a social security system, and so on. Although the compensation standard is on the rise, compensation has actually fallen compared to disposable income [2]. Empirical studies conducted in many countries show that the amount of compensation given to home-lost people is often insufficient to rebuild their livelihoods after expropriation [3], and it is also far lower than the market value [4]. Meanwhile, in order to obtain more fiscal revenue, local governments may carry out illegal expropriation, such as in cases that are not in line with the public interest, reduced compensation standards, forced expropriation, etc. [5]. When home-lost people negotiate with the local government, they usually believe that their legitimate rights and interests have been infringed in the resettlement and compensation process. Therefore, the home-lost people are dissatisfied with this, and they take violent action and appeal [6]. To make matters worse for home-lost people, there are no independent courts that allow them to complain about unfair treatment, as in the Netherlands and Germany, and they are only allowed to negotiate with their local government [7]. In other words, they are at a disadvantage, and the direct consequence of this imbalance of power between local governments and them is that expropriation conflicts are increasingly common. These conflicts range from small-scale instances involving nail houses or individual families to larger-scale instances involving group evictions, casualties, etc. [8]. These expropriation conflicts are widely considered to be one of the most important causes of social instability in China [9].

2.2. The Behavioral Preferences of House Expropriation Compensation

The issue of expropriation has been studied from a variety of different angles within the literature, such as property rights, expropriation policy and the legal system [10,11], satisfaction with expropriation [4], economic and risk assessments [12,13], the logic and strategy behind expropriation conflict [7], and so on. Many scholars have also studied the conflicts and the holdout problem that occurs in expropriation. Normally, the reasons for the holdout problem are vaguely attributed to monopoly power, high transaction costs, incomplete information, etc. Nash’s or Rubinstein’s bargaining models are often used to discuss this issue, but lots of scholars explore the internal causes of the holdout problem by conducting empirical research [14], experiments [15,16], and designing different types of mechanisms, such as budged-balanced semi-anonymous direct mechanisms [17], strong pareto mechanisms [18], and so on.

There are also more and more studies that pay attention to the fairness and justice of expropriation, but most studies are conducted from the perspective of fairness of the expropriation procedure [4]. In addition, most of the studies on expropriation involve compensation and profit distribution. These scholars have conducted a lot of research on expropriation compensation in various countries from the aspects of valuation [19,20], existing laws and policies, innovative compensation models [3,21], and so on, but few studies have considered the behavioral preferences of the owners. Most economic theory research is limited to the study of an individual’s behavior, but the interaction between subjects cannot be ignored [22].

The existing forms of expropriation compensation are almost the quotation model of unilateral execution by the local government, and the houseowners can only choose to accept or refuse the compensation but cannot put forward an ideal compensation scheme. However, there is indeed an invisible negotiation between the houseowners and the local government, which means that the behavior preference of the houseowners in the expropriation process may potentially affect the compensation offered to them by the local government. In this paper, the behavioral preferences of the houseowners include pure self-interest, loss aversion, and inequity aversion. Self-interest, that is, the hypothesis of the rational man, which means the pursuit of one’s maximum interests, is a widely used preference in the current research of the expropriation compensation model, and it has also been a widely used assumption in economic analyses for many years. Since the prospect theory proposed by Kahneman and Tversky [23], more and more economic studies no longer stick to the traditional rational man hypothesis, but they combine people’s behavioral preferences with economic behaviors. Houseowners also have certain behavioral preferences, which affect their decisions. Therefore, these preferences are considered in the analysis of this paper in order to better conform to the psychological characteristics of the houseowners.

3. Theoretical Framework of the Model

In this paper, a two-stage multidimensional preference game model involving the government and two houseowners is established. The government proposes the expropriation contract to the two houseowners at the same time, and the houseowners decide whether to sign the contract immediately in the first stage or delay signing until the second stage. Suppose the two houseowners make their decisions independently; that is, they do not know whether the other one has signed up. The schematic diagram of the basic model is shown in Figure 1.

The government first determines the houses to be expropriated according to the policy planning, and then puts forward the house expropriation compensation contract, including the time of expropriation and the amount of compensation for all the houseowners (for the convenience of our calculations, only two houseowners were studied in this study). It is then up to the houseowner to sign the contract with the government and give up his house. Thus, the model can be divided into four different situations: (1) If both houseowners choose to sign the contract in the first stage, they will obtain $P_i^f$ and $P_j^f$, respectively; (2) houseowner $i$ chooses to sign immediately and obtains $P_i^f$; houseowner $j$ chooses delayed signing and obtains $P_j^s$; (3) In contrast to situation (2), houseowner $j$ chooses to sign immediately and obtain $P_j^f$, while houseowner $i$ chooses delayed signing and obtains $P_i^s$; (4) both houseowners choose delayed signing and obtain $P_i^s$ and $P_j^s$, respectively.

In fact, although only two houseowners are studied in this paper, the houseowners who sign the contract immediately and delay signing are not a single person but they can be regarded as a group.

In addition, the parameters and acronyms used in the model of this paper are shown in the following

Table 1. Parameters and acronym description of the model.

Parameters and Acronym	Meaning
$P_i^f$	The income that the houseowner $i$ chooses after immediate signing.
$P_i^s$	The income that the houseowner $i$ chooses after delayed signing.
$R$	The standard of compensation proposed by the government.
$V$	Additional compensation that the government is willing to pay.
$k_i$	Excess profit obtained by the houseowner after bargaining.
$\delta$	The discounted coefficient of the houseowner, which also represents his time preference.
${\lambda }_i$	The coefficient of loss aversion preference of the houseowner $i$.
$y_i$	The reference point of the houseowner $i$; that is, his expected compensation.
${\alpha }_i$	The coefficient of inequity aversion preference of the houseowner $i$ means that the degree of envy increases when the income of houseowner $j$ is higher than his.
$U_i^{}$	The utility value of the houseowner $i$.
OCS	Optimal compensation standard.

.

3.1. The Optimal Compensation Standard under the Self-Interest Preference

If the houseowner chooses to sign the contract with the government immediately after the negotiation, the income obtained by the houseowner mainly consists of two parts. The first part is the minimum compensation standard, which is the minimum amount of compensation, represented by $R$, $R\ge 0$. The second part is the additional compensation, represented by $V$, $V\ge 0$. This is because the government can make use of the expropriated houses for the development of subsequent projects so as to obtain economic profits. It is paid to ensure a smooth expropriation process and to compensate the houseowner who loses the home that he depends on for a living. Therefore, if the houseowner signs a contract with the government in the first stage, the income that can be obtained is

$$P_i^f=R+V$$

(1)

where the superscript $f$ represents the first stage and $i$ represents the houseowners.

If the houseowner thinks that the compensation proposed by the government is insufficient or he tries to negotiate with the government to obtain a higher income, so he chooses not to sign the contract in the first stage but wait and then bargain with the government in the second stage, the income he can obtain is as follows:

$$P_i^s=\delta \left(R+k_{i}V\right)$$

(2)

Among them, the superscript $s$ represents the second stage, and $k_i$ represents the excess income that the houseowner $i$ can obtain after bargaining with the government in the second stage, $k_i\ge 1$. Meanwhile, $k_i$ also represents the bargaining power of the houseowner. The higher the bargaining power, the higher the excess income that can be obtained. $\delta$ represents the discount coefficient of the houseowner, $0\le \delta \le 1$. In fact, this discount coefficient also represents the time preference of the houseowner. The later the signing time is, the closer $\delta$ is to 0; that is, the smaller the present value of the income obtained. In general, people have a strong preference for timely rewards [24]. Therefore, under the premise of the same income, the houseowner is inclined to sign the contract earlier.

In the actual process of expropriation, the houseowner usually takes various measures, even extreme measures, to negotiate with the government; that is, the houseowner usually thinks that his bargaining power is high and that he can acquire a greater income in the second stage. Therefore, assume that $P_i^f\le P_i^s$. For local governments, if they want to solve the holdout problem in house expropriation, they need to make the houseowners have no motivation to delay their signing of the contract. The income of immediate signing is no less than that of delayed signing; therefore, the houseowners are more inclined to sign the contract immediately; that is, $P_i^f=P_i^s$.

Proposition 1.

Under the self-interest preference, the optimal compensation standard is $R^{*}=\frac{\left(k_i\delta -1\right)V}{1-\delta }$, and the greater the time preference of the houseowner, the lower the optimal compensation standard.

By comparing the income that the houseowner can receive by signing the contract in the first stage and the second stage, that is, $P_i^f-P_i^s=\left(1-\delta k_i\right)V+\left(1-\delta \right)R$, we can see that when and only when $R=\frac{\left(k_i\delta -1\right)V}{1-\delta }$, $P_i^f=P_i^s$. In this case, the payoff from immediate signing is the same as that from delayed signing. In this case, the houseowner will not have the motivation to delay signing, and the process of expropriation will be smoother. Thus, it can be seen that, as long as the compensation standard meets this standard, the houseowner will choose to sign a contract immediately without delay; therefore, this is the optimal compensation standard (OCS), and the proposition is proved.

This is also consistent with the current situation of expropriation; that is, in the current practice of expropriation compensation, the houseowners who choose immediate signing or delayed signing exist at the same time. For the houseowner who chooses to sign the contract immediately, the compensation proposed by the government has already met the OCS, and choosing a delayed signing will not give him a higher income, so the rational houseowner chooses to sign the contract immediately. However, some of the houseowners are not willing to sign the contract that quickly, because the compensation does not meet the OCS, and these houseowners have a higher estimate of their bargaining power and think that they can obtain higher profits by bargaining with the government, so they choose delayed signing.

Therefore, the optimal compensation standard when the houseowners only have a self-interest preference is as follows:

$$R^{*}=\frac{\left(k_i\delta -1\right)V}{1-\delta }$$

(3)

Substituting Equation (3) into Equation (1), the income of the houseowner who immediately signs a contract is

$$P_i^{f*}=\frac{\left(k_i-1\right)\delta V}{1-\delta }$$

(4)

$R^{*}$ is the minimum compensation standard value that makes the immediate signing payoff of the houseowner no smaller than the delayed signing payoff. If $R^{*}$ is given, the houseowner will have no motivation to delay, and extreme conflicts and holdout problems can be resolved. It can be seen that the value of the OCS is related to the bargaining power $k_i$, the discount coefficient $\delta$ of the houseowner, and the additional subsidies $V$ given by the government. As can be seen from $\frac{\partial R^{*}}{\partial k_i}>0$ and $\frac{\partial R^{*}}{\partial V}>0$, when the bargaining power and additional compensation of the houseowner are higher, the OCS is higher, and the income of the houseowner is also higher, which is consistent with our general cognition. It can be seen from $\frac{\partial R^{*}}{\partial \delta }<0$ that the OCS decreases with the increase in the discount coefficient $\delta$. $\delta$ represents the time preference of the houseowner. If the houseowner has a greater preference for an early signing, the greater the $\delta$, the lower OCS he can obtain. On the contrary, if the houseowner does not want to sign early and is willing to bargain with the government, the smaller the $\delta$, the larger the OCS will be. This also explains the reason why some houseowners adopt the delaying strategy: because the more they delay, the more compensation they can receive, and the more they have the motivation to delay. In this case, the gradual delay may lead to the emergence of extreme conflicts, thus causing the abortion of the project.

Meanwhile, because $R^{*}\ge 0$, then $k_i\ge \frac{1}{\delta }$; therefore, for the government, if they give the houseowner a signal in the process of the expropriation negotiation, that is, even if the houseowner takes various extreme means of resistance, the additional compensation will not be improved, which means that the houseowner will not obtain a bigger $k_i$ whatever they do. In this case, the houseowner will be inclined to sign the contract as soon as possible after knowing that his delay will not obtain higher profits, so the OCS will be reduced. That is, the higher the time preference of the houseowner, the tougher and more intransigent the government can be to make the houseowner sign the contract earlier.

3.2. The Optimal Compensation Standard under Loss Aversion Preference

In recent years, although the compensation standard for expropriation has greatly increased in China, conflicts over expropriation are becoming more intense and are increasing rapidly, which indicates that it is difficult to prevent the conflicts by simply increasing the compensation standard. Kahneman and Tversky proposed for the first time in the prospect theory that the behavior of a decision-maker would be significantly affected by the reference point, and that the psychological utility of loss and gain would be different. The objective loss produced greater psychological utility than the same amount of gain, and this phenomenon was named loss aversion.

Under the same interest appeal, minimizing the loss of an individual’s interests is also the basic behavioral logic of the subject, whether it is for the houseowner or the government. If the expropriation compensation is far lower than the houseowner’s expectation, he will avoid the loss of his interests, prevent his house from being expropriated, and become the “nail house”. Thus extreme conflicts arise. Therefore, when a houseowner faces different payoffs and different risks of loss, the discrepancy in their psychological expectation often leads to different results. The equilibrium of self-interest occurs when all the related subjects only pursue profit, while the equilibrium of loss aversion occurs when they engage in loss aversion. In expropriation compensation, fair compensation should be put forward as much as possible in order to minimize the losses of the houseowner.

Under the preference of loss aversion, the valuation by the houseowner is often higher than the market value of his own property, and the government often tends to set the compensation standard below the market value; therefore, the houseowner always thinks that the compensation standard is low and fails to meet his expectation, which comes from the valuation of the property of the houseowner himself and the compensation standard of other expropriated projects. Then, extreme conflicts arise.

By referring to the Shalev Model [25], this section builds a utility function model under the preference of loss aversion. The utility after considering the preference of loss aversion of the houseowner $i$ signing the contract immediately in the first stage is as follows:

$${\hat{U}}_i^f=\{\begin{array}{ccc}{P}_i^f& & P_i^f\ge y_i\\ P_i^f-{\lambda }_i\left(y_i-P_i^f\right)& & P_i^f<y_i\end{array}$$

(5)

The utility of the houseowner $i$ signing the contract delayed in the second stage is as follows:

$${\widehat{U}}_i^s=\{\begin{array}{ccc}{P}_i^s& & P_i^s\ge y_i\\ P_i^s-{\lambda }_i\left(y_i-P_i^s\right)& & P_i^s<y_i\end{array}$$

(6)

According to the above formula, when the reference point $y_i$ of the houseowner $i$ is less than his own payoff, the utility under loss aversion equals his income $P_i$, while when the houseowner’s reference point is greater than his own payoff, there will be a disutility. For the houseowner, there will be a psychologically expected compensation when he receives the expropriation notice, which may be related to the market price of the property, the historical expropriation price of the surrounding expropriation projects, and other factors. If the compensation given by the government is less than this expected compensation, the houseowner will deem this as suffering a loss. ${\lambda }_i$ is the loss aversion coefficient of the houseowner $i$, ${\lambda }_i>1$.

Before the expropriation begins, the houseowner will determine his reference point $y_i$ from various information channels. If this value is smaller than the payoff from immediate signing and delayed signing, that is, $y_i\le P_i^f\le P_i^s$, then its utility has nothing to do with $y_i$. At the same time, no matter what measures the houseowner takes to resist signing the contract and no matter how high his bargaining power is, the payoff cannot exceed the reference point, that is, $P_i^f\le P_i^s<y_i$, and its utility has no relation to the reference point. Therefore, this paper only discusses the situation when $P_i^f<y_i\le P_i^s$, when the houseowner believes that his payoff will not be less than the reference point of the game between him and the government.

Proposition 2.

When the houseowner has a loss aversion preference, the optimal compensation standard is $R^{**}=\frac{\left(k_i\delta -{\lambda }_i-1\right)V+{\lambda }_i{y}_i}{1+{\lambda }_i-\delta }$.

When $P_i^f<y_i\le P_i^s$, the utility of immediate signing is $U_i^{f*}=P_i^f-{\lambda }_i\left(y_i-P_i^f\right)$, and the utility of delayed signing is $U_i^{s*}=P_i^s-{\lambda }_i\left(y_i-P_i^s\right)$. By comparing the utility values of the two, we can conclude the following:

$$R^{**}=\frac{\left(k_i\delta -{\lambda }_i-1\right)V+{\lambda }_i{y}_i}{1+{\lambda }_i-\delta }$$

(7)

when the OCS meets Formula (7), the houseowner’s utility of immediate signing is no less than that of delayed signing; therefore, the proposition is proved.

According to $\frac{\partial R^{**}}{\partial y_i}={\lambda }_i>0$, as the reference point of the houseowner increases, the OCS also increases accordingly, and the government needs to pay more compensation to make the houseowner choose to sign the contract immediately, so as to ensure an early start for the project. Figure 1 numerically simulates the tendency of $R^{**}$ to change with the changes in the reference point values and the time preference.

It can be seen from the figure above that, unlike the case when the houseowner only has a self-interest preference, when the houseowner has a loss aversion preference, the OCS increases with the increase in the houseowner’s discount coefficient, that is, the time preference. The higher the time preference, the greater the expectation of the houseowner for the early transaction, and the higher the OCS, the faster the completion of the expropriation can be promoted. This is one of the reasons why “nail houses” appear in the expropriation process. Nail households usually have a smaller time preference and a higher reference point. In fact, the government only needs to pay a small amount of the compensation to the nail households to make the immediate signing of the contract more effective, because the present value of the expropriation compensation that they can receive is small. However, in reality, it is difficult for the nail households to realize that, and they pay more attention to the absolute value of the expropriation compensation and ignore the present value, which leads to the failure of expropriation.

Proposition 3.

The optimal compensation standard is negatively correlated with the loss aversion coefficient, and positively correlated with the reference point and discount coefficient.

When $P_i^f<y_i\le P_i^s$, $y_i<\frac{\left(k_i-1\right)\delta V}{1-\delta }$, take the derivative of $R^{**}$ to ${\lambda }_i$ to obtain $\frac{\partial R^{**}}{\partial {\lambda }_i}=\frac{y_i-\left[\left(k_i-1\right)V+y_i\right]\delta }{{\left(1+{\lambda }_i-\delta \right)}^2}<0$; that is, the higher the loss aversion coefficient of the houseowner, the smaller the OCS. According to $\frac{\partial R^{**}}{\partial y_i}=\frac{{\lambda }_i}{1+{\lambda }_i-\delta }>0$ and $\frac{\partial R^{**}}{\partial \delta }=\frac{\left(k_i-1\right)\left({\lambda }_i+1\right)V+y_i{\lambda }_i}{{\left(1+{\lambda }_i-\delta \right)}^2}>0$, the OCS increases with increases in the reference point and discount coefficient; therefore, the proposition is proved.

Figure 2 numerically simulates the influence of the loss aversion coefficient and time preference of the houseowner on the OCS.

The larger the loss aversion coefficient, the greater the disutility brought by the difference between the reference point and the compensation; that is, the more the houseowner is afraid of the loss. However, a greater loss aversion coefficient does not mean that the houseowner can acquire more compensation. As can be seen from Figure 3, if the loss aversion coefficient is larger, that is, if the difference between the houseowner’s compensation and the reference point has greater psychological disutility, then the houseowner expects more compensation, so as to avoid psychological losses. However, at this time, the government only needs to provide less compensation to make the utility of immediate signing no less than that of delayed signing. That is, the amount of compensation that the houseowner gains will be less.

3.3. The Optimal Compensation under the Inequity Aversion Preference

In the study in the previous section, we proved that the value of the reference point will have a certain influence on the OCS, and this reference point is not only affected by objective factors such as the situation of the house itself and the previous compensation of the surrounding expropriation projects, but it is also widely concerned by the houseowner; that is, the compensation of the other houseowner. In recent years, a large number of studies have proven that people not only care about the absolute amount of their own payoff, but they also care about the amount of others’ payoffs. That is, an individual’s utility not only depends on his own payoff, but it also depends on the difference between the payoff of others and his own. If the payoff of others is higher than his own, he will have an unfair psychological cognition about it; that is, people have a preference for inequity aversion. Additionally, in the expropriation process, this kind of inequity aversion preference exists. The houses that the government needs to expropriate are usually in adjacent states; that is, the properties owned by the houseowners have the same or similar geographical positions and traffic conditions, so the compensation should not be different between the houseowners. However, because the negotiations between the government and the houseowner are undertaken alone, the houseowner can bargain with the government to acquire more compensation; therefore, the compensation for each houseowner is individually stipulated. In this case, if the houseowner finds that the compensation of others is higher than his own, he will feel jealous about it, which is a kind of disutility for him. If the houseowner foresees this disutility, he may reduce it by delaying the signing of the contract, repeatedly negotiating with the government, or taking extreme resistance to fight for higher returns. This increases the likelihood of extreme conflicts and hinders the smooth development of the expropriation process and the timely construction of the follow-up projects.

Referring to the inequity aversion model of Fehr and Schimdt [26], this section establishes the utility value of the houseowner considering inequity aversion preference:

$$U_i^{\prime }=P_i^{}-{\alpha }_i\max \left\{\left(P_j-P_i\right),0\right\}-{\beta }_i\max \left\{\left(P_i-P_j\right),0\right\}$$

(8)

where $U_i^{\prime }$ represents the utility value of the houseowner $i$; $P_i$ represents the payoff of the houseowner $i$; $P_j$ represents the payoff of the houseowner $j$; ${\alpha }_i$ represents the degree of jealousy of houseowner $i$ when the income of houseowner $j$ is greater than his, ${\alpha }_i>0$; ${\beta }_i$ represents the degree of guilt of houseowner $i$ when the payoff of houseowner $j$ is greater than his, $0\le {\beta }_i<1$, and ${\beta }_i\le {\alpha }_i$. It is assumed that the houseowners make their decisions independently; that is, they have no right to interfere with the other person’s decision, but since the houseowners have bounded rationality, their utility is related to the payoff of another houseowner. If another houseowner’s payoff is greater than his, he will feel unfairly treated and become jealous, thus reducing his psychological utility and increasing the likelihood of negative deviation occurring. The greater the difference, or the greater the envy of the subject is, the higher the disutility will be. Similarly, if one’s own payoff is greater than another houseowner’s payoff, a kind of guilt psychology will occur, which means positive deviation, but negative deviation is taken more seriously by houseowners than positive deviation. Therefore, when the houseowner makes a strategic choice, he will take into account the change in his utility, which is related to the timing of the contract of another houseowner.

In the analysis, we stand in the shoes of the houseowner $i$ and judge the optimal strategy and the optimal compensation standard when he takes two different measures: immediate signing and delayed signing. We assume the following two scenarios:

(1) If the houseowner $j$ chooses to sign the contract immediately, the payoff of the houseowner $i$ is smaller than that of the houseowner $j$, that is, $P_i^f<P_j^f$. If the houseowner $i$ chooses to delay signing, his payoff is greater than that of the houseowner $j$, that is, $P_i^s>P_j^f$;

(2) If the houseowner $j$ chooses to delay signing, then the payoff of the houseowner $i$ who chooses to sign the contract immediately is smaller, that is, $P_i^f<P_j^s$. The payoff of the houseowner $i$ who chooses to delay signing is greater than that of the houseowner $j$, that is, $P_i^s>P_j^s$.

Only when the above hypothesis is true, does the houseowner $i$ have the motivation to adopt the strategy of delaying signing.

Proposition 4.

If other houseowner chooses to sign the contract immediately, the inequity aversion preference has no effect on the OCS.

When the houseowner $j$ chooses to sign immediately, we know that by comparing the utility of the houseowner $i$’s immediate signing with that of the delayed signing and as long as the expropriation compensation standard $R\ge \frac{\left(k_i\delta -1\right)V}{1-\delta }$ is provided by the government, the utility of the immediate signing is greater than that of the delayed signing. Therefore, the proposition is proved. In other words, the OCS is $R^{*}=\frac{\left(k_i\delta -1\right)V}{1-\delta }$, which is the same as the OCS under the self-interest preference. This value has no relationship with the payoff and bargaining power of houseowner $j$ and the inequity aversion coefficient of houseowner $i$.

When the houseowner $j$ chooses the delayed signing strategy, we know by comparing the utility of immediate signing and delayed signing that

$$R^{***}=\frac{\left[\left(\alpha +\beta \right)k_j+\left(1-\beta \right)k_i\right]\delta V-\alpha V-V}{\left(1+\alpha \right)\left(1-\delta \right)}$$

(9)

Proposition 5.

If other houseowner chooses to delay signing, the OCS $R^{***}$ is shown in Formula (9).

As long as the OCS given by the government satisfies Formula (9), then utility of immediate signing is no less than that of delayed signing, and the houseowner lacks the motivation to holdout. Therefore, the proposition is proved.

It can be known by $\frac{\partial R^{***}}{\partial \alpha }=\frac{\left(k_i-k_j\right)\left(\beta -1\right)\delta V}{\left(1-\delta \right)\left(1+\alpha \right)}$ and $\frac{\partial R^{***}}{\partial \beta }=\frac{\left(k_j-k_i\right)\delta V}{\left(1-\delta \right)\left(1+\alpha \right)}$, if the bargaining power of houseowner $i$ is stronger than that of houseowner $j$, that is, $k_i>k_j$, then $\frac{\partial R^{***}}{\partial \alpha }<0$, $\frac{\partial R^{***}}{\partial \beta }<0$, which means that the OCS of houseowner $i$ decreases as the degrees of jealousy and guilt increase. On the other hand, if the bargaining power of houseowner $i$ is weaker than that of houseowner $j$, that is, $k_i<k_j$, then $\frac{\partial R^{***}}{\partial \alpha }>0$, $\frac{\partial R^{***}}{\partial \beta }>0$, which means that the OCS of houseowner $i$ increases as the degree of jealousy and guilt decrease. Figure 4 numerically simulates the OCS of the houseowner $i$.

In the current process of expropriation, the houseowner pays too much concern to whether the other houseowners have signed the contract and their given amount of compensation. When other houseowners are observed to delay signing the contract, he may also take this strategy of delayed signing. If other’s compensation is higher than his own, he will take corresponding or even extreme measures to bargain with the government in order to gain higher compensation.

However, according to our analysis, this concern is actually futile. The houseowner who adopts the strategy of delayed signing usually thinks that he has a higher bargaining power and can obtain higher compensation through delaying the signing, that is, $k_i>k_j$; in this case, the attention to other houseowners can only obtain disutility, and even when the houseowner feels more jealous and guilty about the higher or lower compensation levels, he will receive a lower OCS. Therefore, for the houseowner, paying too much attention to the compensation of others cannot improve their own utility.

3.4. Discussion

From the above analysis, we know the value and characteristics of the OCS when there is only a single preference of the houseowner, namely, self-interest, loss aversion, or inequity aversion preference. When the compensation standard given by the government achieves the OCS, the houseowner has no motivation to delay signing, so he will choose to agree with the expropriation immediately, which avoids extreme conflicts in house expropriation and effectively solves the problem of the houseowner constantly delaying the process of expropriation.

By comparing the values of the OCS under the three preferences in Equations (3), (7) and (9), it can be found that when the houseowner only has a self-interest preference, the OCS is higher than that when he has a loss aversion preference, and it is also higher than that when he has an inequity aversion preference. This indicates that the loss aversion and inequity aversion preference of the houseowner have a large negative deviation from their psychological utility. Only if, that is, when the houseowner thinks his bargaining power is weak, the OCS under the inequity aversion preference is higher. That is to say, under normal circumstances, the houseowner does not need to pay too much concern about the price of other houseowners’ information and payoffs, because this concern not only brings about more costs, such as information costs, transportation costs, etc., but more importantly, it will bring greater disutility.

We divide the houseowners into the following types: Different strategies can be adopted for different types of houseowners to prevent the phenomenon of holdouts and avoid extreme conflicts, see

Table 2. Types and characteristics of the houseowners.

Types		Characteristics
Time preference	Holdout myth	Low preference for time and expectation of gaining more by delaying.
	Urgent signing	High time preference and expectation to sign as soon as possible to receive compensation.
Loss aversion coefficient	Loss fear	High loss aversion coefficient, fear of loss, and expectation of more compensation.
	Loss-free	Low loss aversion coefficient, absence of care about reference points, and more concern about their own interests.
Bargaining power and inequity aversion coefficient	Strong sense of fairness	Higher bargaining power and a higher inequality aversion coefficient; the disutility caused by unfairness is high.
	Lack of fairness	Higher bargaining power and a lower inequality aversion coefficient; the disutility of the compensation difference is low.

.

According to the time preference of the houseowner, we divided them into the “holdout myth” type and the “urgent signing” type. The time preference of the nail house misunderstanding type is low: they do not care about the time cost, and they are not willing to reach an agreement with the government immediately. Most of the holdouts fall into this category. They fall into a “holdouts myth” in the game with the government; that is, they believe that they can gain more compensation by delaying signing. In fact, for such holdouts, there is no difference in the utility of signing immediately and delaying when the government offers less compensation. The issue of extreme conflicts over house expropriation could be greatly alleviated if those holdouts understood this situation before the expropriation began. The “urgent signing” type has a greater time preference, and they expect to sign a contract with the government as soon as possible, complete the expropriation process, and receive compensation with the least delay possible. The government should give more compensation to such houseowners so as to complete the expropriation process quickly.

Based on the loss aversion coefficient, the houseowners can be divided into “loss fear” type and “loss-free” type. “Loss fear” means that the houseowners have a high loss aversion coefficient, they pay more attention to the difference between their own compensation and reference points, and they are afraid of causing psychological utility loss, so they may take various measures to acquire greater compensation. For such houseowners, the government should give less compensation, so that they can achieve their maximum utility. The “loss-free” type refers to those who have a low loss aversion coefficient, and the reference point value has little influence on their utility. They pay more attention to the absolute payoffs that they have obtained, and the government must provide more compensation to make them sign the contract immediately.

On the basis of the bargaining power and inequity aversion coefficients, the houseowners can be divided into “strong sense of fairness” type and “lack of fairness” type. The type with a strong sense of fairness refers to houseowners who consider that they have a higher bargaining power and can acquire more compensation than others through the game with the government. Meanwhile, they also have a higher inequity aversion coefficient, including coefficients of jealousy and guilt. When their compensation is higher or lower than others, they will have a greater sense of injustice. This sense of injustice brings greater disutility to them. After obtaining higher compensation, the psychological utility value of such people will be reduced due to their strong perception of fairness, and the psychological utility of the compensation they obtain will be lower. The “lack of fairness” means that although the houseowners have a high bargaining power, the inequity aversion coefficient is low; that is, the difference in compensation between himself and others will not bring great disutility to him, so the psychological utility of compensation of such persons will not be too much affected by others, and their OCS is also higher.

4. The Optimal Compensation Standard under Combination Preference

The utility of the houseowners not only depends on their single preference, but it is more likely to be affected by multiple preferences at the same time. That is to say, the houseowners not only care about the amount of their absolute payoff, but they also care about the relative value of their payoff to other houseowners and their reference point. Therefore, it is not incomplete to analyze the utility of the houseowners only by considering a single preference; it should be judged comprehensively from combination preference.

Based on the TOPSIS method, a TOPSIS model with a multidimensional preference game is constructed. The preferences of self-interest, loss aversion, and inequity aversion are regarded as the evaluation criteria, and the strategy choice of the houseowner is regarded as an evaluation alternative and sorted by the TOPSIS method. The optimal alternative obtained by calculation is the equilibrium solution under multidimensional preference.

4.1. Evaluation Criteria and Evaluation Alternative

Firstly, the evaluation criteria and alternatives of TOPSIS with the multidimensional preference game are determined. According to the details outlined above, the utility function of the houseowner can be expressed as the function form under the three preferences of self-interest, loss aversion, and inequity aversion. Therefore, three evaluation indicators are constructed in this paper, namely, self-interest value, loss aversion value, and inequity aversion value. Meanwhile, this paper puts forward four strategy combinations, namely, four evaluation alternatives, see

Table 3. Evaluation alternatives.

Alternative	Description of Evaluation Alternatives
Alternative 1	houseowner $i$ choose immediate signing; houseowner $j$ choose immediate signing
Alternative 2	houseowner $i$ choose immediate signing; houseowner $j$ choose delayed signing
Alternative 3	houseowner $i$ choose delayed signing; houseowner $j$ choose immediate signing
Alternative 4	houseowner $i$ choose delayed signing; houseowner $j$ choose delayed signing

.

The matrix of specific alternatives is shown in the following

Table 4. TOPSIS with multidimensional preference game matrix of house expropriation compensation.

Criteria	Alternative 1	Alternative 2	Alternative 3	Alternative 4
self-interest value	$P_i^f$, $P_j^f$	$P_i^f$, $P_j^s$	$P_i^s$, $P_j^f$	$P_i^s$, $P_j^s$
loss aversion value	$U_i^{f*}$, $U_j^{f*}$	$U_i^{f*}$, $U_j^{s*}$	$U_i^{s*}$, $U_j^{f*}$	$U_i^{s*}$, $U_j^{s*}$
inequity aversion value	$U_i^{f^{\prime }}$, $U_j^{f^{\prime }}$	$U_i^{f^{\prime }}$, $U_j^{s^{\prime }}$	$U_i^{s^{\prime }}$, $U_j^{f^{\prime }}$	$U_i^{s^{\prime }}$, $U_j^{s^{\prime }}$

.

4.2. Calculate the Comprehensive Evaluation Index

After the evaluation criteria and alternatives are determined, the comprehensive evaluation index of each alternative is calculated. The specific steps are as follows:

STEP 1: Normalization processing: the range transformation method is used to normalize the values. The self-interest value, loss aversion value, and inequity aversion value proposed in this model are all beneficial indicators.

STEP 2: Determine the ideal solution: determine the positive ideal solution and the negative ideal solution through the results of normalized processing:

$$A^{+}=\left(r_a^{+},r_b^{+},r_c^{+}\right), A^{-}=\left(r_a^{-},r_b^{-},r_c^{-}\right)$$

STEP 3: Calculate the distance between each alternative and the ideal solution:

$$d_i^{*}=\sqrt{{\displaystyle \sum _{j=1}^n{(w_j(r_{ij}-r_j^{*}))}^2}}$$

This paper uses the subjective weighting method of expert consultation to determine the weight $w_j$.

STEP 4: Calculate the comprehensive evaluation index:

$$C{C}_i=\frac{d_i^{+}}{d_i^{+}+d_i^{-}}$$

The smaller the $C{C}_i$, the better the alternative.

5. Case Study

5.1. Case Overview

The information of this case is derived from the Retrial Review and Trial Supervision Administrative Decision Zheng Xiujuan and the People’s Government of Haiyan County of Zhejiang Province (Case No. (2020) 9694 of the Supreme Legal Action) and the Retrial Review and Trial Supervision Administrative Decision Xu Shuiming and the People’s Government of Haiyan County of Zhejiang Province (Case No. (2020) 9692 of the Supreme Legal Action), which is recorded in China Judgements Online.

The government of Haiyan County, Zhejiang Province, plans to expropriate houses in the Donggang District, Xitangqiao Street. The houses owned by Zheng and Xu are on the plot. On 20 April 2018, the People’s Government of Haiyan County issued the House Expropriation Decision of Haiyan County made by the People’s Government No. (2018) 14, which was accompanied by the Plan for the Expropriation, Compensation and Resettlement of Houses on State-owned Land in Xitangqiao ×× East Port Block. On May 5, Jiaxing Qiuzhen Real Estate Appraisal Co., Ltd. was confirmed as the real estate appraisal agency for the expropriation project and issued “The assessment report of house expropriation”. On 21 May, this report was sent to Zheng and Xu.

The certificate of the house owned by Zheng stated that the gross floor area was 381.65 ${\mathrm{m}}^2$, but the net floor area was actually 390.6 ${\mathrm{m}}^2$, including 59.8 ${\mathrm{m}}^2$ of attic. The certificate of the house owned by Xu recorded a gross floor area of 378.33 ${\mathrm{m}}^2$ and a net floor area of 386.02 ${\mathrm{m}}^2$, including a jump floor area of 62.83 ${\mathrm{m}}^2$. The expropriation compensation plan specifies that according to the “Assessment Report”, the house is expropriated according to 6108 yuan/${\mathrm{m}}^2$.

Zheng and Xu argue that (1) the area of compensation for expropriation must be determined based on the net floor area plus the area of the attic; (2) the compensation standard is significantly lower than the market price of the two commercial houses in the same area of 12,500 yuan/${\mathrm{m}}^2$ and 10,687.73 yuan/${\mathrm{m}}^2$; and (3) according to the Measures of Subsidizing and Rewarding the Expropriation of Houses on State-owned Land in the Center of the County of Haiyan County, 30% of the value of the expropriated houses will be rewarded.

The Supreme People’s Court ruled after a review that the compensation should be made according to the gross floor area of the expropriated house plus the attic area, while the net floor area larger than the gross floor area will not be compensated. The house owned by Zheng is outside the scope of application of this subsidizing regulation and has no subsidies.

5.2. Case Data

It can be known from the overview of the case that the government is willing to give the compensation standard of 6108 yuan/${\mathrm{m}}^2$. On the assumption of the rest of the required data, the government is willing to give an additional subsidy of 1800 yuan/${\mathrm{m}}^2$, which is about 30% of the compensation standard. At the same time, assuming that the expected price of Zheng ($i$) is 12,500 yuan/${\mathrm{m}}^2$, and the expected price of Xu ($j$) is 10,687.73 yuan/${\mathrm{m}}^2$.

The government proposed that the area of the house should be calculated on the basis of the gross floor area plus the attic (jumping) area, which is $R_i=6108*(381.65+59.8)=2696376.6$ yuan, $V_i=1800*(381.65+59.8)=794610$ yuan; $R_j=6108*(378.33+62.83)=2694605.28$ yuan, $V_j=1800*(378.33+62.83)=794088$ yuan. Additionally, the expected price of Zheng and Xu is calculated based on the net floor area plus the attic (jumping) area: $y_i^{}=12500*(390.6+59.8)=5630000$ yuan, $y_j^{}=10687.73*(386.02+62.83)=4797187.61$ yuan.

According to the compensation advocated by Zheng and Xu, assuming the additional subsidies that can be obtained by bargaining with the government $k_i=3.5$, $k_j=3$, and the discount coefficient $\delta =0.7$, assuming Zheng’s jealousy coefficient $a_i=0.4$, guilty coefficient ${\beta }_i=0.3$, loss aversion coefficient ${\lambda }_i=1.2$, Xu’s jealousy coefficient $a_j=0.5$, guilty coefficient ${\beta }_i=0.4$, and loss aversion coefficient ${\lambda }_j=1.6$.

5.3. Equilibrium Analysis of the Case

The government proposed the expropriation compensation plan to Zheng and Xu. Zheng and Xu chose the strategy of agreeing to the expropriation and signing immediately, or not agreeing to the expropriation, negotiating with the government on the compensation, and acquiring a certain amount of the subsidies, that is, delaying the signing.

The compensation that Zheng and Xu will receive if they sign a contract immediately or delay it is as follows:

$$P_i^f=R_i+V_i=3490986.6$$

(10)

$$P_i^s=\delta \left(R_i+k_i{V}_i\right)=3834258.12$$

(11)

$$P_j^f=R_j+V_j=3488693.28$$

(12)

$$P_j^s=\delta \left(R_j+k_j{V}_j\right)=3553808.5$$

(13)

Then, the TOPSIS with a multidimensional preference game matrix is as

Table 5. Utility value matrix of TOPSIS with multidimensional preference game.

Alternatives	Self-Interest	Loss Aversion	Inequity Aversion
Alternative 1	3,490,986.60, 3,488,693.28	924,170.52, 1,395,102.35	3,490,986.60, 3,487,546.62
Alternative 2	3,490,986.60, 3,553,808.50	924,170.52, 1,564,401.91	3,465,857.84, 3,528,679.74
Alternative 3	3,834,258.12, 3,488,693.28	1,679,367.86, 1,395,102.35	3,730,588.67, 3,315,910.86
Alternative 4	3,834,258.12, 3,553,808.50	1,679,367.86, 1,564,401.91	3,750,123.23, 3,413,583.68

:

Firstly, the range transformation method is adopted to normalize the value of the game matrix, and the results are as

Table 6. Normalized processing.

Alternatives	Self-Interest	Loss Aversion	Inequity Aversion
Alternative 1	0.0000, 0.0000	0.0000, 0.0000	0.0860, 0.8067
Alternative 2	0.0000, 1.0000	0.0000, 1.0000	0.0000, 1.0000
Alternative 3	1.0000, 0.0000	1.0000, 0.0000	0.9313, 0.0000
Alternative 4	1.0000, 1.0000	1.0000, 1.0000	1.0000, 0.4591

:

We can know that the positive ideal solution is $A^{+}=\left(1,1,1\right)$, and the negative ideal solution is $A^{-}=\left(0,0,0\right)$.

The weights of the three preferences were determined by the expert consultation method as 0.2, 0.4, and 0.4, respectively. The distance between the four alternatives and the positive and negative ideal solutions is calculated as

Table 7. Euclidean distance from alternatives to positive and negative ideal solution.

Alternatives	${\mathit{d}}^{\mathbf{+}}$	${\mathit{d}}^{\mathbf{-}}$
Alternative 1	0.5776, 0.4538	0.0344, 0.3227
Alternative 2	0.6000, 0.0000	0.0000, 0.6000
Alternative 3	0.0275, 0.6000	0.5820, 0.0000
Alternative 4	0.0000, 0.2164	0.6000, 0.4834

:

Therefore, the comprehensive evaluation index can be calculated as follows:

It can be seen from

Table 8. Comprehensive evaluation index of the alternatives.

Alternatives	${\mathit{d}}^{\mathbf{+}}$	${\mathit{d}}^{\mathbf{-}}$	$\mathit{C}\mathit{C}$
Alternative 1	0.5600	0.0963	0.6563
Alternative 2	1.0000	0.0000	1.0000
Alternative 3	0.0438	1.0000	1.0438
Alternative 4	0.0000	0.5538	0.5538

that the comprehensive evaluation index of Alternative 4 is the smallest; that is, Alternative 4 is the optimal strategy for the houseowner. That is to say, when the expropriation is carried out according to the expropriation compensation standard proposed by the government, both Zheng and Xu will adopt the strategy of delaying the signing, which will greatly reduce the efficiency of the expropriation and spend some unnecessary resources on negotiation and resistance. Zheng did take measures to delay signing because he believed that the compensation offered by the government did not meet the optimal compensation standard to maximize his psychological utility, so he filed a lawsuit with the government.

After analyzing the above case, it can be seen that, when the compensation does not reach the optimal compensation standard, the holdout problem may occur, and even more serious issues may appear. Next, we will verify whether Zheng will still adopt the strategy of delaying signing when the compensation meets the OCS we proposed before.

If the compensation provided by the government is $R^{*}=\frac{\left(k_i\delta -1\right)V}{1-\delta }=8700$ yuan/${\mathrm{m}}^2$, and Zheng’s payoff of immediate signing is the same as that of delayed signing, then he has no incentive to holdout. Additionally, when the compensation becomes $R^{**}=\frac{\left(k_i\delta -{\lambda }_i-1\right)V+{\lambda }_i{y}_i}{1+{\lambda }_i-\delta }=10300$ yuan/${\mathrm{m}}^2$, the optimal strategy for Zheng is plan 1, which is immediate signing. Additionally, if the compensation is $R^{***}=\frac{\left[\left(\alpha +\beta \right)k_j+\left(1-\beta \right)k_i\right]\delta V-\alpha V-V}{\left(1+\alpha \right)\left(1-\delta \right)}=7650$ yuan/${\mathrm{m}}^2$, the $CC$ of plan 2 is the smallest, which means that the best strategy for Zheng is to sign immediately and for Xu to choose delayed signing. However, it is also the optimal strategy for Zheng because plan 1 is the second-best strategy.

6. Conclusions and Suggestions

In the face of the major practical problems of numerous related subjects and complex interactive factors in house expropriation compensation, a single standard of compensation makes meeting the internal needs of all the houseowners difficult, which often leads to extreme conflicts. The resolution of extreme conflicts under multidimensional behavioral preference is not an improvement for the absolute payoff of a single houseowner, but a process in which the utility of the houseowners is reasonably balanced and their behavioral preferences are satisfied under the interaction of strategy and belief. This paper studies the optimal compensation standard under the mutidimensional behavioral preferences of self-interest, loss aversion, and inequity aversion in house expropriation, and draws the following main conclusions:

(1) The optimal compensation standard is diverse under different preferences, and the preferences also have a great influence on the value of the optimal compensation standard. The parameters that can make the optimal compensation standard higher mainly include the following: a lower loss aversion coefficient, a larger reference point value, and time preference. When the bargaining power is high, the higher the inequity aversion coefficient, the lower the optimal compensation standard, When the bargaining power is low, the higher the inequity aversion coefficient, the greater the optimal compensation standard.

(2) Compared with those who only have a self-interest preference, the psychological compensation utility of the houseowners decreases with different amplitudes when they have loss aversion and inequity aversion preferences. This indicates that in the process of expropriation, the houseowner should put down excessive attention to the compensation of others and the surrounding similar projects as the reference points, because these concerns will bring negative psychological deviation.

(3) The behavioral preferences of the houseowners may not exist independently but simultaneously; that is, the houseowners may pay attention to the absolute value of their own compensation, the reference point, and the compensation of others. Therefore, when considering their psychological utility, these behavioral preferences can be placed under the same research framework for analysis. Using the TOPSIS multidimensional preference game method, the three behavioral preferences are regarded as the evaluation criteria, and the strategies of the houseowners are regarded as different alternatives, so as to judge the optimal strategies.

This paper attempts to provide some suggestions and a theoretical basis for future house expropriation compensation policies, which are as follows:

(1) Increase the proportion of houseowners participating in the formulation of the expropriation compensation standard.

In the conflicts over expropriation compensation, it is impossible to achieve the balance of Pareto efficiency enhancement of the ideal goal of expropriation compensation system reform without a common strategy change in related subjects. The expropriation compensation game has the characteristics that the game elements are constantly changing, the subject’s strategies and beliefs are evolutionary, and the houseowners pursue the compositive payoff of the economy, society, and policy. The preferences of self-interest, loss aversion, and inequity aversion are the behavioral motivations that all kinds of social subjects cannot remove, so that the equilibrium evaluation of the various preferences reveals the key to resolving the dilemma of the expropriation compensation game. Therefore, in the expropriation compensation, the government should give more back to the people, so as to benefit the people, moderately increase the expropriation compensation, and actively allow houseowners to participate in the construction of the expropriation compensation system, so as to ensure that the houseowners’ living standard does not decline after the expropriation and maintain a sustainable livelihood.

(2) The subjective value of the compensation for expropriation should consider the houseowners’ preferences.

Although the self-interest-based expropriation compensation under the assumption of the “economic man” conforms to the current reality, the repeated expropriation conflicts reflect that this compensation standard experiences difficulties in reaching a fair balance agreed by the subject of expropriation. The research in this paper shows that the essence of the houseowners’ wishes to obtain compensation that is higher than the market value is not to some extent a reflection of excess returns, but that they, as social people, have not only a self-interest preference, but also loss aversion and fairness preferences. In order to satisfy the houseowners’ multidimensional preferences and improve their satisfaction and sense of gain, it is necessary to revise the behavioral preference on the basis of the assessed value of expropriation compensation, adopt the upward correction coefficient to improve the compensation standard, and offer the subjective value of their property. Moreover, the compensation standard containing the subject’s strategic value takes into account the objective value of the expropriated house and the subject’s subjective value of property, which is more in line with the reality of expropriation compensation.

(3) Disclosure of expropriation compensation information to guide the houseowners’ compensation expectations.

Fairness is a subjective judgment, and a fair compensation standard is a relative concept that should reflect fairness to all parties. However, it is unrealistic to rely solely on the government to improve the compensation standard, because the basic motivation for the formation and development of expropriation conflicts is the inconsistent belief, judgment, and extreme strategy of the relevant parties in the expropriation game. Therefore, in order to promote the harmonious implementation of expropriation, it is necessary for the related subjects to form consistent beliefs about fair compensation in the expropriation process. This is an effective way to achieve fair compensation by guiding the houseowners to reasonably expect compensation through the transparency of compensation information.

The research within this paper provides a certain theoretical basis for the formulation of compensation policy in the process of expropriation. The government must consider the related preferences of houseowners when making the compensation standard, so as to formulate a compensation scheme with higher satisfaction for both parties. This paper also has some limitations. For example, it does not consider the preference of the government, which will have a certain impact on the amount of compensation standard awarded. At the same time, it does not carry out a sensitivity analysis, which is insufficient to analyze the sensitivity of the compensation standard. This paper offers directions for future research.