Exploring the Commuting Decision-Making Behavior of Low-Income Groups Based on Cumulative Prospect Theory

Abstract

Based on cumulative prospect theory, this study proposes a decision-making model to reveal the commuting behavior of low-income groups under uncertain conditions. Considering the commuting characteristics of this group, travel economic cost is incorporated into the model. The decision-making behavior of low-income groups under different travel scenarios is analyzed to acquire the priority of commuting plans. Based on a stated preference survey of residents in Beijing, the commuting behavior of low-income groups is empirically analyzed. The results show that low-income groups will be affected by individual risk preference and characterized by bounded rational characteristics when making commuting decisions under uncertain conditions. Moreover, travel economic cost is a crucial factor for the decision-making of this group. When the travel budget time is less than the perceived time, they tend to seek risks and take punctual arrival as their primary goal. On the contrary, they tend to avoid risks. On the basis of ensuring the travel time meets their needs, low-income commuters always seek the economy and reliability of their travel plans. The empirical results further verify that the proposed model effectively describes the commuting decision-making behavior of low-income groups, and it is superior to the expected utility theory with respect to performance and behavior disclosure. This study provides a reference for improving the commuting efficiency and experience of low-income groups.

Keywords

planning and analysis traveler behavior and values behavior analysis decision analysis and processes public transportation bus transit systems

The acceleration of urbanization and the expansion of urban land have led to the commuting distance and travel time of some residents far away from the downtown are gradually increasing. To some extent, this has caused the anxiety for travelers during commuting, and reduced residents’ subjective well-being ( 1 , 2 ). Existing works have indicated that the factors affecting commuting decisions mainly include deterministic factors such as personal attributes, family attributes, travel attributes, and transportation service characteristics ( 3 – 5 ), as well as uncertain factors such as the travelers' risk preference, travel time reliability, and external environment ( 6 – 8 ). How commuters make decisions under risky and uncertain conditions has been widely discussed as a research field. From the perspective of income attributes, one study provides evidence that high-income groups need more time to satisfy their daily minimum travel needs than low-income groups ( 9 ). However, as a disadvantaged group in travel, low-income groups faced more uncertainty in commuting. On the one hand, rising housing prices have forced some low-income residents to move to peripheral areas, far away from the city center and convenient transport areas ( 10 , 11 ). This increases the commuting distance of this group, making it uncertain in obtaining efficient and convenient transportation services ( 12 – 14 ). On the other hand, restricted by economic conditions, low-income groups usually have poor affordability of commuting, with few alternative travel modes and poor mobility ( 15 , 16 ), which makes their normal travel activities in cities, especially commuting, face great uncertainty ( 17 ). Moreover, for low-income groups, transportation costs are rising faster than income, and they face increasing traffic pressure during medium and long distance travel. Travel distance and activity space are closely related to social resources, employment opportunities, convenience of life and other aspects. With the rapid advancement of urbanization, economic and employment opportunities in a city region will rapidly decrease and concentrate in the core area ( 15 , 16 ). Under such circumstances, the inequality in travel patterns will often transform the economic differences into differences in society, life, and subjective feelings, and thus lead to possible social disparities. Therefore, it is crucial to study the commuting decision behavior of low-income groups under uncertain conditions to improve their travel fairness and satisfaction.

In the past, when studying commuting decisions, alternatives were usually evaluated according to the expected utility theory (EUT), assuming that travelers were completely rational ( 18 – 20 ). The decision weight of a plan with high deterministic travel utility is relatively high, which leads to a large difference between the perceived value and the actual utility. In fact, affected by risk preference and a complex psychological mechanism, the decision-making behavior of individuals usually presents bounded rational characteristics ( 21 , 22 ). The existence of the above issues has resulted in scholars attempting to reveal risk decision-making under uncertain conditions through other theories. Kahneman and Tversky ( 23 ) proposed prospect theory (PT) on the basis of bounded theory. Compared with EUT, PT replaced the utility function with the value function and introduced individual value feeling into the decision-making research, making up for the deficiency of EUT. It is similar to EUT in form and can be regarded as a modification of EUT ( 19 , 24 ). PT is suitable for exploring the actual decision-making behavior of travelers under uncertain conditions. It mainly studies the attitude of decision-makers toward risks from the perspective of gains and losses through the sensitivity of individuals to changes ( 23 , 25 ). However, PT is not able to always satisfy random dominance and is only applicable to analyze a few results. On this basis, Quiggin ( 26 ) proposed rank dependent utility theory (RDUT) and overcame the limitation of PT. After that, Tversky and Kahneman ( 25 ) improved PT and developed it into cumulative prospect theory (CPT), which expanded the application scope and allowed different weight functions for gains and losses. CPT is suitable for both risk and uncertain decision-making ( 27 ). Because of the ability to truly describe the decision-making behavior of travelers, PT and CPT are widely used in traffic behavior studies, such as in route choice, risk assessment, and decision analysis ( 28 , 29 ).

However, the existing studies based on CPT have some limitations to be addressed. Firstly, many relevant works pay more attention to the parameter estimation of route choice behavior, and few studies deeply analyze commuting decision-making behaviors ( 27 , 30 ). Secondly, existing works have not sufficiently analyzed decision-making behavior for different groups, such as low-income groups, elderly groups, and other travel disadvantaged groups. These groups often face greater uncertainty in travel ( 15 , 31 ). Thirdly, many existing researches merely selected partial components of CPT to discuss its applicability in decision analysis ( 32 ), and lack a specific analysis of the relationship between risk preference and decision-making. This study stands in the wake of the literature, proposing a framework to reveal the commuting decision of low-income groups under uncertain conditions based on CPT. In view of the commuting characteristics of this group, the travel economic cost is incorporated into the framework. All the components of CPT are fully used to describe the evaluation process of low-income commuters on each alternative travel plan. According to the difference of travel time budgets, the commuting decision-making behavior is analyzed in different scenarios to acquire the risk preference and the priority of commuting plan choice of this group. Based on a stated preference (SP) survey of typical low-income communities in Beijing, the commuting behavior of low-income groups is empirically analyzed. The effectiveness of the proposed decision-making model is verified by combining scenario analysis and empirical application. It provides a reference for improving the commuting efficiency of low-income groups.

The rest of this paper is arranged as follows. The second section provides a literature review of relevant works. The third section presents the framework structure and all components of the proposed model. After that, the fourth section provides a multi-scenario analysis on commuting decision based on CPT and EUT. Furthermore, the fifth section verifies the effectiveness of the proposed model through an empirical application in Beijing. Finally, conclusions and future research directions are provided in the sixth section.

Literature Review

Application of Cumulative Prospect Theory

In previous studies, the application of PT and CPT in traffic practice has included many aspects, such as the choice of departure time ( 24 , 33 , 34 ), travelers’ risk attitude and preference ( 30 , 35 ), route choice ( 10 , 21 , 36 ), travel mode choice (19, 37 –39), travel satisfaction evaluation ( 40 ), and other aspects (29, 41 –43). These works have all successfully used PT or CPT to describe individuals’ bounded rationality and risk attitude in decision-making. Avineri ( 21 ) discussed the travel decision-making behavior of passengers who choose bus routes based on PT. Through the investigation of actual bus routes, the influence of personal preference on decision-making was verified. Moreover, he reported that there was a difference in risk attitudes between PT and EUT, where PT revealed the irrational psychological factors affecting choice behavior from the perspectives of passengers’ psychological traits and behavioral characteristics; the prediction results using PT were closely related to the selection of reference points, where the reference point is the basis used to judge relative gains and losses when making decisions using PT. Subsequently, he further discussed the selection of key parameters of the travel choice model when PT was applied to risky travel environments, and proposed several effective approaches for setting reference point and loss aversion factors ( 28 ). Xu et al. ( 27 ) established a travel utility measurement system based on CPT, compared the results under the EUT framework to prove the effectiveness of CPT in route choice, and explored the setting approach of reference points. Jou and Chen ( 30 ) discussed the risk attitude of drivers in route choice under the condition of given real-time traffic information through a CPT-based framework, and proved the superiority of CPT in capturing reference dependence, loss aversion, risk-seeking, and nonlinear preference.

With respect to comparison between different theories, Ramos et al. ( 44 ) used EUT, PT, and regret theory (RT) to analyze travel behavior under the condition of uncertain travel time, explored the advantages and disadvantages of each theory, and discussed the differences among the three theories through examples. They mentioned that EUT had no obvious theoretical advantages other than an easy-to-handle framework. Although PT violates the principles of EUT, it is the best framework for analyzing travel behavior. Besides, in other traffic practices, cumulative prospect theory learning (CPTL) could provide a valid prediction of travelers’ dynamic route choice behavior ( 45 ) under the condition of uncertain travel time and is based on CPT. Yang et al. ( 39 ) explored the CPTL model to capture the learning process of travelers' daily mode choice behavior; the CPTL model is improved to some extent and the application scope of CPT is extended. In addition, Hu et al. ( 35 ) proposed a CPT-based modeling framework, estimated the risk attitude parameters of electric vehicle charging behavior by introducing a cost function. The results showed that the drivers will decide whether to charge or not according to the cumulative prospect value (CPV). Meanwhile, the proposed model provided a reference for the use of electric vehicles, the planning of charging infrastructure, and the expansion of power grid capacity. Ghader et al. ( 19 ) used CPT to explore the impact of travel perceived reliability on choice behavior, and estimated the parameters of the utility function, value function, and weight function in combination with the data of family travel time in Washington, D.C. The study results are not only applicable to mode choice, but also applicable to the choice of other dimensions. As mentioned above, although the application of EUT is relatively mature in practice, PT and CPT do have greater advantages in reflecting individuals' actual travel route choice and travel attitude preference under uncertain conditions ( 44 ).

Travel Decision-Making of Low-Income Groups

Although some studies have verified the effectiveness of CPT when applied to travel decision-making ( 38 , 45 ), few works have explored the relationship between individual risk preference and decision-making. Meanwhile, few studies have paid special attention to low-income groups. The current research on this group mainly includes travel temporal and spatial characteristics ( 46 , 47 ), influencing factors of mode choice ( 48 – 50 ), accessibility of infrastructure ( 12 , 15 ), and travel satisfaction ( 17 , 51 , 52 ). The research on commuting decisions for low-income groups mainly focuses on commuting frequency, mode choice, and commuting distance. Moreover, some studies have explored the differences in commuting behavior between low-income groups and other income groups ( 50 , 53 ). With respect to theoretical frameworks, many relevant works have adopted the binomial logit (BL) model, nest logit (NL) model, multinominal logit (MNL) model, structural equation model (SEM) ( 54 , 55 ), and so forth.

Hu and Schneider ( 56 ) adopted the BL model to explore the relationship between commuting modes of different income groups and their workplaces. By establishing the interaction term of income and workplace dummy variables, it explained the commuting differences based on income level. Furthermore, Lucas et al. ( 15 ) explored the mode choice behavior of low-income groups in the urban core and peripheral area based on the geographically weighted regression (GWR) model, and provided a reference for the formulation of a travel policy for this group in different city areas. Jang and Lee ( 57 ) constructed an accessibility model reflecting the transport characteristics of different income groups, and conducted a comparative evaluation of the accessibility of low-income groups and high-income groups. The analysis results show that because of housing costs, low-income groups rarely live in areas conducive to their travel activities. Ao et al. ( 58 ) adopted the MNL model to discuss how the built environment affects the mode choice of low-income groups. The results show that the MNL model had a good explanation for objective built environment indicators, such as building density, road density, and traffic distance. Most of these studies are based on random utility theory (RUT), and rarely consider potential variables closely related to this group, such as emotional preferences, intrinsic feelings, and risk attitudes. For risks and uncertainties, it is usually difficult to accurately reflect the actual choices of commuters with RUT. In comparison, CPT is applicable to both risk and uncertain decision-making, and it can truly describe the decision-making behavior of commuters. When making commuting decisions, low-income groups usually evaluate the travel cost and make the final decision based on the comparison of travel budget costs. This decision-making process is consistent with that of CPT, which selects the maximum CPV from the perspective of value gain and loss by comparing with the reference points. Therefore, it is worth using CPT to study the commuting decision-making behavior of low-income groups in different scenarios ( 19 , 41 ).

Contributions Differing from Existing Works

This work presents four points that differ from the existing works. Firstly, it is the first attempt to use CPT in the commuting decision analysis of low-income groups, which provides enlightenment for the application of CPT in different groups, especially the disadvantaged groups. Secondly, this study includes all the components of CPT and considers the economic cost according to the travel characteristics of low-income groups. Thirdly, a CPT-based commuting decision model for low-income groups is proposed for the first time. Each alternative commuting plan is evaluated under different scenarios, and the relationship between individual risk preference and commuting decision is discussed. Finally, the effectiveness of the proposed decision-making model is further verified by an empirical application in a typical low-income community in Beijing. This work provides a valuable attempt for the commuting study of low-income groups.

Methodology

CPT is capable of reflecting travelers' risk attitudes and subjective preferences for travel decisions ( 27 , 32 ). When making commuting decisions, low-income groups tend to choose transportation modes with relatively low economic costs. When a single mode is not enough to support them to reach their destination, they often choose to commute through a combination of multiple low-cost modes, in which the time cost is relatively uncertain. Therefore, the group usually evaluates the travel cost and make the final decision based on the comparison of travel budget costs. This decision-making process is consistent with that of CPT, which selects the maximum CPV from the perspective of value gain and loss by comparing with the reference points. Therefore, this study proposed a commuting decision-making model of low-income groups based on CPT. Firstly, the value function is determined by reference point selection. Secondly, the cumulative probability weight of low-income commuters in the face of gains and losses is analyzed. After that, the commuting cost function is established. Finally, the CPVs of different commuting decisions are calculated, and the travel plan with maximum prospect value is determined.

Reference Point and Value Function

In the actual decision-making process, low-income travelers make final decisions based on limited information and their own travel needs, weighing travel risks and forming a perceived value in an uncertain condition. CPT provides a new way to simulate this decision-making psychology better. By the virtue of the value function, the absolute utility of a commuting plan is transformed into the relative value felt by travelers ( 25 ). As shown in Figure 1a, the value function of a single reference point can be expressed as follows:

V (Δ x) = {\begin{cases} {(Δ x)}^{α} Δ x \geq 0 \\ - λ {(- Δ x)}^{β} Δ x < 0 \end{cases}

(1)

where $Δ x = x - x_{0}$ is the gain and loss relative to the reference point; λ is greater than 1, which is the risk aversion coefficient, reflecting that individuals are more sensitive to losses; α (0 < α ≤1), β (0 < β ≤1) are the risk preference coefficients, which measure the sensitivity degree away from the reference point. The greater the values of α, β, the more sensitive the traveler is to risk.

Figure 1.

Value function: (a) one reference point and (b) two reference points.

Low-income commuters always hope to arrive at the workplace at the time closest to the start of work. There are often two psychological reference points ( 59 ), the earliest acceptable arrival time $t_{e}$ and the latest work start time $t_{w}$ . If the actual arrival time is earlier than $t_{e}$ or later than $t_{w}$ , the commuter will face the loss of early or late arrival. If the arrival time is between $t_{e}$ and $t_{w}$ , the commuter will face a gain. Since travelers tend to arrive early, they usually choose a time $t_{b}$ close to $t_{w}$ as their preferred arrival time to ensure that they can get ready for work within the reserved time period $t_{w} - t_{b}$ . According to the distribution characteristics of the time points, the value function of the two reference points, as shown in Figure 1b, is obtained ( $t_{b}$ is a pseudo-reference point). Here, $t_{e}$ , $t_{w}$ , and $t_{b}$ divide the arrival time into four areas, which are the early loss area, the early gain area, the late gain area, and the late loss area. Commuters tend to avoid risk in the gain area and seek risk in the loss area. Therefore, the slope of the value function curve in the loss area is greater than that in the gain area, and the corresponding value function is expressed as follows:

{\begin{matrix} v_{1}^{-} (t_{A}) = - λ_{1} (t_{e} - t_{A})^{ξ_{1}}, 0 \leq t_{A} \leq t_{e} \\ v_{1}^{+} (t_{A}) = λ_{2} (t_{A} - t_{e})^{ξ_{2}}, t_{e} \leq t_{A} \leq t_{p} \\ v_{2}^{+} (t_{A}) = λ_{3} (t_{w} - t_{A})^{ξ_{3}}, t_{p} \leq t_{A} \leq t_{w} \\ v_{2}^{-} (t_{A}) = - λ_{4} (t_{A} - t_{w})^{ξ_{4}}, t_{A} \geq t_{w} \end{matrix}

(2)

where $t_{0}$ , $t_{A}$ , and $t_{d}$ represent the departure time, the arrival time, and the commuting duration, respectively, and $t_{A} = t_{0} + t_{d}$ . $ξ_{i}$ $(0 \leq ξ_{i} \leq 1, i = 1, 2, 3, 4)$ is the risk preference coefficient, representing the concave–convex degree of the curve in the gain or loss area, reflecting the sensitivity of the commuter to minor changes.

Probability Weight Function

The probability weight function of the commuting decision is shown in Figure 2, which gives a higher decision weight to extreme risks and is more consistent with the decision tendency of low-income commuters in uncertain conditions. The solid line in Figure 2 is the probability weight function curve considering risk decision preference, and the dotted line is the weight function curve under ideal conditions. When decision-makers face gains and losses, the probability weights are as follows ( 25 ):

w^{+} (p) = \frac{p^{γ}}{{[p^{γ} + {(1 - p)}^{γ}]}^{1 / γ}}

(3)

w^{-} (p) = \frac{p^{δ}}{{[p^{δ} + {(1 - p)}^{δ}]}^{1 / δ}}

(4)

where P is the actual probability of outcome occurrence; $w^{+} (p)$ and $w^{-} (p)$ are the decision probability weights in the state of gain and loss, respectively, reflecting travelers' subjective cognition of the plan choice probability under different states ( 23 ); γ and δ are probability offset coefficients, which determine the characteristics of the probability weight function overestimating low probability and underestimating high probability. Assuming that the alternative commuting plan $ϕ = {(x_{i}, p_{i}), i \in [- m, n]}$ , the cumulative decision weight $π_{i}^{+}$ of low-income commuters in the face of gains and the cumulative weight $π_{i}^{-}$ in the face of losses can be expressed as follows ( 25 ):

\begin{matrix} π_{i}^{+} = & w^{+} (p_{i} + \cdot \cdot \cdot + p_{n}) - w^{+} (p_{i + 1} + \cdot \cdot \cdot + p_{n}), \\ 0 \leq i < n \end{matrix}

(5)

\begin{matrix} π_{i}^{-} = & w^{-} (p_{- m} + \cdot \cdot \cdot + p_{i}) - w^{-} (p_{- m} + \cdot \cdot \cdot + p_{i - 1}), \\ - m < i \leq 0 \end{matrix}

(6)

π_{n}^{+} = w^{+} (p_{n})

(7)

π_{- m}^{-} = w^{-} (p_{- m})

(8)

where $x_{i}$ represents the possible result when plan $ϕ$ occurs, positive and negative subscripts respectively represent the positive and negative possible results, and $P_{i}$ represents the occurrence probability corresponding to $x_{i}$ .

Figure 2.

Decision weight function.

Commuting Cost Function

Assuming that all low-income commuters are homogeneous, the commuting cost consists of two parts: actual travel cost and delay cost caused by early or late arrival. In view of the commuting needs of low-income groups, the economic cost is incorporated into the actual travel cost, and the commuting cost function is defined as follows:

C = C_{T} + C_{S} + C_{E} + C_{L}

(9)

C_{E} = ρ η_{E} (t_{w} - t_{A})

(10)

C_{L} = (1 - ρ) η_{L} (t_{A} - t_{w})

(11)

ρ = {\begin{matrix} 0, t_{A} > t_{w} \\ 1, t_{w} < t_{A} \end{matrix}

(12)

where $C_{T} = η_{d} t_{d}$ is the actual commuting time cost, $C_{E}$ is the early arrival delay cost, $C_{L}$ is the late arrival delay cost, $η_{d}$ , $η_{E}$ , and $η_{L}$ represent the cost per unit time, early arrival cost per unit time, and late arrival cost per unit time, respectively, and $η_{L} > η_{d} > η_{E}$ ( 60 ). Here, $C_{S} = η_{s} p_{s}$ is the is the actual economic cost of commuting. Therefore, the commuting cost can be expressed as follows:

\begin{matrix} C = & [η_{d} - ρ η_{E} + (1 - ρ) η_{L}] t_{d} + η_{s} p_{s} \\ + [ρ η_{E} - (1 - ρ) η_{L}] (t_{w} - t_{0}) \end{matrix}

(13)

In actual travel, commuters cannot accurately know the actual travel time in advance, and only estimate the subjective perceived time of a certain travel plan based on their own judgment. Besides, for each commuter, there is a travel budget time, so the perceived cost and the budget cost of low-income commuters choosing a certain travel plan are as follows:

\begin{matrix} C_{perceived} = & [η_{d} - ρ η_{E} + (1 - ρ) η_{L}] t_{perceived} + η_{s} p_{s} \\ + [ρ η_{E} - (1 - ρ) η_{L}] (t_{w} - t_{0}) \end{matrix}

(14)

\begin{matrix} C_{Budget} = & [η_{d} - ρ η_{E} + (1 - ρ) η_{L}] t_{Budget} + η_{s} p_{s} \\ + [ρ η_{E} - (1 - ρ) η_{L}] (t_{w} - t_{0}) \end{matrix}

(15)

Comparing the perceived cost and the budget cost, when the perceived cost is greater, low-income commuters feel losses. On the contrary, they feel gains. Since low-income groups pay less attention to the early arrival cost and tend to mind a late arrival penalty more, assume that $η_{d} = 1$ , $η_{s} = 3$ , $η_{E} = 0$ , $η_{L} = 1.5$ ( 19 ).

CPV and Decision-Making

Based on establishing the commuting cost function, the cumulative decision weight and value function of different commuting modes are utilized to obtain the CPV of alternative commuting plans as follows ( 25 ):

CPV = CP V^{+} + CP V^{-}

(16)

CP V^{+} = \sum_{i = 1}^{n} π_{i}^{+} v (Δ x_{i})

(17)

CP V^{-} = \sum_{i = - m}^{0} π_{i}^{-} v (Δ x_{i})

(18)

where CPV⁺ is the CPV of gains and CPV^— is the CPV of losses. The steps of using the CPT model to analyze commuting plan selection are as follows. Step 1: determining the two psychological reference points of low-income travelers, namely the earliest arrival time and the latest start time of work. Step 2: determining the commuting plans that travelers can choose from the residence to the work place, constructing the value function and the probability weight function of the commuting decision. Step 3: using the commuting cost function to calculate the commuting cost of each plan. On this basis, the CPV of all alternative commuting plans is obtained by combining the cumulative decision weights and value functions. Step 4: the scheme corresponding to the maximum CPV is the preferred scheme for low-income commuters.

Scenario Analysis

Based on the establishment of the proposed model, a multi-scenario analysis of the commuting decision behavior for low-income groups is conducted. As shown in Figure 3, assuming that the work start time is 09:00 a.m., the earliest acceptable arrival time for commuters is 08:30 a.m. and the time commuters expect themselves to arrive is 08:50 a.m. Scenario 1: starting from the place of residence, the commuter expects to arrive at the workplace within 40 min (i.e., t_Budget = t_w−t₀ = 40 min). Scenario 2: starting from the place of residence, the commuter expects to arrive at the workplace within 55 min (i.e., t_Budget = t_w−t₀ = 55 min). Scenario 3: starting from the place of residence, the commuter expects to arrive at the workplace within 70 min (i.e., t_Budget = t_w−t₀ = 70 min).

Figure 3.

The research process of the commuting decision for low-income groups.

With respect to travel mode, only walk, bicycle, bus, and metro are considered. Cars are not included because they are rarely used in commuting for low-income groups. In addition, most low-income groups live on the periphery of cities, while jobs tend to be concentrated in the city center, so this group has to travel a long distance to meet their commuting needs ( 15 , 17 ). Based on the actual survey results of commuting choices in low-income communities, the commuting travel alternatives of this group are obtained, as shown in Figure 4. Normally, the travel time of the metro is relatively stable, while that of the bus is uncertain because of climatic conditions, traffic accidents, daily road congestion, and maintenance. The time cost of the nine plans shown in Figure 4 is statistically analyzed and the perceived time and probability of different schemes were obtained, as shown in Table 1.

Figure 4.

The commuting plans of low-income groups.

Table 1.

Basic Travel Attributes of Low-Income Groups

#	Travel plan	Time consumption (min)	Travel cost (CNY)	Abbreviation
1	Walk–bus–walk	65 (40%) 75 (60%)	2	WBW
2	Walk–metro–walk	50 (100%)	3	WMW
3	Bicycle–bus–bicycle	55 (30%) 65 (70%)	3	BBB
4	Bicycle–metro–bicycle	45 (100%)	6	BMB
5	Walk–bus–bicycle	60 (30%) 70 (70%)	3	WBB
6	Walk–metro–bicycle	45 (100%)	7	WMB
7	Walk–bus–metro–bicycle	45 (30%) 55 (70%)	8	WBMB
8	Walk–bus–metro–walk	50 (40%) 60 (60%)	7	WBMW
9	Bicycle–bus–metro–bicycle	40 (30%) 50 (70%)	8	BBMB

The perceived cost of the nine travel plans under three scenarios and the expected travel cost under the EUT framework are shown in Table 2. The expected cost of bicycle–metro–bicycle (BMB) is the minimum in all scenarios, which means that BMB is the first choice of low-income commuters; walk–metro–walk (WMW) or walk–metro–bicycle (WMB) is the second choice, and the choice priority is not affected by the change of travel scenarios. It indicated that under completely rational conditions, the metro is the most reliable travel mode for low-income groups, and the commuting plan connecting the metro with the bicycle can minimize the cost for low-income travelers. In addition, Figure 5 shows the comparison results of EUT and CPT under different scenarios. In Figure 5a, the expected travel costs of walk–bus–walk (WBW), walk–bus–bicycle (WBB), walk–bus–metro–walk (WBMW), and bicycle–bus–bicycle (BBB) are relatively high, which indicates that under the EUT framework, low-income commuters will not choose these four travel plans in any scenario. However, under the CPT framework, the priority of commuting plans in each scenario is different (Figure 5b). Besides, low-income groups tend to choose BBB and WBB for commuting when the travel budget time is sufficient. This means that the commuting decisions under the two theoretical frameworks are quite different. Therefore, it is necessary to conduct a specific analysis of the CPV under each scenario.

Table 2.

Expected Travel Cost of Each Travel Plan

Travel plan	t_Perceived (min)	$ρ_{s}$ (CNY)	Scenario 1		Scenario 2		Scenario 3
Travel plan	t_Perceived (min)	$ρ_{s}$ (CNY)	C_Perceived	C_Expected	C_Perceived	C_Expected	C_Perceived	C_Expected
WBW	65 (40%) 75 (60%)	2	108.5 (40%) 133.5 (60%)	123.5	86 (40%) 111 (60%)	101	71 (40%) 63.5 (60%)	66.5
WMW	50 (100%)	5	80 (100%)	80	65 (100%)	65	65 (100%)	65
BBB	55 (30%) 65 (70%)	3	86.5 (30%) 111.5 (70%)	104	64 (30%) 79 (70%)	74.5	64 (30%) 74 (70%)	71
BMB	45 (100%)	6	70.5 (100%)	70.5	63 (100%)	63	58 (100%)	58
WBB	60 (30%) 70 (70%)	3	99 (30%) 124 (70%)	116.5	76.5 (30%) 101.5 (70%)	94	69 (30%) 79 (70%)	76
WMB	45 (100%)	7	73.5 (100%)	73.5	66 (100%)	66	66 (100%)	66
WBMB	45 (30%) 55 (70%)	8	76.5 (30%) 101.5 (70%)	94	69 (30%) 79 (70%)	76	69 (30%) 79 (70%)	76
WBMW	50 (40%) 60 (60%)	7	86 (40%) 111 (60%)	101	71 (40%) 88.5 (60%)	81.5	71 (40%) 81 (60%)	77
BBMB	40 (30%) 50 (70%)	8	64 (30%) 89 (70%)	81.5	64 (30%) 74 (70%)	71	64 (30%) 74 (70%)	71

Note: WBW = walk–bus–walk; WMW = walk–metro–walk; BBB = bicycle–bus–bicycle; BMB = bicycle–metro–bicycle; WBB = walk–bus–bicycle; WMB = walk–metro–bicycle; WBMB = walk–bus–metro–bicycle; WBMW = walk–bus–metro–walk; BBMB = bicycle–bus–metro–bicycle.

Figure 5.

Comparison of three scenarios under the expected utility theory framework and cumulative prospect theory framework: (a) expected travel cost and (b) cumulative prospect value.

Analysis of Scenario 1

In this study, the probability of arriving within a certain time limit directly indicates travel reliability. In Scenario 1, the traveler’s departure time is 08:20 a.m., t_Budget = 40 min. As shown in Table 3, bicycle–bus–metro–bicycle (BBMB) has the maximum CPV, which means that this plan is superior to others under the CPT framework, so low-income travelers will choose BBMB to commute. With respect to travel reliability, the probability of using BBMB to arrive within 40 min is 30%, which is the only travel plan that may arrive on time under this scenario. With respect to travel cost, although the ticket price is relatively high in this plan, low-income travelers are limited by the work start time, so economic cost is not the main consideration. In addition, in Table 3, the CPV of each travel plan is negative, indicating that low-income travelers always face losses in this scenario, so they tend to seek risk when making decisions and choose BBMB as the main commuting plan. Moreover, WBW, WBMW, BBB, and WBB have relatively small CPVs, and under the CPT framework, these four plans are not the first choice for low-income commuters, which is consistent with the results under the EUT framework.

Table 3.

Cumulative Prospect Value of Each Travel Plan Under Scenario 1

Travel plan	$Δ x$	$v (Δ x)$	$π_{i}$	CPV
WBW	−62.5 (40%) −87.5 (60%)	−85.62 (40%) −115.12 (60%)	0.48 0.52	−100.90
WMW	−25 (100%)	−38.23 (100%)	1	−38.23
BBB	−37.5 (30%) −62.5 (70%)	−54.62 (30%) −85.62 (70%)	0.41 0.59	−72.84
BMB	−9.5 (100%)	−16.31 (100%)	1	−16.31
WBB	−50 (30%) −75 (70%)	−70.35 (30%) −100.52 (70%)	0.41 0.59	−88.08
WMB	−12.5 (100%)	−20.77 (100%)	1	−20.77
WBMB	−12.5 (30%) −37.5 (70%)	−20.77 (30%) −54.62 (70%)	0.41 0.59	−35.44
WBMW	−25 (40%) −50 (60%)	−38.23 (40%) −70.35 (60%)	0.48 0.52	−54.87
BBMB	0 (30%) −15 (70%)	0 (30%) −10.84 (70%)	0.41 0.59	−6.37

Note: α = β = 0.88, λ = 2.25, γ = 0.61, δ = 0.69. WBW = walk–bus–walk; WMW = walk–metro–walk; BBB = bicycle–bus–bicycle; BMB = bicycle–metro–bicycle; WBB = walk–bus–bicycle; WMB = walk–metro–bicycle; WBMB = walk–bus–metro–bicycle; WBMW = walk–bus–metro–walk; BBMB = bicycle–bus–metro–bicycle; CPV = cumulative prospect value.

Analysis of Scenario 2

In Scenario 2, the traveler's departure time is 08:05 a.m., t_Budget = 55 min. As shown in Table 4, WMW has the maximum CPV, which means that this plan is the first commuting choice for low-income travelers under the CPT framework. In this scenario, the perceived time of seven plans is less than the budget time, so there are more plans for commuters to choose. Moreover, in Table 4, the CPV of each travel plan has both positive and negative values. For instance, WBW has a value of −54.87 and BBMB has a value of 6.26, indicating that low-income commuters have both gains and losses from their choices. Therefore, the choice of commuting plans for low-income groups will inevitably show the characteristics of risk aversion, that is, they tend to choose WMW with low ticket price and high travel reliability.

Table 4.

Cumulative Prospect Value of Each Travel Plan Under Scenario 2

Travel plan	$Δ x$	$v (Δ x)$	$π_{i}$	CPV
WBW	−25 (40%) −50 (60%)	−38.23 (40%) −70.35 (60%)	0.48 0.52	−54.87
WMW	15 (100%)	10.84 (100%)	1	10.84
BBB	0 (30%) 15 (70%)	0 (30%) 10.84 (70%)	0.32 0.68	7.37
BMB	6 (100%)	4.84 (100%)	1	4.84
WBB	−12.5 (30%) −37.5 (70%)	−20.77 (30%) −54.62 (70%)	0.41 0.59	−40.67
WMB	4 (100%)	3.39 (100%)	1	3.39
WBMB	10 (30%) 0 (70%)	7.59 (30%) 0 (70%)	0.32 0.68	2.42
WBMW	5 (40%) −12.5 (60%)	4.12 (40%) −20.77 (60%)	0.37 0.52	−9.24
BBMB	15 (30%) 5 (70%)	10.84 (30%) 4.12 (70%)	0.32 0.68	6.26

In addition, unlike Scenario 1, BBB is the second travel choice in Scenario 2. This plan has a 30% probability of arriving at the destination within 55 min, and the ticket price is lower than WMW. Therefore, although there is a certain risk of late arrival, considering the travel economy, some low-income residents may still choose BBB for daily commuting. Different from the preference for BMB under the EUT framework, the CPV of BMB is 4.84 based on the commuting decision model, which is only the fourth choice in Scenario 2, that is, under the CPT framework, when the travel budget time is sufficient, the time cost is not the only factor affecting the commuting decision of low-income groups.

Analysis of Scenario 3

In Scenario 3, the traveler's departure time is 07:50 a.m., t_Budget = 70 min. As shown in Table 5, the CPV of each travel plan is positive, indicating that low-income travelers always face gains in this scenario, so they inevitably tend to risk aversion when making commuting decisions. Among all commuting plans, BBB has the maximum CPV, and the probability of arriving at the workplace within 70 min is 100%. Besides BBB having high time reliability, the relatively low ticket price makes it the preferred commuting plan for low-income groups. Different from the EUT framework, the results of the commuting decision model show that under the CPT framework, WBB is the second commuting choice for low-income groups, and travelers also take travel economy as an important consideration when choosing this plan.

Table 5.

Cumulative Prospect Value of Each Travel Option Under Scenario 3

Travel plan	$Δ x$	$v (Δ x)$	$π_{i}$	CPV
WBW	5 (40%) 12.5 (60%)	4.12 (40%) 9.23 (60%)	0.37 0.63	7.34
WMW	20 (100%)	13.96 (100%)	1	13.96
BBB	29 (30%) 19 (70%)	19.36 (30%) 13.34 (70%)	0.32 0.68	15.26
BMB	18 (100%)	12.72 (100%)	1	12.72
WBB	28 (30%) 18 (70%)	18.77 (30%) 12.72 (70%)	0.32 0.68	14.65
WMB	16 (100%)	11.47 (100%)	1	11.47
WBMB	18 (30%) 8 (70%)	12.72 (30%) 6.23 (70%)	0.32 0.68	8.30
WBMW	20 (40%) 10 (60%)	13.96 (40%) 7.59 (60%)	0.37 0.63	9.95
BBMB	26 (30%) 16 (70%)	17.59 (30%) 11.47 (70%)	0.32 0.68	13.42

The comprehensive analysis of the three scenarios shows that under the CPT framework, low-income groups will engage in risk-seeking if the travel budget time is less than the perceived time when making commuting decisions. At this time, they take punctual arrival as their primary goal. However, if the budget time is more than the perceived time, they tend to avoid risks. On the basis of ensuring the travel time meets their needs, low-income commuters always seek the economy and reliability of the travel plan, as the travel economic cost is a crucial factor affecting their commuting decisions. Moreover, low-income groups usually do not pay too much attention to the convenience and comfort of travel.

A comparative analysis of the CPVs for low-income travelers choosing various plans under different budget times is shown in Figure 6. The results show that the CPV of each commuting plan increases with the increase of the budget time and gradually tends to be consistent. When the motorized mode of commuting is mainly bus, the CPV of BBB is maximum at all time points, indicating that bicycle connecting bus is the best choice in this situation. Besides, when the motorized mode is mainly metro, if the budget time is less than 50 min, BMB is the best choice. In contrast, the emphasis on travel economy will make WMW the best choice for low-income commuters. Moreover, when the motorization mode is mainly bus connecting metro, BBMB is the preferred choice at each time point. In addition, WMW is the best commuting choice when transferring to public transit by walking, and BBMB is the relatively preferred commuting plan when transferring to public transit by bicycle. In general, bicycle and metro are relatively safe and reliable commuting modes for low-income groups, and commuting plans that include either or both of these modes are often preferred by this group. Therefore, to ensure the commuting fairness of low-income groups, traffic managers should improve bicycle parking facilities and metro transfer conditions accordingly, so as to improve the commuting efficiency and travel experience of this group.

Figure 6.

Comparison of cumulative prospect values (CPVs) among different travel plans: (a) mainly travel by bus, (b) mainly travel by metro, (c) mainly travel by bus and metro, (d) transfer to public transit by walking, (e) transfer to public transit by bicycle, and (f) transfer to public transit by walking and bicycle.

Empirical Application

Survey Area and Data

We further verify the effectiveness of the proposed model for low-income groups, and test whether the actual commuting choice behavior is more consistent with the CPT framework. Besides, the starting point and main purpose of the empirical application is to provide valuable suggestions for improving the commuting plight of low-income groups in the study area. This study conducted a commuting SP survey on low-income groups in March 2021. The survey site was the Bao-li-fang-yuan community, a typical low-income community located in Chaoyang District, Beijing (Figure 7). The community covers an area of 71.8 km² and has a permanent population of 15,000. The building type is mainly affordable housing, and most of the residents are low-income migrants. To ensure that the survey data can reflect the real travel will of individuals, face-to-face interviews were conducted in the three scenarios. Because of the relatively special survey population and the impact of COVID-19, the actual survey data collection is quite tricky. In the end, we only acquired 1283 valid survey samples, 418 samples for Scenario 1, 443 samples for Scenario 2, and 422 samples for Scenario 3.

Figure 7.

The location of the survey area.

When defining low-income groups, this study adopts the Beijing regional standards and the international poverty line standards. In 2020, the per capita disposable monthly income in Beijing was 5786 RMB ( 61 ). According to the international poverty line, the definition standard of low-income groups is 5786 × 50% = 2893 RMB ( 62 ). Meanwhile, the Beijing Municipal Civil Affairs Bureau defines households with a per capita monthly income of less than 2120 RMB (290 U.S. dollars) as low-income families. On this basis, the residents with per capita monthly income of less than 3000 RMB (410 U.S. dollars) are defined as low-income groups. According to this standard, the number of low-income travelers in all survey samples is 978, accounting for 76.23%.

Descriptive Analysis

Table 6 provides the basic attributes of the respondents. The statistical results show that there is a slight gender difference, with the male and female ratios being 48.25% and 51.75%, respectively. With respect to age distribution, the respondents are mainly young people under 30, accounting for 42.32%. In addition, the occupations of the respondents are mainly service staff, self-employed, and workers. Their education levels are relatively low, with a high school degree or below accounting for 55.96%. Besides, the annual income of most families is less than 80,000 RMB, and the car ownership rate in low-income families is relatively low, while the bicycle ownership rate is high.

Table 6.

Description of Sample Characteristics

Item description	No.	Pct. (%)	P-value
Gender
Male	619	48.25	0.503
Female	664	51.75	0.503
Age
<30	543	42.32	0.371
30–65	477	37.18
>65	263	20.50
Occupation
Service staff	248	19.33	0.034
Self-employed	217	16.91
Worker	335	26.11
Enterprise staff	280	21.83
Personnel of public institutions	203	15.82
Education level
≤High school	718	55.96	0.000
Undergraduate	447	34.84
≥Master	118	9.20
Personal income (CNY/month)
<3000	978	76.23	0.021
3000–6000	218	16.99
>6000	87	6.78
Household income (CNY/year)
<80,000	897	69.91	0.000
80,000–150,000	199	15.51
>150,000	187	14.58
Driving license
Yes	554	43.18	0.000
No	729	56.82	0.000
Ownership of bicycles
Yes	809	63.06	0.106
No	474	36.94	0.106
Ownership of cars
Yes	564	43.96	0.000
No	719	56.04	0.000
Household size
1	538	41.93	0.000
2–3	498	38.82
4–6	247	19.25

Empirical Results

As shown in Table 7, when the budget time is 40 min, 66.57% of low-income respondents prefer BBMB to travel, followed by BMB (10.43%) and WMB (11.35%), which is consistent with the analysis results under the CPT framework. Some 70.64% of middle-income respondents also prefer BBMB to travel, and the priority of each travel plan is basically the same as that of the low-income groups. Besides, although the high-income groups also prefer BBMB (85.06%), they pay more attention to the travel time cost. Therefore, the four plans of WBW, WBB, BBB, and WBMW with perceived time greater than 50 min are not selected.

Table 7.

Actual Travel Choices of Different Income Groups in the Three Scenarios

Budget time (min)	Travel time (min)	Travel cost (CNY)	Low-income		Middle-income		High-income
Budget time (min)	Travel time (min)	Travel cost (CNY)	No.	Pct. (%)	No.	Pct. (%)	No.	Pct. (%)
WBW
40	65 (40%) 75 (60%)	2	8	0.82	1	0.46	0	0.00
55			9	0.92	2	0.92	0	0.00
70			11	1.12	1	0.46	0	0.00
WMW
40	50 (100%)	5	51	5.21	6	2.75	1	1.15
55			622	63.60	129	59.17	7	8.05
70			59	6.03	21	9.63	6	6.90
BBB
40	55 (30%) 65 (70%)	3	8	0.82	3	1.38	0	0.00
55			126	12.89	21	9.63	1	1.15
70			681	69.63	141	64.68	2	2.29
BMB
40	45 (100%)	6	102	10.43	20	9.17	5	5.75
55			37	3.78	12	5.50	14	16.08
70			28	2.86	8	3.67	15	17.25
WBB
40	60 (30%) 70 (70%)	3	10	1.02	3	1.38	0	0.00
55			8	0.82	1	0.46	0	0.00
70			110	11.25	21	9.63	0	0.00
WMB
40	45 (100%)	7	111	11.35	17	7.80	5	5.75
55			27	2.76	10	4.59	11	12.64
70			30	3.07	8	3.67	12	13.79
WBMB
40	45 (30%) 55 (70%)	8	28	2.86	11	5.04	2	2.29
55			15	1.53	8	3.67	8	9.20
70			8	0.82	4	1.83	9	10.34
WBMW
40	50 (40%) 60 (60%)	7	9	0.92	3	1.38	0	0.00
55			13	1.33	2	0.92	3	3.45
70			12	1.23	3	1.38	2	2.29
BBMB
40	40 (30%) 50 (70%)	8	651	66.57	154	70.64	74	85.06
55			121	12.37	33	15.14	43	49.43
70			39	3.99	11	5.05	41	47.14

When the budget time is 55 min, consistent with the analysis results of the proposed model, most low-income respondents prefer WMW (63.60%) to travel, followed by BBB (12.89%) and BBMB (12.37%). In contrast, the middle-income groups are basically the same as the low-income groups in the commuting choice, preferring WMW (59.17%), but this group pays more attention to the time cost. Moreover, significantly different from the middle-income and low-income groups, 49.43% of high-income respondents prefer BBMB, followed by BMB (16.08%) and WMB (12.64%), and neither WBB nor WBW with perceived time greater than 60 min are selected. When the budget time is 70 min, most low-income respondents prefer BBB (69.63%), followed by WBB (11.25%) and WMW (6.03%). The priority of high-income respondents’ commuting plan choice is basically the same as when the budget time is 55 min, indicating that this group pays more attention to time cost than economic cost.

The empirical application results show that the actual commuting choices of most low-income travelers are consistent with the results based on CPT. When this group makes commuting decisions under uncertain conditions, they will indeed be affected by individual risk preference and have bounded rational characteristics ( 30 ). At this time, EUT cannot effectively evaluate the alternative travel plans, while CPT is more suitable for evaluating the travel decision-making behavior of this group. In addition, the empirical results further verify the effectiveness of the proposed commuting decision model in evaluating the travel choices of low-income groups.

We found that compared with the EUT framework, the results predicted by the CPT framework were more consistent with the actual characteristics of the commuting behavior of low-income groups. The EUT framework also analyzes commuting behavior under the condition of risk decision-making; however, as a standardized behavior theory, it does not need to describe the actual behavior of this group ( 58 ), but rather explain how the group will behave under certain rational decision-making conditions.

In the analysis results of scenario 2, the BMB mode with the lowest expected travel cost is chosen under the EUT framework, while under the CPT framework, BMB is only the fourth choice. Thus, EUT provides a clear set of basic assumptions for rational decision-making: order (including completeness and transitivity), continuity, and independence. Based on these four assumptions, low-income groups under the EUT framework always choose the scheme with the greatest expected utility, that is, the scheme with the smallest comprehensive cost such as time cost and economic cost, in actual travel choice. In fact, because of various external conditions and changes in commuting time, travelers may face various risks and uncertainties, so low-income groups cannot always choose the plan with the greatest expected utility.

Since the commuting choice of low-income travelers is a dynamic and repetitive behavioral process, travelers will adjust their choice behavior on the way or day by day, according to the travel information provided by traffic managers, or found by themselves, and the travel experience each time. Therefore, considering the influence of subjective factors such as attitude and cognition of the group in the face of risks and uncertainties on the commuting decision-making process, it is helpful to deeply understand and explain the travel behaviors of low-income groups. From this perspective, the commuting decision-making model proposed based on the CPT framework is reasonable and necessary.

Summary and Conclusions

This study aims to reveal the commuting decision behavior of low-income groups under uncertain conditions. Based on CPT, a commuting decision-making model considering the travel economic cost is proposed. In view of the commuting characteristics of low-income groups, the commuting decision behavior in different travel scenarios is analyzed to acquire the priority of commuting plans. Then, based on a SP survey of residents in Beijing, the commuting behavior of this group is empirically analyzed. The results show that low-income groups will be affected by individual risk preference and characterized by bounded rational characteristics when making commuting decisions under uncertain conditions. At this time, EUT cannot effectively evaluate alternative travel plans, while CPT is more suitable to evaluate the decision behavior. In addition, travel economic cost is a crucial factor for the decision-making of this group. When the travel budget time is less than the perceived time, they tend to seek risks and take punctual arrival as their primary goal. On the contrary, they tend to avoid risks. On the basis of ensuring the travel time meets their needs, low-income commuters always seek economic and reliable travel plans. The empirical results further verify that the proposed model effectively describes the commuting decision-making behavior of low-income groups, it is superior to EUT in performance and behavior disclosure. Furthermore, bicycle and metro are relatively safe and reliable modes for low-income travelers, and commuting plans include either or both of these two modes are often preferred by this group. Although low-income groups do not pay much attention to the convenience and comfort of travel, bicycle parking facilities and metro transfer conditions should be improved to ensure commuting fairness.

Meanwhile, further research is still needed. Firstly, the definition of each parameter in the commuting cost function is relatively simple, which affects the calculation of travel perceived cost, and is not enough to analyze the commuting decision behavior of different income groups under complex conditions. Secondly, because of the relatively special study population, motorization only considers public transit and ignores the car mode. In addition, because of the particularity of the CPT model itself, this study mainly uses travel time and cost data for model construction, without considering the contribution of socio-economic and location characteristics, which is indeed the direction for further research in the next step. Finally, the survey site for empirical application is relatively single, and subsequent SP surveys in different regions should be conducted to enhance the data diversity and further improve the proposed model. Indeed, considering the low-income group alone cannot verify the applicability of the proposed model to other income groups. Comparative analysis with other income groups is what we will carry out in the follow-up study, and the application effect of the CPT model in the middle-income group and high-income group is our next research direction.

In addition, because of the small sample size of other income groups included in the collected data, corresponding comparative analysis cannot be carried out with the existing studies. At present, we are carrying out investigation and data collection for the next research direction to further verify the applicability of the CPT model in other income groups.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: Q. Geng, Y. Wang; data collection: S. Cui; analysis and interpretation of results: Q. Geng, S. Cui, J. Wang; draft manuscript preparation: Q. Geng, Y. Wang, J. Wang. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by the Fundamental Research Funds for the Central Universities of China (No. 2021YJS080).

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