Assessing the level of activity opportunities secured by rural public transport services: the capability approach

Kita, Hideyuki (1); Yotsutsuji, Hirofumi (2) (2016). 'Assessing the level of activity opportunities secured by rural public transport services: the capability approach' Paper presented at the annual conference of the HDCA, Tokyo 2016.

1. Background
   In hyper-aged and depopulating regional areas in Japan, as well as the 3.11 disaster-stricken areas in Japan, residents in villages who cannot do daily-life activities without moving from the villages to neighboring city, can barely do their basic activities such as buying food and taking medical treatment, because of the poor level of rural public transport services between the villages and the city. Considering how local society should support mobility of each resident in the society, this research focuses on activity opportunities secured by the public transport services.
   It can be understood that a rural public transport plan is to plan to what extent public transport services should secure opportunities of residents’ activities, for the purpose of making them capable of doing their basic activities by utilising the services. From the aspect of well-being of the residents, therefore, in order to plan the level of rural public transport services, it is necessary to assess the level of their activity opportunities secured by the services.
   Employing the capability approach (Sen, 1985), this research defines a public transport timetable as a “resource”, an individual’s ability of outing as a “resource availability” and an accessibility to activity opportunities as a “functioning”. Hereby, this research regards a set of the activity opportunities as a “capability”. The aim of this research is to develop a method of measuring the capability defined by the activity opportunity set, and to show a methodology for assessing the level of activity opportunities secured by the rural public transport services.
2. Methodology
   This study especially focuses on the service level of a bus with a fixed route connecting a city to a village, and examines the bus timetable which is chosen among several indices of the level of bus service. The proposed methodology has two stages, which consists of individual assessment stage and social assessment stage.
   In the stage of individual assessment, firstly, an accessibility index is formulated on the basis of the bus timetable and the individual’s ability of outing. Calculating the value of this index, a planner of the rural public transport plan estimates the accessibility to activity opportunities for each individual, i.e. the functioning. Secondly, a functioning space is defined as a spatial coordinate system which makes multiple functionings the axes of coordinate. The planner lets each individual choose a “compositional ratio of functionings”. This research, then, regards a set mapped on a spatial diagonal line via the chosen compositional ratio in the functioning space, as a set of activity opportunities, i.e. the capability.
   In the stage of social assessment, based on the capability that each individual has revealed, the planner checks the existence of any individual whose capability does not exceed a planned level of activity opportunities secured by the bus service. If such individual exists, the planner revises the given bus timetable, otherwise, the planned level is considered to be a level of activity opportunities that has been socially secured.
   Now, we display an example regarding the proposed method of measuring the capability. Two activities, λ1 and λ2, and two bus timetables, ω1 and ω2, are handled. We define the accessibility to opportunities of any activity λ which an individual n is capable of doing by utilising given timetable ω, as the accessibility index, fnλ(ω). Then, we illustrates a functioning plane which makes two functionings, fnλ1(ω) and fnλ2(ω), the two axes of coordinate, on which every coordinates, {fnλ1(ω1),fnλ1(ω2)} and {fnλ2(ω1),fnλ2(ω2)}, are plotted corresponding to bus timetables, ω1 and ω2, respectively.
   After drawing a 45-degree line from the origin in the functioning plane, we focus on a coordinate corresponding to two accessibility indices, {fnλ1(ω1),fnλ2(ω1)}, defined by arbitrary bus timetable ω1. Then a “ray” along a gradient toward the 45-degree line from this coordinate is drawn by an individual. This research regards a vertex of this ray to the 45-degree line as the value of capability. The more the vertex corresponding to arbitrary bus timetable locates on the upper right of the 45-degree line from the origin, the higher the capability is valued. When each individual chooses this ray, the value of capability can be evaluated. Here, we define the following two equations.
v(ω   πn1/πn2)=E[Anλ]=πn2fnλ2(ω)+πn1fnλ1(ω) --- (1)
πn2+πn1=1 --- (2)
   Equation (1) can be changed as -πn1/πn2=(E[Anλ]-fnλ2)/(E[Anλ]-fnλ1) using equation (2). As described in the functioning plane, the vertex of arbitrary ray to the 45-degree line can represent the E[Anλ] of equation (1). Then, we term the πn1/πn2 a “combination ratio of functionings” regarding λ2 and λ1. The E[Anλ] of equation (1) means the expected accessibility. The v(ω   πn1/πn2) of equation (1) is a function representing that individual n evaluates bus timetable ω as the level of capability equals the E[Anλ] on the basis of the chosen πn1/πn2. We term the v an “individual assessment function”.
   Thus, individual assessment value of capability is regarded as the expected value of functionings based on a combination ratio of the functionings which the individual has chosen.  This is an operational meaning to the capability approach of this research.
3.Findings and Implication
   As the results of numerical example this research has shown, in the case that residents can wait for bus service without difficulty and one activity bears complementary relationship to another, the activity opportunities are easily secured even under the low service-frequency conditions, in contrast, in the case that one activity bears substitutable relationship to another, alternatives such as the added buses are worth considering.
   The level of daily-life activity opportunities secured by rural public transport service, which is quantitatively assessed by using the proposed methodology in this research, is expected to be useful planning information, in comparison with the level of the service. In this sense, the capability measurement method proposed by this research is considered to a profoundly-pragmatic method.

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