ASSESSING THE LEVEL OF ACTIVITY OPPORTUNITIES SECURED BY RURAL PUBLIC TRANSPORT SERVICE: THE CAPABILITY APPROACH

Transcription

1 ASSESSING THE LEVEL OF ACTIVITY OPPORTUNITIES SECURED BY RURAL PUBLIC TRANSPORT SERVICE: THE CAPABILITY APPROACH KITA, HIDEYUKI GRADUATE SCHOOL OF CIVIL ENGINEERING, KOBE UNIVERSITY YOTSUTSUJI, HIROFUMI ORGANIZATION OF ADVANCED SCIENCE AND TECHNOLOGY, KOBE UNIVERSITY KISHINO, KEIICHI KISHINO TRANSPORT PLANNING CO. LTD. This is a abridged versio of the paper preseted at the coferece. The full versio is beig submitted elsewhere. Details o the full paper ca be obtaied from the author.

2 Assessig the level of activity opportuities secured by rural public trasport service: ASSESSING THE LEVEL OF ACTIVITY OPPORTUNITIES SECURED BY RURAL PUBLIC TRANSPORT SERVICE: THE CAPABILITY APPROACH KITA, Hideyui; Graduate School of Civil Egieerig, Kobe Uiversity ( for correspodece: YOTSUTSUJI, Hirofumi; Orgaizatio of Advaced Sciece ad Techology, Kobe Uiversity ( KISHINO, Keiichi; Kishio Trasport Plaig CO. Ltd. ( ABSTRACT I a age of a shriig, sparse ad agig populatio i Japa, regioal areas ofte maitai poor coditios o public trasport service such as local bus service. May residets uder the poor level of public trasport service ca barely do daily-life activities at the adjacet dowtow, such as commodity shoppig, receivig regular medical care, or withdrawig deposits, etc. I cosiderig how regioal society itself should formulate a rural public trasport pla to improve ad support mobility ad accessibility of such trasportdisadvataged people i society, this study focuses o residets activity opportuities secured by rural public trasport service. A rural public trasport pla ca be uderstood as a descriptio about to what extet a public trasport service should secure opportuities to mae all residets be capable of doig dailylife activities by usig the service. Plaig the level of the rural public trasport service requires the aspect of well-beig for assessig the level of the activity opportuities secured by the service. This study aims at developig a methodology for this assessmet, by employig Amartya Se s capability approach, through the defiitios of the activity opportuities as fuctioigs ad a set of the activity opportuities as a capability. Securig the miimum of opportuities of wholesome ad cultured activities is essetially based o securig through the mutual aid of residets themselves i regioal society. Hece 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 1

3 Assessig the level of activity opportuities secured by rural public trasport service: aturally the extet of what ca be secured will be limited. Authors thi that this limitatio is determied by social choice for a combiatio of the level of activity opportuities secured by rural public trasport service, ad the burde of costs of the service. A collective security level of activity opportuities, which is assessed by use of the methodology proposed i this study, is expected to be useful for plaig iformatio regardig this combiatio. Keywords: Rural public trasport pla, Trasport-disadvataged people, Collective security level, Activity opportuities, Capability approach, Measure of accessibility satisfactio INTRODUCTION Japa s 3.11 earthquae resulted i remidig most Japaese of the importace of security ad coexistece i all regioal societies, ot oly i the disaster-strice area. Regioal areas i Japa are facig a age of a shriig, sparse ad agig populatio. I some such areas, there exist residets who ca barely do daily-life activities such as commodity shoppig, receivig regular medical care, or withdrawig deposits, etc. which are achieved by usig public trasport service such as local bus service, because of the followig three reasos (Kita, 011). The first is that, because service providers i these areas, such as shoppig cetres ad hospitals, have tae the scrap-ad-build strategy as they caot esure the sphere of service, the travel distace from the customers residetial areas to the locatio areas of adjacet service facilities has icreased. The secod is that, despite the presece of the trasport-disadvataged people who have o choice but to deped o public trasport service such as local bus service, ad also who do ot ow a family car or motorbie, the service levels of rural public trasport, such as service frequecy, umber of services ad time schedule, are lower tha urba oes. The third is that, despite the presece of agig people with physical disabilities who are ot free to go out without ay support, there are o eighbourig supporters ear such people. Uder these circumstaces, i the regioal areas, whe public trasport service providers caot help but pull the plug o a area due to low profitability, such areas have several bla zoes i the sphere of public trasport service. Therefore, rural public trasport plas should obey ew methodology which is essetially differet from a urba public trasport pla which does ot have such bla zoes. I regioal areas, oe of the mai purposes of local govermets that maitai rural public trasport service is to secure opportuities for daily-life activities which trasportdisadvataged residets caot help but obtai by meas of public trasport (Kita, Taimoto, 009; Kita, 01). Rural public trasport plas ca be uderstood to be a descriptio about residets decisios ad choices amog various alteratives regardig to what extet public trasport service should secure opportuities to mae all residets be capable of doig dailylife activities by use of the service (Kita, Taimoto, 009; Kita, 01). Securig the miimum of opportuities of wholesome ad cultured activities is essetially based o securig the mutual aid of residets themselves i regioal society. Hece aturally the extet of what ca be secured will be limited. Authors thi that this limitatio is determied by social choice, ad is a combiatio of the level of activity opportuities secured by the rural public trasport service ad the burde of costs of the service. The methodology proposed i this 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil

4 Assessig the level of activity opportuities secured by rural public trasport service: paper ca provide useful plaig iformatio regardig this combiatio i the process of assessig a collective security level of activity opportuities. I order to assess the collective security level of activity opportuities from the aspect of well-beig, this study employs Amartya Se s capability approach. The aim of this study is to develop a methodology by which a plaer for the rural public trasport pla assesses the collective security level of activity opportuities. I this methodology, based o Se s capability approach, the activity opportuities, ad a set of the activity opportuities, are defied as fuctioigs ad a capability, respectively. I various variables represetig the service level of public trasport service, this paper focuses o time schedule. The framewor of the methodology is composed of two phases. The first is the idividual assessmet phase. I this phase, the plaer measures the fuctioigs for each idividual by use of a measure of accessibility satisfactio, ad the maes each idividual choose a combiatio of the fuctioigs. I this regard, the accessibility-satisfactio measure, the value of which is calculated based o the time schedule, is idicative of how sufficiet the accessibility is. I this study, the importat thig is that ot that mobility of public trasport service is required for activity opportuities, but rather that accessibility to the opportuities resultig from the service is dealt with for the purpose of explicitly focusig o the activity opportuities. The secod is the social assessmet phase. I this phase, the plaer measures the capability of each idividual based o the combiatio of fuctioigs that each idividual has chose, ad the evaluates the collective security level of activity opportuities. This collective security level is such a level that has falle below the capability of every residet. I the sese of focusig o a maximi rule i which the situatio of the uhappiest people must be improved, the proposed methodology follows the Rawlsia priciple (Rawls, 1979). The structure of this paper is as follows: the framewor of the methodology i chapter, the mathematical models i chapter 3 ad a umerical example i chapter 4. FRAMEWORK A basic cocept of drawig up a rural public trasport pla, as illustrated i Figure 1, is that it is thought that residets themselves choose a combiatio of the level of activity opportuities secured by public trasport service ad the burde of costs of the service (Kita, Taimoto, 009; Kita, 01). I order for the residets to choose ay combiatio, a plaer for the rural public trasport pla is required to provide a list of the combiatios for them i the easiest maer possible. I particular, the object of this study is a assessmet methodology regardig the security level of activity opportuities. The proposed methodology is premised o the followig assumptios. The first is that the types of daily-life activities ecessary for the residets ca be specified by themselves is commo owledge. I this regard, however, it does ot matter if the preferece orderig of the activities is differet from perso to perso. The secod is that all residets are aware of the presece of other residets who are ot free to carry out daily-life activities that are livig i the same area. The third is that all residets ca uderstad the accessibility-satisfactio 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 3

5 Assessig the level of activity opportuities secured by rural public trasport service: Residets The level of activity opportuities secured by public trasport service Public trasport service provider The burde of costs of public trasport service A list of combiatios Social choice of a combiatio by residets themselves The object of the proposed assessmet methodology Figure 1: A basic cocept of rural public trasport pla ad the object of the proposed methodology. measure, which is idicative of how sufficiet accessibility is, as a substitutig measure for the security level of activity opportuities. The fourth is that all residets have a preferece orderig for a list of combiatios of the fuctioigs. I the proposed methodology, the plaer follows the path of the process flowchart as illustrated i Figure. The first phase is idividual assessmet. Firstly, with respect to the types of public trasport services, the types of daily ecessary activities, the slots of time i which the activities ca be secured, etc., the plaer sets several coditios which should be covered i the rural public trasport pla. Secodly, focusig o time schedule i various variables represetig the level of service of the public trasport, ad defiig a fuctioig of the residet as a opportuity that maes him/her be capable of doig various activities uder a give time schedule, the plaer measures the value of the fuctioig by use of the accessibilitysatisfactio measure. Thirdly, defiig a set of opportuities that mae the residet be capable of doig various activities uder various time schedules as a capability of the residet, ad focusig o a frotier of the capabilities emergig o the space where the axis of coordiate represets the fuctioig, the plaer maes each residet choose a combiatio of the fuctioigs o the frotier. The secod phase is social assessmet. Firstly, employig a expected accessibilitysatisfactio measure, the value of which is calculated based o the combiatio of the fuctioigs chose by each idividual, the plaer evaluates the value of the capability of each idividual. Secodly, i order to chec the collective security level of activity opportuities, the plaer checs whether or ot there exists a residet whose capability does ot exceed a give security level. If such a residet exists, the the plaer revises the time schedule because the situatio of the uhappiest residet must be improved. Otherwise such a security level which has falle below the capability of every residet is cosidered to become the collective security level of activity opportuities as a reasoable level. I this sese, the social assessmet follows a maximi rule (Rawls, 1979). 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 4

6 Assessig the level of activity opportuities secured by rural public trasport service: Idividual assessmet Coditio settig Activity opportuities => Fuctioigs A set of activity opportuities => Capability ( Measure ) Accessibility satisfactio Choice of a combiatio of the fuctioigs o a frotier of the capability Social assessmet Expected accessibility-satisfactio measure for each idividual Capability of each idividual A give security level YES Collective security level of activity opportuities NO Revise Figure : Process flowchart o the proposed methodology. MODELS Premises I a regioal area separated ito two locatios cosistig of a cetral city ad a agig village, the target of this study is the residets i the village. The aggregate umber of the residets is set as N. The meas of trasport iteded for the residets movig betwee the two locatios is oly a local bus service. The place of begiig ad edig the bus-service operatio, i.e. bus garage, is located i the city. The bus service frequecy is at a very low level i the preset situatio. The travel time betwee the two locatios eeps at a costat level. The residets i the village do daily ecessary activities at the facilities i the city by usig this bus service. A fiite set of activity types is defied as Λ. Now we assume that the activity time of the residets ad the time schedule of the bus ca be calculated based o a commo miimum uit of time feasible i a day,. A set of times couted per i a day is defied as T. I members of T, a time t ' behid a give time t i a clocwise fashio is described as t t', as a matter of practical coveiece. The we have t' t i for ay atural umber i. Regardig opeig time of a facility providig a give activity Λ, a set of the opeig times is defied as T i the uiversal set T. Ay scheduled startig time ad ay scheduled edig time of a give activity Λ become members of T. 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 5

7 Assessig the level of activity opportuities secured by rural public trasport service: Idividual assessmet Accessibility Regardig a ordered pair ( a, d) cosistig of a arrival time a T ad a departure time d T of the bus at a facility, a set of time schedules satisfied with the coditio of a d is defied as D. The set D is defied as the followig equatio. D { ( a, d) T T a d, a d T} (1) Regardig a scheduled startig time s T ad a scheduled edig time e T of a give activity, the schedule cost for the wait time whe arrivig ahead of time or departig behid schedule, ad the schedule cost for the brea-up whe arrivig behid schedule or departig ahead of time are defied as c as ad c de, respectively. The c as ad c de are defied as the followig equatios (Kita, Taimoto a d Kishio, 011). c c max{ s a, 0} max{ a s, 0} max{ e d, 0} max{ d e, 0} ( a) as sa (a) d) (b) as de ( de ed O the basis of the schedule costs defied above, a measure of accessibility for a idividual N is defied as the followig equatio, where the parameter represets the frictio of decay depedig o utilizig ability of the idividual, ad the parameter c represets the frictio of trasport. f ) (1 c)exp[ { c ( a) c ( d)}] (3) ( as de Now a measure of the accessibility with which ay residet who ca oly use the bus service may be provided with o-time travel by use of a family car is defied as Acar 1 ccar. I order to express how the value of the accessibility of the bus, f (), is sufficiet for the value of the o-time accessibility, A car, we itroduce the followig measure, where 0 f ( ) 1. f ( ) f ( ) A (4) car We term Equatio (4) a accessibility-satisfactio measure, which is provided by a time schedule for a activity of a idividual. Fuctioig A set i which members of the set Λ have bee arraged, i order of 1ˆ,ˆ,, rˆ from the most importat activity iteded for a idividual, is defied as Λ. The Λ is defied as the followig equatio. 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 6

8 Assessig the level of activity opportuities secured by rural public trasport service: Λ 1ˆ,ˆ,, rˆ 1; } (5) { 1 Whe a measure of the accessibility satisfactio with which a give time schedule ( a, d) provides the th importat activity Λ for a idividual is defied as f ( ), the f ( ) is cosidered to express the opportuities maig the idividual beig capable of doig ay activity by use of a give time schedule ( a, d). For all activities of, a set of fuctios regardig f is defied as f. I this regard, a evaluated value A for the opportuity of a give activity ca be expressed by usig the fuctio f f correspodig to the, as follows: A ( ) f f f. (6) Equatio (6) expresses the structure of idividual assessmet whe uder a give time schedule a idividual assesses the opportuity of the th importat activity, whether or ot to do the activity i fact. The fuctio f of equatio (6) idicates the correspodece of a give time schedule to a value of the accessibility-satisfactio measure, A, provided by the. We term the fuctio f a fuctioig of the idividual. I plai writig, for example, the accessibility A provided by give three time schedules 1,, 3 is expressed as ( ( ), ( ), ( 3 )) ( 1,, A 1 f 1 f f A A 3 ) with respect to the fuctioig f, or ( f ( 1), f ( ), f ( 3 )) ( A1, A, A 3 ) with respect to the fuctioig f, ad the the cosequeces deped o the set f cosistig of f 1, f f. Such a lattice of fuctioigs meas the capability. Capability Give a set of time schedules, D, ad a set of fuctioigs, f, a opportuity set of fuctioigs potetially achieved by a idividual is defied as the followig equatio. ( : ), ; ' QD f A D f f A f ' ( ) (7) We term Equatio (7) a capability of the idividual. Now i order to avoid the complicated process i which the A correspodig to all members of Λ is dealt with o the rˆ dimesioal space, we alteratively cosider to deal with a Cartesia coordiate system of A ' ad A correspodig to the first importat activity ad the secod importat activity '. If uder a give security level there are ot ay time schedules which ca secure the activity opportuities regardig ad, we cosider to deal with aother Cartesia coordiate system usig the third importat activity, or to deal with former system uder the lower security level. This idea is based o a '' lexicographic orderig rule. ' 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 7

9 Assessig the level of activity opportuities secured by rural public trasport service: A 1 Capability frotier ( ' ) f ( ) 0 ' Ray ' ( ) 1 f ' A Figure 3: The value of capability Accordig to this lexicographic orderig rule, we cosider a plae surface with two axes of coordiate, A ' ad A, where 0 A, A ' 1. I this plae surface, each axis of coordiate represets the achieved level of fuctioig. We term this plae surface a fuctioig plae. O the fuctioig plae, whe plottig every coordiate f ( ), ' f ( ) correspodig to all of D, we ca draw a frotier curve as illustrated i Figure 3, because the D is the fiite set. This frotier curve expresses a frotier regardig the capability QD : f ). We term this ( frotier curve a capability frotier. Figure 3 illustrates by a example the case that the capability frotier is cocave with respect to the origi, while the case of covex will occur. The followig is that the idea of this study is oted regardig idividual assessmet of capability. Firstly, after drawig a 45 degree lie from the origi o the fuctioig plae as illustrated i Figure 3, cosecutively we draw a ray alog a gradiet toward this 45 degree lie from a coordiate correspodig to each value of A ' ad A defied by a arbitrary time schedule D. I this study, we cosider a vertex of this ray to the 45 degree lie as the value of capability. The more the vertex correspodig to arbitrary time schedule locates o the upper right of the 45 degree lie from the origi, the higher the capability is valued. Whe each idividual chooses this ray, the value of capability ca be evaluated. Secodly, we defie the followig equatio. Equatio (8a) ca be chaged as ' / ( [ ] ) /( [ ] ' A f A f ), as described i Figure 3. Accordigly, the vertex of arbitrary ray to the 45 degree lie represets the [ A ] of equatio (a). We term ' / a combiatio ratio of fuctioigs regardig ad. ' ' ( / ) ( ) ' A f f ( ) (8a) ' 1 (8b) ' 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 8

10 Assessig the level of activity opportuities secured by rural public trasport service: The [ A ] of equatio (8a) represets the expected accessibility-satisfactio measure. ' Besides, the ( / ) of equatio (8a) represets a fuctio for idividually assessig a ' time schedule, as beig the level of [ A ] for the capability o the basis of the / chose. We term the a idividual assessmet fuctio. Thus, i idividual assessmet i this study, the expected value of fuctioigs based o the combiatio ratio of fuctioigs which a idividual chooses is the value of capability. This is a operatioal meaig to the capability approach i this study. Social assessmet I social assessmet, we cosider that importat activity opportuities for each idividual ca be socially secured accordig to several ras. The, as the criteria required regardig the security level of activity opportuities, we provide a example as show i Table 1. Whe defiig a set of these ras as L ad a security level accordig to a ra l L as l, where 0 l 1, we defie a set of the security levels, l, as θ. We assume that the θ depeds o oly the activity opportuities which should be socially secured. I this study, the situatio that a accessibility-satisfactio level, A, exceeds a give security level, l θ, is expressed as a idividual has the activity opportuities of ra l for the th importat activity,, by use of the time schedule satisfyig { mi( f ( )) l }. Besides, we term the time schedule satisfyig { mi( f ( )) l } a time schedule securig the activity opportuities of ra l for the activity. NUMERICAL EXAMPLE Settig The public trasportatio service is set as oly a local bus service. Two activity types are set, medical examiatio 1, ad shoppig, i order of importace. The miimum icremet of time,, is set as 1 hour, ad the possible operatig time for bus service, T, is set as the time betwee 7:00 ad :00, with bus service at 1 hour itervals. Table 1: Criteria of the security level of activity opportuities (Example) Ra Criterio 1 Ca do ay activity without ay difficulty Ca ot very well do ay activity 3 Ca maage to do ay activity with difficulty 4 Ca ot do ay activity 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 9

11 Assessig the level of activity opportuities secured by rural public trasport service: I additio, the opeig time of the hospital where medical examiatio 1 is provided is set as T 1, ad the opeig time of the store where shoppig occurs is set as T. The, it is assumed that the residets scheduled activity startig time s ad scheduled activity edig time e regardig medical examiatio 1 ad shoppig are each uiformly distributed over T 1, T. Whe the maximum ad miimum values for the scheduled activity startig time are defied as s, ad s, respectively, ad the maximum ad miimum values for the scheduled activity edig time are defied as e, ad e, respectively, formula (a)(b) ca be derived as follows (Appedix). c c as( as sa de( a) de( e d) / ed a) ( s a) / ( a s) / (9a) ( d e) / (9b) where the term such as ( s a) meas a time iterval, i.e., a period betwee times. Here, the parameters for the measure of accessibility for both the medical examiatio ad shoppig are defied as c = 0.5, = 1.0, as = 1.0, sa = 1., de = 1., ad ed = 1.0. As umerical examples, the followig two cases will be cosidered. I Case 1, medical examiatio 1 has s = 9:00, s = 11:00, e = 15:00, e = 17:00, ad shoppig has s = 9:00, s = 11:00, e = 13:00, e = 15:00. I Case, medical examiatio 1 has s = 9:00, s = 11:00, e = 13:00, e = 15:00, ad shoppig has s = 14:00, s = 15:00, e = 15:00, e = 17:00. Results ad discussio The results of Case 1 ad Case are show i Figure 4 ad Figure 5. However, 1 : is set as 1:1. I additio, the security level of activity opportuity for ra 1 ad ra was set at 0.6 ad 0.4, respectively. I Case 1 of Figure 4, the time schedule to secure activity opportuity at ra 1 is represeted by a set of blue poits eclosed by a red circle i Figure 3. The time schedule where the expected accessibility-satisfactio measure was highest is (10:00, 15:00). I additio, whe the time schedule is (10:00, 14:00), this time schedule is oe that the value of the expected accessibility-satisfactio measure is lowest i the set of schedules where the value of the expected accessibility-satisfactio measure is higher tha the security level for ra 1. However, whe looig at idividual activities, this time schedule does ot satisfy the ra 1 security level regardig medical examiatio, ad istead satisfies the security level of ra. I Case of Figure 5, a time schedule where the expected accessibility-satisfactio measure satisfies a ra 1 security level for activity opportuity o loger exists. Therefore, a ra security level will be focused o. As i Figure 4, time schedules to secure activity opportuity at ra are show i Figure 5, represeted by a collectio of blue poits eclosed withi a red circle. Of these time schedules, (1:00, 15:00) is the oly time schedule where the 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 10

12 Assessig the level of activity opportuities secured by rural public trasport service: Figure 5: Capability of public trasport service i Case 1 Figure 4: Capability of public trasport service i Case expected accessibility-satisfactio measure satisfies a ra security level as well as the security level for idividual activities. Regardig medical examiatios ad shoppig, looig at the scheduled activity time startig at the scheduled activity startig time to scheduled activity edig time, Case 1 is set i such a way that the scheduled activity time for shoppig is icluded i the scheduled activity time for medical examiatio. I this case, there is a high possibility that residets will coduct 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 11

13 Assessig the level of activity opportuities secured by rural public trasport service: both shoppig ad medical examiatio i the urba area i accordace with a sigle time schedule. Thus, if the activity is complemetary, the capability frotier becomes cocave with respect to the origi, as show i Figure 4. Therefore, i this case, it becomes easy to create a time schedule where the expected accessibility-satisfactio measure satisfies the security level of both activities. Case, o the other had, is set i such a way that the scheduled activity time for shoppig comes after the scheduled activity time for medical examiatio. Hece, if the activity is substitute, the capability frotier becomes covex with respect to the origi, as show i Figure 5. Cosequetly, it becomes difficult to create a time schedule where the expected accessibility-satisfactio measure satisfies the security level of both activities without reducig the security level ay further. I this case, rather tha isistig o securig activity opportuities with a sigle time schedule, there is a eed to cosider icreasig the umber of services. CONCLUSION I this paper, i order to evaluate activity opportuities provided by rural public trasport service, first, we quatified accessibility satisfactio of activity opportuities, employig a measure which has time schedule of the public trasport service as a variable. The, we defied the expected accessibility-satisfactio measure by usig a compariso ratio of fuctioigs that are desirable from a ormative perspective betwee differet activities. Next, we provided a activity opportuity security level relatig to the ra of importace of the activity. I additio, we defied a time schedule that provides a expected accessibilitysatisfactio measure that is higher tha this security level, as capability of public trasport service to secure activity opportuities. Lastly, we proposed a graphical solutio to the evaluatio of time schedule to secure activity opportuity, ad cosidered the relatioship betwee the capability of public trasport service ad the substitutability ad complemetarity of activity opportuities, usig a umerical example. If the activity opportuity is complemetary, evetually there is a eed to mae a choice amog time schedules whe there was more tha oe time schedule that secured the activity opportuity. Furthermore, if the activity opportuity is substitute, there is a eed to thi about icreasig the umber of public trasport services whe the activity opportuity has a high security level. Regardig this method of decisio-maig, it is advisable that each regioal area choose from a combiatio of level of service ad burde of cost. At that time, it is ecessary to evaluate a appropriate service level that is comparable to the burde of cost. The evaluatio method proposed i this paper should be employed i situatios where such evaluatio occurs. APPENDIX Derivatio of formula (9a) (9b) is show below. The elicitatio process of both formulae is the same, so oly formula (9a) is derived. 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 1

14 Assessig the level of activity opportuities secured by rural public trasport service: max{ s a, 0} a s 0 f ( s) ds s a ( s a) f ( s) ds s a s f ( s) ds a F ( s) a F ( a) a s a max{ a s, 0} ( a s) f ( s) ds 0 f ( s) ds a F( a) a F( s) s Whe distributed uiformly, F (s) ad F (s) are defied as a s s f ( s) ds s a F ( s) ad s a respectively. Accordigly, F ( s) 1, F ( a) 0, F ( s) 0 ad F ( a) 1. Therefore, c as ( a) as max{ s a, 0} max{ a s, 0} s a a s as sa sa s a a s as a sa a s s F( s), a s REFERENCES Alire, S. (005). Why the capability approach? J. Huma Developmet, 6 (1), Alire, S. ad J. Foster (011). Coutig ad multidimesioal poverty measuremet. J. Public Ecoomics, 95 (7), Atiso, A. B. (1970). O the measuremet of iequality. J. Ecoomic Theory, (3), Bradolii, A. (009). O applyig sythetic idices of multidimesioal well-beig: Health ad icome iequalities i Frace, Germay, Italy ad the Uited Kigdom. I: Agaist ijustice: The ew ecoomics of Amartya Se (Gotoh, R. ad P. Dumouchel eds.), pp. 1-51, Cambridge Uiv. Press. Kishio, K. ad H. Kita (010). A evaluatio idex of bus diagram to equalize activity opportuity. Proc. 1th World Coferece o Trasport Research Kita, H. ad K. Taimoto (009). Editorial: Special issue o ew movemet for local trasport plaig. J. Japa Soc. of Civil Eg., Divisio D: Ifrastructure Plaig ad Maagemet, 65 (4), (I Japaese). Kita, H., K. Taimoto ad K. Kishio (011). A time accessibility measure for plaig public trasport i rural areas. (Upublished paper). Kita, H. (011). Rural public trasport as social capital. I: Trasport Policy Studies; The Special 15th Aiversary Issue (Istitute for Trasport Policy Studies ed.), (I Japaese). Kita, H. (01). Basic act o trasport ad local public trasport pla. J. IATSS Review, Iteratioal Associatio of Traffic ad Safety Scieces, 37 (1), (I Japaese). Rawls, J. (1979). A theory of justice. Harvard Uiversity Press. Robeys, I. (006). i Practice. J. Political Philosophy, 14 (3), Se, A. K. ad R. Gotoh (008). Well-beig ad justice. Uiversity of Toyo Press. Se, A. K. (1985). Commodities ad capabilities. Amsterdam; North-Hollad. 13 th WCTR, July 15-18, Rio de Jaeiro, Brazil 13