Free riders and public transport

Transcription

1 MASTER DEGREE IN ECONOMICS UNIVERSITA DI TORINO Free riders and public transport Simulation models for Economics -2012/2013 Stefania Basiglio, Matteo Mondino, Davide Ritaccio

2 Index Index... 2 Introduction... 3 Procedure and assumptions... 3 Inside the program... 4 Setup... 4 Code... 5 Experiments... 8 Case 1: Relationship between the duration of the travel and the probability of non-owning the ticket. 8 Case 2: Memory effect on rational choices...10 Verbania s simulation...13 Case 3: Environmental sensibility (ES)...15 Case 4: Lazy inspectors...18 Case 5: Oil crisis...20 Case 6: More and more inspectors...23 References

3 Introduction Starting from an empirical observation of public transport in the city of Turin, we decided to build a simulation model in order to better understand and analyze the social and economical dynamics of the free riding problem and the consequences of choosing a public or private mean of transportation. The aim is to create an accurate representation of the reality and to highlight how the choice of few people can affect collectivity s decisions. We are interested in the consequences of choosing between public or private transports in terms of environmental issues, costs and benefits. In particular, referring to public transportation, we want to focus on the free riding problem where the law violation is not analyzed just from an economical point of view but also from a social one. In this perspective, the tickets inspector is not only the agent who is able to make people respect the rules but he assumes also a symbolic dimension. His presence reduces the social discomfort and can have an influence on imitative behaviors: free riders could, in fact, stop to misbehave and start paying for the services due to external pressure and to a deeper insight of the consequences of their choice. At the same time, a non-efficient control could lead normal users towards misconducts: they could stop paying and decide to become free riders instead. It would be due to increased social discomfort or for the same reason, they could decide to prefer private transport. Variables such as ticket prices, environmental sensibility, cars costs and bus costs are implemented and changeable in order to have some meaningful economical results. Procedure and assumptions Two different kinds of choices are taken into account in our model: random ones and rational ones. Random choices reflect a stochastic component in the population that represents users who prefer to move by bus or by car according to their specific necessity or irrational preferences (i.e. no driving license, office not reachable by public transports, people who do not enjoy public transportation ). On the other hand, rational choices consist of comparing Costs and Benefits of moving by public transports or by private transports. Within this context, an important assumption has been made in our model: in fact, considering equal costs for public transport and for private transport, users earn more benefits by moving by car than by taking bus. Furthermore, we want to consider environmental sensibility and car costs in order to simulate different situations and in order to have different cases to analyze. Nevertheless, preferences are changeable, each cycle users come back to home and re-decide how to move around. So again, we will have a part of the population choosing randomly and a part that form preferences by rational comparisons. 3

4 Inside the program Setup Now, let us concentrate more on the code behind the model, in particular focusing on the most relevant procedures. The setup of the model looks as it follows: From the setup, we can modify the length of the time-cycle (specified in number of ticks from 5 to 50), the cars costs, the bus cost, the environmental sensibility, the number of inspectors, the probability of nonowning the ticket (pticket) and we can decide whether or not inspectors are doing their job efficiently (laziness variable on or off). The world is divided into three subspace with three different colors: the turquoise area represents a no choice solution for the users and for the catched free-riders who will not be able to move by bus up to the next cycle; in the orange area, there are going to be placed the ones moving by public transports while in the yellow zone, there will be the ones moving by cars. Different colors have been used also for the turtles, as it follows: the green has been used to highlight the inspector(s) among all users; the blue identifies users who move by public transports; the magenta characterizes agents who travel by private transports; the white users are the ones choosing randomly their mean of transport; the red is exclusively for the free-riders caught by the inspector(s). In the interface, there are also three charts in order to report more clearly the important data produced in the simulations. The upper chart reflects the users choices between public and private transports; under this one, on the left, there is a comparison between total free-riders and caught free-riders whereas on the right, it is reported the pticket (i.e. the probability of non-owning the ticket). 4

5 Code The first procedure that determines the behavior of all the users either moving by bus or by car is the go home one. Here it immediately appears the cycle nature imposed on the model and the memory component. In fact, a new day starts when the chosen amount of ticks, imposed through the cyclelength, is reached but each new day, the users remember what happened yesterday and use this information in their evaluations (by recording only the last value). This main topic of this paper is the trade-off between public services and private means, so let us analyze the decision-making procedures and how they have been implemented. We start from the assumption that a part of the population will choose_randomly ; the following procedure explains how this has been done: 5

6 Briefly, ten out of one hundred users, each cycle, are going to choose between buses and cars relying only on a random procedure. More specifically, their random behavior derived from the random-float command. More interesting is the case in which users rationally make their decision by comparing costs and benefits arising from one choice instead of the other. This part is the core of the code, since all the main features of the model have a relevant role in determining the output. In fact, the output, here, is influenced by the environmental sensibility variable, the memory of the users and the costs-benefits analysis. Two procedures have been used for this purpose and their functions can be intuitively derived by their names: choose-private and choose-public. 6

7 In order to choose private transports, agents firstly compare costs and benefits (by taking into account also environmental sensibility) then, by considering the number of users who have travelled by public or private transports, they could decide to change their mind and move towards public zone; in this case agents will (randomly) decide whether taking the ticket or not. Conversely, in order to choose public transports, agents always make a comparison between costs and benefits then, if an excessive number of users have chosen to travel by bus, a part of the population will prefer to travel by private transports (i.e. in a more comfortable way). Moreover, in the free-riding issue, the inspector has a central role. Let us report the part of code reflecting the behavior of the inspector, the laziness influence, the definition of the free-rider and what happens to the free-rider once is caught by the inspector. When the bus-cost is equal to zero the inspector stops, in all other cases he goes around the public zone and control whether agents own the ticket or not: when the inspector finds a free-rider the probability of non-owning the ticket slowly decreases (the free-rider is catched and punished). 7

8 Experiments In this section the model has been used to simulate different pattern of situations reporting the output produced. Case 1: Relationship between the duration of the travel and the probability of non-owning the ticket This experiment is devised to highlight the relationship between the duration of the travel (cycle-length), standard for all users, and the probability of non-owning the ticket with the resulting determination of the number of free-riders on public transports. Starting with the following setup: After 1200 ticks, pticket (the probability of non-owning the ticket) has the following trend: 8

9 When the cycle-length is at its minimum value, pticket tends towards 1 (its possible maximum value): At this point, by increasing the duration of the travel, it is possible to notice how the probability of nonowning the ticket falls down very quickly. Here it is reported the case in which the cycle-length is equal to 25: The value of pticket, after 2400 ticks, has significantly decreased (it started from a value of 0.94 and it reaches the value of 0.27); also the number of total free-riders has importantly reduced. If we raise again the travel length (cycle-length equal to 50), we obtain, as result, the following graphical behaviour: 9

10 After 3600 ticks, pticket value has decreased by reaching a value very close to zero: furthermore, the number of total free-riders dropped as well. Eventually, by following the logic process of our model, we can affirm that the duration of the travel is a very important element in determining the probability of non-owning the ticket and, as a consequence, the number of free-riders in the public area. This consideration strengthens the idea that free-riders are more easily caught by the inspector(s) if the travel duration is longer; such a punishment helps to, somehow, interiorise the norm driving down the probability of non-owning the ticket. Case 2: Memory effect on rational choices Let us analyze the relationship between rational choices and memory through the following experiment. In this case, we define the starting setup as follows: According to costs and benefits analysis, we expect that a small number of users will choose private transports, since cars-cost is very high (we have imposed it to 0.9); in this way, it seems reasonable to suppose that the majority of agents will prefer public transports, since they are more convenient than the other ones (bus-cost fixed at 0.1). 10

11 In the first travel, users behave in this way: The number of agents who use private transports is represented by cars-time, while the number of public users is shown by bus-time. Up to now, everything follows our forecasts but what is it going to happen during the next day in the new cycle? Since the excessive use of public transports in the first cycle creates a crowded situation (i.e. an uncomfortable situation for the users), despite the uneconomical reasons, one part of the population is going to prefer private transports rather than cheaper buses. On the right side of the previous graph, we can notice the presence of users who would have anyway chosen private transports (identifiable with the magenta colour) and users who should have preferred public transports (identifiable with blue colour) but, since they have memorized the previous and uncomfortable travel, they choose to use private transports even if the relied cost is very high. 11

12 The effect towards which the experiment tends, is that, by repeating this simulation and maintaining the same setup as starting point, a part of agents, after the first cycle, since they remember the crowded situation previously happened, will distribute themselves, in a equitable way, between private transports and public ones. A long-run trend appears in which these two situations alternatively repeat each other: economical-choices and then-comfortable ones. Graphically, the trend looks like: 12

13 Verbania s simulation Analogously at the case previously described, we can design the Verbania experiment where a stronger assumption is made by considering bus costs equal to zero. The corresponding setup is: In this case, outputs produced are similar to the ones obtained in the case previously described: in fact, for the first cycle, most of agents prefer buses but now there is an important difference because in this case, we have that pticket and the number of free-riders is equal to zero: 13

14 As in the previous case, the memory effect determines a change on the next decision of choosing between public transports and private ones. Nevertheless, even if public transports are free, a part of users decide to choose private ones: this problem arises from the memory effect, i.e. the crowded situation previously happened, leads users towards private zone. Again a long-run trend appears in which these two situations alternatively repeat each other: economicalchoices and then-comfortable ones. Graphically, the trend looks like: 14

15 Case 3: Environmental sensibility (ES) In this experiment, it is represented a situation in which for the agents moving by cars (since cars-cost and bus-cost are fixed, respectively, to zero and to 1) should be convenient but, according to their beliefs, relied to the presence of the maximum level of environmental sensibility, they will not do so. It is easy to see how the environmental sensibility affects agents decisions. At the beginning, users decide just in terms of the comparison between costs and benefits and the greater the environmental impact is the bigger amount of users would think green and, as a consequence, could decide to avoid private transports. The output appears as follows: Fig. 1 ES equal to 1 When the environmental sensibility has a deep effect on agents choices (Fig.1) only a small part of the population still prefers private transports. It is relevant to highlight that this output is driven by the random nature of the ES procedure (we can always notice the presence of the irrational choice of the white agents who acts randomly). 15

16 By decreasing the impact of the environmental sensibility (for example by considering the case in which the environmental sensibility is fixed to 0.4), we can notice that the number of private users increases while the other part of the population always prefers not moving (since bus-cost is too high): Fig. 2 ES equal to 0.4 The really interesting thing to highlight is how the decision changes when the environmental sensibility assumes quite a marginal effect (by putting it at 0.1) according to their past experiences (this effect is evident in the long-run). In fact, since now the environmental sensibility has not a great impact on agents decisions, a notable number of users use private transports until this creates traffic jam: this information is memorized by the agents who decide to move by bus even if it is not economically convenient. 16

17 The outputs are: Furthermore, in next cycles, agents will prefer again private transports generating again traffic jam and so on. Eventually, a long-run trend appears in which private choices, no-choices and public ones alternatively repeat each other. From a graphical point of view, the trend appears as it follows: 17

18 Case 4: Lazy inspectors Inspectors do not always do their job properly, but what are the consequences on our world in such a case? In order to answer to this question: let us simulate it. Consider the following setup we compare two situations which differ the one from the other because of the presence of the laziness (or not) of inspector(s). Fig. 2 Laziness on In this simulation, our aim is to show that the lack of control by ticket-inspector(s) directly affects the pticket (defined as the probability of non-owning the ticket): agents who use public transports understand, cycle after cycle, that the inspector is not properly doing his job; as a consequence, users will not pay for the ticket and pticket slowly increases until reaching the maximum value (it is important to have a sufficient number of ticks, in the cycle-length, in order to give to agents the time to understand that inspector(s) are not working so, if they do not pay the ticket, they will not be punished and identified as free-riders). Fig. 3 No Catched FR 18

19 The probability of non-owning looks like: Fig. 4 Laziness on Fig. 5 Laziness off On the left, it is possible to immediately identify the effect on pticket of the inspector(s) laziness: in fact, there is an overall growth on the probability of non-owning the ticket that leads to an extreme situation in which all users moving by public transports are free riders. Meanwhile, in a more realistic situation in which laziness does not take place, there is a decreasing tendency that does not disappear and it is around

20 Case 5: Oil crisis An increase of oil prices would affect both cars costs and bus costs. What are going to be the strategies adopted by the agents? How much are they sensitive to the overall increasing cost? Let us start from the free-lunch case in which both public and private transports are totally free. Even if it is an unlikely situation the corresponding simulation could give more insight about the model and how it has been built. Therefore, we will focus on the marginal effect of cost, by assuming a constant and equal growth for both of them. Starting from the free-lunch world, the setup is: Such a setup has an important result because it displays an important assumption implied in our model: in fact, whenever environmental sensibility is zero, at the same costs, users prefer their own cars. The logic behind this is that cars allow users to achieve a greater utility in terms of benefits. Of course, we are strictly referring to rational choices: in fact, a portion of the population is still moving by buses but they are based on stochastic choices (white agents). As already mentioned, this result holds only for the first cycle and the odd cycles, since in the even cycles the memory of users redistribute them almost exactly among private and public transport. We repeated the same setup focusing on the marginal effects of costs. Therefore, a total of eleven simulation has been run and the data have been collected in the following framework: column cost refers to both costs (public and private), meanwhile the count of users by cars or by bus is automatically reported 20

21 by the corresponding monitors; column on foot, instead, reflects the remaining part composed of whom do not find convenient to move by car neither by bus and move on their foots. Data collected are: Costs by bus on foot by car 0, , , , , , , , , , , Graphically we then have: The chart on the left is hiding some information: in fact, the blue line, representing the users moving by bus, is covered by the green line since they have the same decreasing behavior from 0.5 onward. To better understand another chart has been used. The chart on the right gives us, for each cost level (ordinate axis), the resulting population proportion (x-axis) distributed among the mode of transport. 21

22 The results arising from the data are quite interesting: in fact, we observe how the car component, even though highly preferred for low costs at the beginning, starts decreasing constantly for costs higher than zero. Especially looking at the first chart, the bus choice appears as a parabola with negative a coefficient, appearing up-side down. In particular, it reaches its maximum value at costs 0.5. In this point, the bus-line and car-line intersect each other reflecting a perfect fifty-fifty distribution between bus and car transports. From 0.5 onward, an on foot choice starts to be adopted by the agents with an increasing path and linearly dependent on cost. As overall costs increase, the higher amount of people prefers to move on foot. On the long run, will the memory of the agents modify their choices? Considering the extreme case with costs equal to one the output for the long and almost 500 ticks: The world output is similar for each cycle and each repetition. Only the stochastic component of the population is splitting among buses and cars: such part could represent, for instance, who cannot reach their jobs on foot because of a far work location. The same stochastic behavior appears in the long-run where, opposite to other cases, we cannot find any kind of trend. 22

23 Case 6: More and more inspectors Does the presence of more inspectors affect free-riders behaviors? And in which direction does it affect pticket? Furthermore, up to which level is convenient to add inspectors? And for what purpose? In order to answer to these questions we create an experiment with the following setup: We already saw the effect of the cycle length on the pticket, so, here, it will be considered a fixed cycle of 25 ticks. The key variable is the number of inspectors: in particular, we are interested in showing the impact of the presence of more inspectors on pticket and on the amount of free-riders. Starting from the case of only one inspector, let us run the model for 2 thousand ticks; we obtain the following results: This output seems to tell us that one inspector has already some effect on fighting the crime. In fact, the pticket is overall decreasing during all the simulation reaching a final value of At the same time, the number of total free-riders is decreasing (reflecting the same tendency of pticket). With two inspectors we obtain a better situation. In particular, it seems that pticket decreases faster and it reaches a lower level than in the one-inspector case. In fact, we observe: 23

24 The final pticket is here lower (equal to 0.11) and the same happens to the number of free-riders. It is very interesting to notice that as the pticket decreases, by almost 50 %, the same happens to the number of free riders. In order to have clearer data let us put them in the following framework also for further simulations: Inspectors Final pticket pticket Bus-users Free-riders % FR in pop. FR catched %FR catched 1 0, ,17% 1 7,14% 2 0,11-52,17% ,22% 1 14,29% 3 0,059-46,36% ,24% 1 16,67% 4 0,049-16,95% ,20% 1 20,00% 5 0,029-40,82% ,33% 2 50,00% 6 0,029 0,00% ,00% ,029 0,00% ,00% 1 33,33% 8 0,029 0,00% ,00% , ,07% ,25% 2 66,67% 10 0,029 45,07% ,04% 1 100,00% It is interesting to highlight how increasing the number of inspector seems effective in terms of a decreased pticket only up to the fifth inspector. In fact, from the fifth inspector onward, the probability of non-owning the ticket seems to be constant except for the 9 th inspector case, where it seems plausible to account the increased pticket to the stochastic movement of agents. Conversely, if our purpose is to catch the free riders, we can see how increasing the number of inspectors is indeed effective. Even though we obtained significant results, a better and more complete analysis should be done in the future: such analysis should compare not only the final results of the simulation but the overall behavior of pticket, percentage of free-riders in the population and percentage of free-riders caught by using the sample mean of the values assumed by those variables. 24

25 References J. P. Carpenter Punishing Free-Riders: How Group Size Affects Mutual Monitoring and the Provision of Public Goods Source: IZA (Institut zur Zukunft der Arbeit Institute for the Study of Labor) Discussion Paper n. 1337, October 2004 Available at: U. Fischbacher & S. Gaechter Heterogeneous Social Preferences and the Dynamics of Free Riding in Public Goods Source: IZA (Institut zur Zukunft der Arbeit Institute for the Study of Labor) Discussion Paper n. 2011, March 2006 Available at: N.M. Gotts, J. G. Polhill & A. N. R. Law Agent-Based Simulation in the Study of Social Dilemmas Artificial Intelligence Review 19: 3 92, 2003 Available at: Non saranno più gratis i bus a Verbania, from Eco delle Città, 29/04/2013 Available at: 25