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Appendix A Trade-Off Decisions in Selecting Driving Speeds In all day-to-day travel decisions, drivers are compelled to make trade-offs among the various costs and benefits associated with each trip. One of the trade-offs an automobile driver faces is between safety and travel time. At one extreme, a driver unconcerned with safety and concerned only with minimizing travel time would likely drive at the maximum speed the vehicle and the road would allow. Travel at very high speeds clearly increases the severity of any crash in which the driver becomes involved, and it may increase the prob- ability of being in a crash. Such a driver would probably also choose a vehicle designed to maximize speed and handling, perhaps at the expense of crashworthiness. At the other extreme, a driver uncon- cerned with minimizing travel time and concerned only with safety would probably drive much more slowly and would likely choose a vehicle designed primarily for crashworthiness. In practice, drivers rarely, if ever, adopt such extreme positions. Instead, they balance a desire for shorter travel time with a desire for greater safety and select an intermediate speed. The purpose of this appendix is to present a 215

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MANAGING SPEED 216 more formal treatment of how drivers make these trade-offs. The role of public policy in affecting these trade-offs is also discussed. A basic question is whether people deliberately trade off safety and travel time when making their trips. Some motorists indicate that this trade-off is not foremost in their minds while driving; others say that they are not conscious of making this trade-off at all. For drivers in many situations, the choice of driving speed is strongly influenced by speed limits and their enforcement, so the trade-off may be more one of travel time versus the likelihood and severity of penalties for exceeding the speed limit. But even in situations where there is little or no speed limit enforcement and many drivers exceed the posted speed limit, virtually no drivers are observed to drive as fast as their vehicles can go. Something other than the fear of speed limit enforcement must affect their choice of speed. Similarly, when weather and visibility are poor, drivers tend to slow down, often to speeds well below the posted limits. In many of these situations the driver's choice of a lower speed and increased travel time is almost certainly made with safety in mind. Thus, it appears that drivers do trade off travel time and safety even in the absence of speed limits and their enforcement. Rather than making these trade-offs consciously each time they drive, however, motorists may rely on rules of thumb based on their past driving experience. When faced with the myriad of choices in day-to-day living, people often develop rules of thumb or other heuris- tics rather than make the considerable effort to continuously optimize over all their choices. With driving, people may well rely on their past experience with particular roads or driving situations to select a driving speed that has proven to be a reasonable trade-off for them in the past. Only when faced with unfamiliar or unusual conditions would drivers be more conscious of explicitly making such a trade-off. Since speed limit signs often convey useful information about the road, some peo- ple may base these rules of thumb on the speed limit, not necessarily adhering to the speed limit but keying the speed they choose to that limit. Reliance on past experience and rules of thumb does not mean that people are ignoring the trade-off. Rather, it means that they have used their past experience to convert that trade-off to an easy-to- follow set of internal behavioral guidelines.

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217 Trade-Off Decisions in Selecting Driving Speeds How should one think about these trade-offs? In economics, such trade-offs are usually posed in terms of the benefits of one activity versus the benefits of another activity. In this case, however, the basic trade-off approach from economics is modified slightly. Safety is usually quantified in terms of probability of death or injury. Speed can just as easily be quantified for a given trip in terms of trip time. So the trade-off question is posed in terms of those two dimen- sions--the probability of death or injury (risk)1 and travel time-- rather than the two benefits of speed and safety. Consider Figure A-1, in which the trip time and risk are repre- sented.2 What one would like, of course, is to be at the origin with zero time and zero risk, but that is not possible. Instead, a driver faces a choice among the alternatives represented in the figure, indicated by the letters A to L, which are attainable combinations of both trip time and risk. In making the actual choice, an individual need not consider all points shown in the figure. Some alternatives clearly dominate others. Point E, for example, offers both lower risk and shorter trip time than Point F, so the traveler need not even consider Point F. More generally in the example, C dominates B, D dominates F, E dominates both D and F, and J dominates both H and K. All the points that are not dominated by some other point are worthy of con- sideration by the decision maker; the others are not. The set of non- dominated points is called the Pareto frontier.3 Notice that along the Pareto frontier, a driver must increase risk to reduce travel time and vice versa. 1 Risk is commonly defined as the product of probability and severity for a particular event. In this case serious injury is implicitly assumed to be equivalent to death. If degrees of severity of injury are considered, a more complex definition of risk is required. 2 This figure represents a simplification of the major trade-offs between safety and travel time that drivers face in determining optimal driving speeds. Real-world choices are more complex. They involve continuous (as opposed to discrete) decisions about speed as motorists proceed along their trips. Factors other than safety and travel time may influence the speed choice. Finally, drivers may face a route decision (e.g., to take a higher- or lower-speed road), which in turn affects their speed choices. 3 Named after the 19th century economist Vilfredo Pareto.

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MANAGING SPEED 218 Figure A-1 Pareto optimal frontier of alternatives to be explored and optimized or satisficed. How do the decision makers, the drivers, decide among the non- dominated points? Certainly they cannot all be equally desirable to a particular individual. The choice depends on how each decision maker makes the trade-off between trip time and risk. Figure A-1 shows lines of constant utility, meaning indifference as to relative preference, with the lines of higher utility (more desirable) closer to the origin. The driver's goal, then, is to select the point on the Pareto frontier that gives the highest utility, in this case Point E. Drivers who place a very high value on their lives and are relatively indiffer- ent to trip time will have relatively flat constant utility lines and will choose points with longer travel time and lower risk, like J or L. Alternatively, drivers who place a high value on trip time and are less concerned about safety will have steep constant-utility lines and will choose points with shorter travel time and higher risk, like A or C. In summary, in formal decision theory the Pareto frontier specifies the "best" (nondominated) set of physically constrained trade-offs or options among which the driver must select. The Pareto frontier is independent of the driver's subjective trade-off between risk and

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219 Trade-Off Decisions in Selecting Driving Speeds travel time (i.e., his constant-utility or preference-indifference curve). The selection amounts to finding the point on the Pareto frontier that just touches the constant-utility curve with the highest (best) utility. If the probability of death or injury is left on the Y-axis and trip time is left on the X-axis, the utility lines intersect the Y-axis at a small probability number, decrease in probability with time, and are curved, concave up. The reason why the utility lines intersect the Y-axis at a small number is that even if trip time were zero, no rational traveler would ever go on such a trip for a risk greater than some very small probability value. (Of course this intersection would differ with dif- ferent travelers and differing trip urgency.) As trip time increased, the traveler would demand in trade some improvement in risk, such that the probability of death or injury would decrease with increasing trip time. However, adding 1 h to a very long trip time would not require the same demand for incremental improvement in risk as would adding 1 h to a very short trip time, and for that reason the curves must be shaped concave up. Further extension of the curves would require them to level off to some constant risk or else be asymptotic to the X-axis (zero risk) at an infinite trip time number, but this region is undefined and makes little practical sense to consider. One critical point to observe is that, faced with the same set of alternatives, different drivers will choose different combinations of travel time and risk on the basis of how they value the trade-off. Thus, some motorists will choose to reduce their travel time by driv- ing faster and assuming more risk, while others will choose to assume less risk and drive more slowly. The same driver may even make dif- ferent trade-offs depending on the nature of the trip and the time of day or day of the week. For example, drivers may choose to travel faster on long trips where the time savings can be substantial. Thus, the variance observed in highway speeds is, in part, a natural conse- quence of these different choices. The situation portrayed in Figure A-1 is further complicated because the Pareto frontier is subject to change, both by the individ- ual and by public policy. Individuals may be able to change their risk by selection of safer vehicles. A safer vehicle may be more crashwor- thy or may have more features that make it easier to avoid certain

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MANAGING SPEED 220 kinds of crashes (e.g., antilock brakes on wet or icy roads). The risk may also be influenced by driver skill, and that skill can be enhanced by certain types of training. Thus, an individual may invest resources to alter the shape and position of the frontier. Not only do different drivers make trade-offs along the frontier differently, they may also face different frontiers. As an example of how public policy can alter the shape of the fron- tier, over time safety regulations have made vehicles more crashwor- thy, and manufacturers have introduced new technologies (e.g., antilock brakes) to assist the driver in avoiding crashes. Some of these changes enable drivers to increase speed and decrease trip time with- out increasing risk, flattening the Pareto frontier. Highway design and construction can also change the frontier. Highways built to Interstate standards provide a driving environment with a lower risk for a given speed than do two-lane rural roads. Finally, through reg- ulations such as speed limits combined with enforcement, public pol- icy may prevent (or attempt to prevent) drivers from choosing some combinations of trip time and risk and may force them to choose others. The reason for regulation of individual driver speed choices is the effect of these choices on the risks faced not only by those drivers but also by other road users, including pedestrians and bicyclists. The transfer of risk to others is the primary rationale for policy interven- tion to restrict individual driver speed choice through regulation, a subject covered at greater length in the first section of Chapter 3.