«BASIC HUMAN DECISION MAKING: An Analysis of Route Choice Decisions by Long-Haul Truckers John Holland Knorring Advisor: Professor Alain L. Kornhauser ...»
is the most efficient way to account for as many of the factors that are important for making routing decisions as possible. A brief list of these decision factors includes such things as availability of alternate routes, length of alternate routes, perceived speeds on alternate routes, anticipated congestion, weather on alternate routes, scenery encountered, and hazards avoided. While this list is only a brief look at the factors involved with decision-making, it sheds light on the complexity of route choice decision making. When making decisions about planning for future use, designers look to optimize the usefulness or utility of the system. They look to get the most benefit from the least amount of input effort. This concept of cost/benefit analysis is the central tenet of utility maximization.
A good place to start when talking about utility maximization and preferences is to make a few definitions. The following properties are also the same definitions used to define rational decision-making. First, utility needs to be defined. Most economists find it easiest to define utility in terms of its characteristic properties.
The properties for Utility Maximization are as follows:6
2.2.1 Completeness The first property that most refer to is the completeness property. This property is used to rank options available. For any two options available, A and B, an individual can
always select one of the three following statements to be true. Either:
6 Nicholson, Walter. “Microeconomic Theory: Basic Principals and Extensions” Harcourt College Publishers. Fort Worth, TX. Copyright 1998. pg 69-70.
3. “A and B are equally attractive.” Given these three options to select from, the result is that the individual will always have exactly one option to select from. Given these statements, it is understood that an individual can always completely comprehend and make a decision about the attractiveness of two alternatives. The completeness assumption also eliminates the possibility that an individual can report that A is preferred to B and B is preferred to A.
An easy way to conceptualize this concept is to think about two options. Option A is you receive $20. Option B is you die. Most decision makers would prefer decision A to decision B. The completeness assumption states that, all other things being equal, if you choose A over B, you will never choose dying over receiving $20. This assumption: “all other things being equal”, as we will see later, is very important as it relates to route choice decision-making.7
The second property of preference relation is transitivity. The transitivity property is used when ranking three or more choices. This property states, “If an individual reports that ‘A is preferred to B’ and that ‘B is preferred to C,’ then he or she must also report that ‘A is preferred to C.’” This property strengthens the consistency argument in decision-making. In other words, individuals will act consistently when
faced with a decision between A and C. Since they already know that they prefer B to C, and A is preferred to B, the decision is essentially already made for the individual. 8 2.2.3 Continuity The last property of preference relation is continuity. This property states that “If an individual reports ‘A is preferred to B,’ then situations suitably ‘close to’ A must also be preferred to B.” This assumption is used when it is necessary to look at changes in responses due to a marginal change in the given information.9
2.3 Quantifying Utility: Utils Given the three properties of preference relation: completeness, transitivity, and continuity, it is possible to prove that decision makers can rank all possible decisions available to them from least attractive to most attractive. This ranking of prospects defines utility. More formally, if a persons favors A to B we would say that the utility afforded A, written as U(A), is greater than the utility afforded B, U(B).10 Utility however is more complex than just ranking prospects. It is possible to assign numbers to utility rankings. However, the numbers that are attached to an option or prospect do not signify a specific value judgment in terms of the unit of utility, utils. This assumption is referred to as the Non-uniqueness of Utility Measures.11 In other words, if U(A) = 50 and U(B) = 10, this does not mean that A is preferred to B at a rate of 5 times that of B.
Rather, these numbers are used to imply that A is simply preferred to B. The U(A) could have been equal to 1000 and the U(B) could have been equal to 1 and there would be no loss of significance to either statement. As a result, it does not make sense to ask, “How much more does the decision maker prefer A to B?” Rather, it is only possible to declare that A is preferred to B. One interesting result of the non-uniqueness principle is that now it is not possible to compare utilities of different individual decision makers because the value of utils for one person is not transferable.12
2.4 The Truck Driver Utility Function Having covered the concept of utility, it is now important to cover how utility relates to truck drivers as a decision making class. Traditional economic theory suggests that the summation of factors involved in the decision making process can be gathered in a single output utility function. Rankings and preferences can then be determined by examining the output values of several utility functions. These output values are compared using the three preference relation properties of utility maximization to come up with a final ranking of preferences. Each individual decision maker’s utility function is composed of a number of factors. Each of these factors carries a different weight in the utility function based on the decision maker’s preferences. More formally:13 12 Ibid.
13 Burner, Todd. “Exploring the Effects of Anticipated Congestion on Truck Driver Route Choice Behavior.” Princeton University, 1999. pg 12.
Given this utility function, and also assuming that the given truck drivers are utility maximizers, it is now possible to model the truck drivers preferences. It is generally assumed that it is not possible to view each truck driver’s utility function directly, however, much work has been done in the past to suggest factors that contribute to the decision making process and thus the utility function.
2.5 Factors in the Utility Function Now that the utility function has been defined, it is necessary to then determine what all of the ai and Xi factors are. In general, the process for coming up with such values is done in one of two ways. The first method, while significantly easier to do, is not as precise and does not always capture all factors well enough. This method is referred to as the stated preference method. Essentially, this method uses surveys of decision makers to determine what their preferences are. A typical question involves figuring out what the individual’s aversion to risk by posing a real world tradeoff. The typical question asked in many psychological studies is: “Would you rather get $100
right now, or take a gamble where there is a 50% probability of getting $0 and a 50% probability of getting $200?” From a probabilistic and expected value perspective, these options are equal. From this question one can determine if someone is risk neutral, risk averse, or risk seeking via the completeness property of utility maximization. Also, by adjusting the probabilities and amounts, one can begin to determine a decision makers risk aversion curve. Taken in the context of truck drivers and the real world options available to them, they will be asked if they would prefer to take a route that will take them 1 hour to cover every day, or to take a route that is 50 minutes with a probability of four out of five days, and 1 hour and 15 minutes on one out of five days. In the first case, the driver knows with certainty how long the trip is going to take him. In the second case, the driver has to choose to gamble that when he drives the second route that it will hopefully be faster. He knows that on the average choosing the second route will save him five minutes, but that the standard deviation of the trip time is over 10 minutes. This is a tradeoff of shorter times with greater variance versus longer times with certainty.
This topic will be covered again in greater detail later in this thesis.
While relatively easy to do, there are significant drawbacks to the stated preference method. First, using a stated preference method requires that the surveyed individual be able to recount past actions with a very high level of detail.14 For most individuals this is hard to do. Next, the stated preference method requires that the decision maker be totally honest with his responses to questions. This is also hard to accomplish, for two reasons. First, the decision maker may not have known exactly what happened and is unable to entirely recount the past accurately, or it is possible that the decision maker knows what happened, but for some reason chooses to answer the survey 14 Ibid.
in a non truthful manner. Lastly, the stated preference method is not nearly as scientific as the revealed preference method as it does not replicate the actual choice process that individuals face when they are driving.15 For this thesis, the revealed preference method will be used. Having a revealed preference data set means that we have data on what people actually have done, as opposed to what they think they did or what they think they would prefer to do. In general, the data for these types of studies is collected via some sort of third party observer. In collecting this data, it is important to try very hard to influence the system as little as possible in the data collection. This idea of not disturbing the system is very important because if the data collection influences the choices or behavior of the studied group, then the value of the data is significantly reduced. While harder to work with, a revealed preference data set is generally considered more valuable. As was alluded to earlier, revealed preference data sets reveal decisions that were made. Stated preference data sets allow for individuals to state their preferences. When formulated as a question, many individuals do not always state their preferences to be the same as the preferences that they demonstrate by their actions.
To come up with the Xi factors for the utility function using a revealed preference data set, the analyzer suggests a possible factor that could contribute to the utility of the decision maker. Then, an analysis is done to see if this factor is relevant to the utility function. If it is relevant, it will be included in the next step of analysis. After the number of different possible Xi factors has been exhausted, the analyzer moves to the next stage of analysis. He now needs to determine the level of contribution that each Xi factor has to the overall utility. To accomplish this, the analyzer gathers a number of 15 Ibid. pg. 22
decisions that the decision maker has made and also looks at alternatives that were available. A regression is done to estimate the contribution of each factor to the overall utility function. The results are seen as the ai factors. As simple as this sounds, it is actually very difficult to determine all of the Xi factors and their respective magnitudes of contributions to the utility function. Luckily though, there has already been much research on passenger vehicle route choice decision making to suggest some possible decision factors in the utility function. This thesis will assume that a portion of the error term is explained by non-considered decision factors.
In coming up with possible factors that would effect the decision making process for truckers, this study will start with factors that have been shown to be significant contributors in the utility function of passenger vehicles. While passenger vehicles are not expected to have utility functions that are identical to long haul truckers because of the different nature of their trips, it is safe to assume that their utility functions will be at least similar to long haul truckers. This thesis will use generally accepted passenger vehicle decision factors as a base of study for the truck driver analysis.
2.5.1 Income and Education In looking at decision makers, individuals that have a higher household income have been shown by Abdel-Aty et al. to consider a larger number of alternate routes.16 Household income is an important factor in route choice determination because as income increases, drivers are willing to consider more possible routes in their analysis of 16 Abdel-Aty, Mohamed et. Al. Models of Commuters’ Information Use and Route Choice: Initial Results Based on Southern California Commuter Route Choice Survey. In Transportations Research Record 1453, TRB, National Research Council, Washington, D.C., 1994, pp. 46-55.
picking routes. A brief example of this might be that higher income individuals are more likely to consider taking expensive toll roads. While it is important to note that higher household income is correlated to a larger number of alternate routes considered, whether or not higher income is causing more routes to be considered is a much more important question. Additionally, Khattak et al. showed that higher income drivers not only considered more alternate routes, but they also were more likely to use the alternate routes.17 Some have suggested that the correlation between income and route choice is a result of higher income drivers placing a higher value on their time, and thus they seek out more alternate routes that could potentially save them time. While this relationship has not been proven entirely, there is a strong correlation between the two.