- The Tepperspectives Podcast is a conversation about research and insights into how artificial intelligence and machine learning intersect with business, management science and organizational behavior. Tepperspectives is guided by The Intelligent Future, a data-informed and human-driven approach to innovation and problem solving for today and tomorrow.
- Hello everyone and welcome to the Tepperspectives Podcast. Our guests today are John Hooker, the T. Jerome Holleran Professor of Business Ethics and Social Responsibility and University Professor of Operations Research Emeritus at the Tepper School of Business. And Peter Zhang, an Assistant Professor of Operations Research at the Heinz College of Information Systems and Public Policy. They're co-authors of the book, "The Structure of Fair Solutions, Achieving Fairness in an Optimization Model," along with doctoral alumnus Özgün Elçi. Gentlemen, welcome to the podcast. Peter, I'll start with you, book subtitle is Achieving Fairness in an Optimization Model. What is an optimization model and how is it used in business and public policy decisions?
- Right, so an optimization model is basically mathematical tool that helps people formulate questions formally, like into objectives, goals and constraints. For example, when we want to route trucks to deliver things or allocate medical resources, these are questions that can be in many parts, mostly quantified and then also formalized into the language of optimization. And we utilized and mathematical machinery behind optimization models to help us understand what is the best decision or what are the best decisions.
- Okay, and John, why is fairness important to include in an optimization model, and what are some examples of unfair outcomes when fairness isn't explicitly addressed?
- Okay, well first I should point out that optimization is everywhere and many of these applications involve fairness issues that we're not aware of. For example, suppose you stop at a traffic signal, at a red light and you're on a side street that crosses a main thoroughfare, then what is the best way to time the red light? Well, the optimal way is to give the thoroughfare the green light all the time and make you wait forever. That increases, it maximizes throughput. So engineers have built a fairness objective into this problem so that you get to go across the street now and then. Okay, and there are many, many other applications. So for example, there's a hurricane that wipes out the power grid. In fact, we had a storm to wipe out the power grid in Pittsburgh not long ago. So that poses the problem, do you first repair the power grid in the city where most people live? That's because it takes care of most people first, but at the same time, the people who live in the suburbs and the countryside may have to go without power for weeks. In fact, this has happened in several cases. So there we need a fairness measure somehow to balance the interests of optimization with the interest of fairness.
- Yeah, and that brings up an interesting point. Can you describe some of those fairness criteria that are discussed in the book, such as utilitarian maximum leximax or et cetera, and how someone may choose the most effective fairness criteria for a specific optimization model or use case?
- Well, I'll begin with something called the Nash bargaining solution, which was developed by John Nash, who happens to be a graduate of Carnegie Mellon. And his first paper back in 1950 proposed a formula for achieving fairness that has been generalized to something called alpha fairness, which is used in engineering, for example, that's used in regulating the internet. So the possibility of your phone achieving signals and transmitting its information depends on a fairness measure based on alpha fairness and in some cases, a Nash bargaining solution. There are others as well, which I could go into if you'd like.
- The description that you gave earlier about restoring the power grid to the locations where they're the most people first, would you consider that a more utilitarian approach to it, or is that a different type of approach?
- Yeah, a utilitarian measure is part of it, that asks us to maximize utility, that is maximize the most welfare for the most people. That's good, but the outcome can be very unfair, as I mentioned, another case might be you're designing a transit system, where do you put the bus stops? Okay, well, utilitarian measure would tell you to put most of the bus stops downtown in the city center where most of the people are. But then the people out in the suburbs have to walk two and a half miles to the nearest bus stop. Is that fair? Well, somehow you have to balance those two.
- Thinking about combining efficiency with fairness, how do you explain why both are necessary in practice when developing solutions?
- The examples that John gave a very good, for example, if you think about designing traffic lights to control the traffic in different directions. If you allow the main street to have green lights all the time, then you maximize throughput. You in some sense maximize efficiency, but that's obviously not the purpose of designing that intersection to start with. So in that case, we have very apparent case to show that considering both sides, both directions would be important. So that I think speaks to the sort of the two necessary aspects of combining fairness and efficiency. One is that fairness in some cases is a ethical and societal concern that we have to deal with or we have to protect. And the other one is that sometimes the definition of efficiency itself may be very much flawed, so therefore having a fairness consideration that contains, for example, more diverse and longer term views of the system for which the efficiency criteria may not be able to capture, just because it's too many complicating factors and a lot of implicit factors, that fairness criteria can help us balance the system in terms of helping the worst off or balancing the short term versus long term goals.
- Yeah, and you brought up an interesting point. The definition of efficiency could be flawed. And I am curious because fairness is a subjective idea and how, you know, an agreed upon definition of fairness is difficult. What may be fair to me may not be fair to other people. So how can fairness be mathematically defined and incorporated into these optimization models? And also what role do the social welfare functions play in this process?
- Yeah, completely, yes. So the definition of fairness is very subjective, and also my answer might be very subjective, John might have a different answer. The way I think about it is what we're trying to do is trying to provide a set of insights and tools for people to play with or to open the box and understand what we are doing with these technical optimization or sort of automation and AI related tools in general, it's almost like with efficiencies, like if you only have one type of objective designed, then people using the tool could be, okay, think of them as driving a car that can only go straight, but by providing the different tools in the toolbox, we allow them to turn left, turn right, and then turn around. And so that actually allows them to do things in a better way. Or from the other perspective is that I don't think we're trying to prescribe where people should go from point A to point B, but we are enabling ability to go in different directions. And also, of course, we're emphasizing the fact that we should be aware of the fairness objectives.
- So instead of just maximizing that total utility, the book does explore maximizing social welfare subject to constraints. John, can you talk about why this approach is preferred for balancing the total benefit and fairness?
- I think it may be helpful to draw an analogy with conservation of energy and physics. So there's an underlying principle in conservation of energy, but energy is measured in very different ways depending on the context, and you get a very different regime for achieving conservation of energy. So it's similar to that in fairness, there are underlying philosophical principles that help us deduce what's fair in a given case, but measuring what's fair in a given case depends very much on the situation. And a social welfare function is actually a class of functions that allows you to measure fairness. In a way it's appropriate to many different situations. So what we want to do is to illustrate what happens when you apply various social welfare functions to specific cases, what kind of results you get, and you can judge whether this is correctly measuring a type of fairness that applies to that situation.
- One thing I'm curious about with that is does that allow for what I would consider a single person's judgment to still sort of have governance over that fairness? Meaning if, you know, it's not a matter of what I would consider like something as simple as following a law. It is still left to human judgment.
- Well, human judgment is an inevitable part of any kind of modeling. So if you're maximizing profit or income or revenue or minimizing costs, you have to decide what's important, what sort of revenue matters, whether profit matters, whether it's long term or short term or stock price, you know, what kind of costs should be measured, which ones are important. All of these modeling issues are subjective in a sense, and they all have to be resolved, and they are resolved every day in thousands of applications of optimization. I believe the same can be done with fairness.
- One final question for both of you. What is the one thing that you would like any given reader to take away from this book and put into practice?
- I would say this book helps again, open the box of understanding what's the relationship between one type of design of social welfare function, fairness, objective, what is the relationship between that, and then the consequence, that goes back to the point of human subjective judgment or single person's ideas implemented in these models. By illuminating the structures or the consequences of different design, types of designs with model and fairness, we then automatically allow everyone to examine whether certain designs are appropriate for certain applications. And I think that's in my mind one way that the book can be used as a sort of a good reference for people to quickly chat. And I haven't seen anything before, I haven't seen any books before that does something like that.
- No, I would say that another objective, it's to emphasize that fairness modeling can and should be an integral part of mathematical modeling in general. So engineers and efficiency experts, students here in the Tepper School are taught how to write mathematical models for problems. They're taught how to write an objective function, which measures what you're trying to achieve. Well, fairness modeling can and should be part of that instruction and part of that body of theory and practice, no less than modeling costs and benefits.
- So John Hooker, Peter Zhang, thank you for joining us. The book is "The Structure of Fair Solutions, Achieving Fairness in an Optimization Model." And its available from Springer Nature.
- The Tepperspectives podcast is a production of the Carnegie Mellon University Tepper School of Business. To learn more, visit Tepperspectives.cmu.edu.
- Hello everyone and welcome to the Tepperspectives Podcast. Our guests today are John Hooker, the T. Jerome Holleran Professor of Business Ethics and Social Responsibility and University Professor of Operations Research Emeritus at the Tepper School of Business. And Peter Zhang, an Assistant Professor of Operations Research at the Heinz College of Information Systems and Public Policy. They're co-authors of the book, "The Structure of Fair Solutions, Achieving Fairness in an Optimization Model," along with doctoral alumnus Özgün Elçi. Gentlemen, welcome to the podcast. Peter, I'll start with you, book subtitle is Achieving Fairness in an Optimization Model. What is an optimization model and how is it used in business and public policy decisions?
- Right, so an optimization model is basically mathematical tool that helps people formulate questions formally, like into objectives, goals and constraints. For example, when we want to route trucks to deliver things or allocate medical resources, these are questions that can be in many parts, mostly quantified and then also formalized into the language of optimization. And we utilized and mathematical machinery behind optimization models to help us understand what is the best decision or what are the best decisions.
- Okay, and John, why is fairness important to include in an optimization model, and what are some examples of unfair outcomes when fairness isn't explicitly addressed?
- Okay, well first I should point out that optimization is everywhere and many of these applications involve fairness issues that we're not aware of. For example, suppose you stop at a traffic signal, at a red light and you're on a side street that crosses a main thoroughfare, then what is the best way to time the red light? Well, the optimal way is to give the thoroughfare the green light all the time and make you wait forever. That increases, it maximizes throughput. So engineers have built a fairness objective into this problem so that you get to go across the street now and then. Okay, and there are many, many other applications. So for example, there's a hurricane that wipes out the power grid. In fact, we had a storm to wipe out the power grid in Pittsburgh not long ago. So that poses the problem, do you first repair the power grid in the city where most people live? That's because it takes care of most people first, but at the same time, the people who live in the suburbs and the countryside may have to go without power for weeks. In fact, this has happened in several cases. So there we need a fairness measure somehow to balance the interests of optimization with the interest of fairness.
- Yeah, and that brings up an interesting point. Can you describe some of those fairness criteria that are discussed in the book, such as utilitarian maximum leximax or et cetera, and how someone may choose the most effective fairness criteria for a specific optimization model or use case?
- Well, I'll begin with something called the Nash bargaining solution, which was developed by John Nash, who happens to be a graduate of Carnegie Mellon. And his first paper back in 1950 proposed a formula for achieving fairness that has been generalized to something called alpha fairness, which is used in engineering, for example, that's used in regulating the internet. So the possibility of your phone achieving signals and transmitting its information depends on a fairness measure based on alpha fairness and in some cases, a Nash bargaining solution. There are others as well, which I could go into if you'd like.
- The description that you gave earlier about restoring the power grid to the locations where they're the most people first, would you consider that a more utilitarian approach to it, or is that a different type of approach?
- Yeah, a utilitarian measure is part of it, that asks us to maximize utility, that is maximize the most welfare for the most people. That's good, but the outcome can be very unfair, as I mentioned, another case might be you're designing a transit system, where do you put the bus stops? Okay, well, utilitarian measure would tell you to put most of the bus stops downtown in the city center where most of the people are. But then the people out in the suburbs have to walk two and a half miles to the nearest bus stop. Is that fair? Well, somehow you have to balance those two.
- Thinking about combining efficiency with fairness, how do you explain why both are necessary in practice when developing solutions?
- The examples that John gave a very good, for example, if you think about designing traffic lights to control the traffic in different directions. If you allow the main street to have green lights all the time, then you maximize throughput. You in some sense maximize efficiency, but that's obviously not the purpose of designing that intersection to start with. So in that case, we have very apparent case to show that considering both sides, both directions would be important. So that I think speaks to the sort of the two necessary aspects of combining fairness and efficiency. One is that fairness in some cases is a ethical and societal concern that we have to deal with or we have to protect. And the other one is that sometimes the definition of efficiency itself may be very much flawed, so therefore having a fairness consideration that contains, for example, more diverse and longer term views of the system for which the efficiency criteria may not be able to capture, just because it's too many complicating factors and a lot of implicit factors, that fairness criteria can help us balance the system in terms of helping the worst off or balancing the short term versus long term goals.
- Yeah, and you brought up an interesting point. The definition of efficiency could be flawed. And I am curious because fairness is a subjective idea and how, you know, an agreed upon definition of fairness is difficult. What may be fair to me may not be fair to other people. So how can fairness be mathematically defined and incorporated into these optimization models? And also what role do the social welfare functions play in this process?
- Yeah, completely, yes. So the definition of fairness is very subjective, and also my answer might be very subjective, John might have a different answer. The way I think about it is what we're trying to do is trying to provide a set of insights and tools for people to play with or to open the box and understand what we are doing with these technical optimization or sort of automation and AI related tools in general, it's almost like with efficiencies, like if you only have one type of objective designed, then people using the tool could be, okay, think of them as driving a car that can only go straight, but by providing the different tools in the toolbox, we allow them to turn left, turn right, and then turn around. And so that actually allows them to do things in a better way. Or from the other perspective is that I don't think we're trying to prescribe where people should go from point A to point B, but we are enabling ability to go in different directions. And also, of course, we're emphasizing the fact that we should be aware of the fairness objectives.
- So instead of just maximizing that total utility, the book does explore maximizing social welfare subject to constraints. John, can you talk about why this approach is preferred for balancing the total benefit and fairness?
- I think it may be helpful to draw an analogy with conservation of energy and physics. So there's an underlying principle in conservation of energy, but energy is measured in very different ways depending on the context, and you get a very different regime for achieving conservation of energy. So it's similar to that in fairness, there are underlying philosophical principles that help us deduce what's fair in a given case, but measuring what's fair in a given case depends very much on the situation. And a social welfare function is actually a class of functions that allows you to measure fairness. In a way it's appropriate to many different situations. So what we want to do is to illustrate what happens when you apply various social welfare functions to specific cases, what kind of results you get, and you can judge whether this is correctly measuring a type of fairness that applies to that situation.
- One thing I'm curious about with that is does that allow for what I would consider a single person's judgment to still sort of have governance over that fairness? Meaning if, you know, it's not a matter of what I would consider like something as simple as following a law. It is still left to human judgment.
- Well, human judgment is an inevitable part of any kind of modeling. So if you're maximizing profit or income or revenue or minimizing costs, you have to decide what's important, what sort of revenue matters, whether profit matters, whether it's long term or short term or stock price, you know, what kind of costs should be measured, which ones are important. All of these modeling issues are subjective in a sense, and they all have to be resolved, and they are resolved every day in thousands of applications of optimization. I believe the same can be done with fairness.
- One final question for both of you. What is the one thing that you would like any given reader to take away from this book and put into practice?
- I would say this book helps again, open the box of understanding what's the relationship between one type of design of social welfare function, fairness, objective, what is the relationship between that, and then the consequence, that goes back to the point of human subjective judgment or single person's ideas implemented in these models. By illuminating the structures or the consequences of different design, types of designs with model and fairness, we then automatically allow everyone to examine whether certain designs are appropriate for certain applications. And I think that's in my mind one way that the book can be used as a sort of a good reference for people to quickly chat. And I haven't seen anything before, I haven't seen any books before that does something like that.
- No, I would say that another objective, it's to emphasize that fairness modeling can and should be an integral part of mathematical modeling in general. So engineers and efficiency experts, students here in the Tepper School are taught how to write mathematical models for problems. They're taught how to write an objective function, which measures what you're trying to achieve. Well, fairness modeling can and should be part of that instruction and part of that body of theory and practice, no less than modeling costs and benefits.
- So John Hooker, Peter Zhang, thank you for joining us. The book is "The Structure of Fair Solutions, Achieving Fairness in an Optimization Model." And its available from Springer Nature.
- The Tepperspectives podcast is a production of the Carnegie Mellon University Tepper School of Business. To learn more, visit Tepperspectives.cmu.edu.
