Consumer Optimization Problem Solving

Alfred L Norman

• Publisher: WSPC
• Year: 2014
• eBook ISBN: 9789814635301
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

What algorithms are tractable depends on the speed of the processor. Given the speed of digital computers, polynomial algorithms are considered tractable. But, a human can take several seconds to make one binary comparison between two pens. Given this slow speed, sublinear algorithms are considered tractable for an unaided human and this defines Simon's concept of bounded rationality.

Humans make simplifications to solve the intractable consumer optimization problem. Consumers search for goods and services item-by-item, which greatly reduces the number of alternatives to consider. In addition, consumers have operators that can process a set in a single operation. Also, consumers budget by incremental adjustment.

In considering consumer performance the question to ask is how close to optimal is consumer performance and not whether consumers optimize as a yes/no question. Given the ordinal nature of utility theory this creates a basic measurement problem. The book presents a review of the literature on consumer performance.

This is an opportune time to study consumer procedures because the Internet provides a media to make substantial improvements in consumer performance. The book includes a case study comparing the performance of a digital camera selection code with the advice of sales people. A field experiment demonstrates that the software code provides better advice.

Contents:

• Introduction
• Computational Complexity
• Ordering
• Computational Complexity: Decision Rules
• Repeated Price Search
• Repeated Item Search: Forecasting
• Repeated Item Search: Choice
• Budgeting
• How Close to Optimal?
• Improving Consumer Performance
• Appendix: CC of the Discrete Two-Stage Budgeting Problem

Readership: Students at postgraduate level and academics researching theoretical, computational, behavioural and experimental economics with a specific focus on consumer behaviour, decision making, and optimization.

Chapter 1

Introduction

1.1 Introduction

What algorithms are tractable depends on the speed of the processor. A cell phone processor can execute millions of instructions per second. Solving the consumer optimization problem is known to be tractable for a digital processor. In contrast, the System 2 (conscious) processor of the human brain is known to be very slow. For example, a human can take several seconds to make one binary comparison between two pens. Given the slow speed of the human conscious processor we argue that solving the consumer optimization problem is intractable for an unaided human.

We study the simplifications consumers employ to solve the consumer problem. Consumers search for goods and services item-by-item, which greatly reduces the number of alternatives to consider. In addition, consumers have operators that can process a set in a single operation. Finally, consumers budget by incremental adjustment.

In considering consumer performance we focus on how close to optimal is consumer performance and not whether consumers optimize as a yes/no question. Given the ordinal nature of utility theory this creates a basic measurement problem. We review the literature on consumer performance.

This is an opportune time to study consumer procedures because decision aids presented on the Internet can make substantial improvements in consumer performance. We create software for digital camera selection that we demonstrate with a field experiment provides better advice than the advice of sales people.

We now discuss the organization of the book in greater detail.

1.2 Computational Complexity and Consumers

Chapter 2: Computational Complexity

In this book, formal models of consumer procedures will be specified as algorithms that will be defined in terms of the specified elementary operations, which, as will be discussed in Chapter 2, are defined as System 2 (conscious) operations. These will include psychological decision rules, information operations, as well as arithmetic operations that will be treated as black boxes with execution costs. We will not consider the details of how the human neural network performs these elementary operations. There is a precedent for this approach in that [Huber (1980)] and [Johnson (1988)] proposed studying decision strategies by their elementary information processes.

Algorithms can be analyzed by computational complexity, which is a measure of the difficulty in solving a problem asymptotically. The analysis focuses on determining how the cost function of an algorithm increases with respect to one or more growth parameters. An example of a growth parameter would be the number of alternatives for the consumer to consider. Given the large number of alternatives and astronomical number of corresponding bundles in the marketplace, this type of analysis is appropriate.

A basic overview of these techniques used in the book is presented. We also present our analysis of the computational complexity of a discrete consumer utility optimization model and a review of the subsequent literature.

How difficult a problem a processor can solve depends on the speed at which the processor executes an elementary operation. Problems which a processor can solve in a “reasonable” amount of time are called processor tractable. Let us first consider DC tractable, which is tractable for digital computer processors. A computer with a processor capable of computing 1 billion floating point operations a second could complete a linear program over 1 million alternatives executing 1000 operations per alternative in 1 second. This is clearly DC tractable. Given the speed at which digital computers execute operations, algorithms for which the cost function increases as a polynomial of the growth parameter are considered tractable in that it could be executed in a time considered economic. Nevertheless, the discrete consumer utility optimization problem in the general case is not DC tractable, unless we impose an additional condition on the problem.

Now let us consider a human as a computational agent executing System 2 (conscious) operations. Compared with a digital computer, an unaided human is generally very slow in executing an operation. For example, we determined that subjects took about 3.2 seconds to execute a binary comparison involving two pens, [Norman et al. (2004)], and we are 90% confident that is is greater than 1.5 seconds. A linear human algorithm requiring 3.2 seconds to compare two alternatives would take 889 hours to process a million alternatives. This is not tractable for unaided humans. Human tractable will be abbreviated to H tractable.

Theories of human procedures must not require more computational resources than humans possess. Faced with the number of alternatives that a consumer encounters in the marketplace we assert that sublinear algorithms are H tractable and that algorithms linear and higher are not except for a small number of alternatives. This defines Simon’s concept of bounded rationality in terms of computational complexity. Computational complexity analysis is useful because if a consumer model created by economic theorists is not H tractable then the researcher should ask how does the consumer simplify the problem to obtain a H tractable algorithm, and what is the performance of such an algorithm relative to the optimal solution of the theoretical model.

We consider how consumers simplify the consumer optimization problem in order to obtain an H tractable problem. In the theoretical model consumers maximize their utility by evaluating alternative bundles of goods subject to the budget constraint. But, in the marketplace consumers purchase their goods item by item. In order to intuitively understand why this is the case, let us consider two models of a grocery store. The first model is the traditional grocery store where the consumer traverses the aisles filling the shopping cart item by item. An item-by-item grocery store organizes close substitutes such as brands of cereal in the same aisle.

A second model is a bundles grocery store that enables the consumer to compare bundles of groceries. In such a store the consumer walks down a single aisle comparing shopping carts, each loaded with a basket or bundle of groceries. In addition to the current practice of listing the price of each item, assume the store lists the price of the entire bundle on the shopping cart. Also, assume the store organizes the giant line of shopping carts containing all the possible bundles in ascending order by bundle price.

To obtain some perspective of the number of alternatives that must be considered, let us assume that the two grocery stores each carry 30 categories of goods and 10 alternatives in each, for example, 10 types of cereal and 10 types of bread. These numbers are very conservative for a modern grocery store. In this case the number of shopping carts that the consumer must consider in the bundles grocery store is 10 × 10 × 10 × ... × 10 = 10³⁰. If it only took 10 seconds to make a binary comparison between two bundles of 30 items, it would take 1.59 × 10²³ years to find the preferred bundle using the linear procedure of comparing the first with the second and the preferred with the third and so on. If each bundle were placed in a 3-foot-long shopping cart then the consumer would have to travel 5.68 × 10²⁷ miles just to view all the bundles.

To drastically reduce their display space, sellers organize their goods for item by item acquisition, and consumers acquire goods item by item to drastically reduce the number of alternatives they need to consider. In the case above acquiring groceries item-by-item reduces the number of alternatives to consider from 10³⁰ to 10 + 10 + 10 + ... + 10 = 300 that is the number of alternatives increase additively not geometrically.

We assert that humans achieve sublinear algorithms to solve their consumer optimization problem by making the following simplifications:

1. They search for goods and services item-by-item. These searches are sublinear because as we shall show, humans have operators that can process a set in a single operation.

2. They budget using an incremental adjustment process.

Consumers make sequential item searches for goods and services all their lives. While consumers may not be optimal in their searches, they do have an incentive to improve the efficiency of their searches. This raises a basic question: How do consumers improve the efficiency of their item searches over time?

1.3 Component Studies

Before examining how consumers learn to be efficient in repeated searches, we present preliminary studies of some components of the consumer problem in the next three chapters.

Chapter 3: Ordering

We use experiments to show that humans can order a small number of items using a linear procedure. Binary comparison operators form the basis of consumer set theory. If humans could only perform binary comparisons, the most efficient procedure a human might employ to make a complete preference ordering of n items would be a n log₂ n algorithm. But, if humans are capable of assigning each item a utility value, they are capable of implementing a more efficient linear algorithm. We consider six incentive systems for ordering three different sets of objects: pens, notebooks, and Hot Wheels. We establish that subjects are using a linear procedure by performing regression analysis, observing the hand motions of the subjects, and talking with the subjects about which algorithm they used. What makes regression analysis possible is that a binary comparison takes seconds not nanoseconds.

This research demonstrates a case where being able to create a utility value leads to a more efficient algorithm than just using a binary comparison. The fact that humans can order a small number of alternatives such as stores, products, or attributes using a linear procedure is useful to develop efficient search procedures over time.

Chapter 4: Computational Complexity: Decision Rules

A consumer entering a new bookstore can face more than 250,000 alternatives. We then consider the efficiency of using various known psychological decision rules in search procedures. In this analysis we assume that the cost of creating such decision rules is fixed and that a consumer uses the same decision rule plus an information operator from start to finish. We show that procedures based on these known rules in search are linear procedures and that such rules are not H tractable given the number of alternatives the consumer faces in the marketplace.

We introduce a new psychological decision rule based on a set information operator, and show that it leads to a sublinear procedure. Next, we perform an experiment to show that humans have the ability to employ such a rule effectively, and finally we show that markets in both physical space and cyberspace are organized to facilitate the use of such set rules by consumers. In cyberspace, decision rules can be encoded as decision aids, which can be considered to have an H tractable constant complexity from the perspective of the user.

Chapter 5: Repeated Price Search

In this chapter we consider repeated price search. Consumers check few sites in online purchases. We perform repeated price search experiments that are dynamic Bayesian optimization problems for which the subjects could not calculate the optimal strategy. Instead, they used heuristics whose performance is better than random and less than optimal. To investigate online price search performance we surveyed students on their online text-book purchases. Students achieve good performance because they start with a good strategy and because of the online market organization of marketplace and meta-search sites. An important factor is that algorithms at sites searched perform calculations that reduce the computational complexity of the search.

We argue that economic price search theory is flawed because computing the reservation price is H intractable and in repeated price searches consumers learn relative prices of sellers not the distribution of prices of the current search. Finally, new decision aids on the internet and on smart phones that effectively reduce the computational complexity of a price search to an H tractable constant complexity are changing price search strategies.

1.4 Item Search and Budgeting

In the next three chapters we present our theory of how consumers solve the economic consumer problem. We relax the assumption that tastes are given and assume that preferences are learned. If pressed, very few economists would assert that consumers acquire a complete preference ordering neatly encoded in their genome at conception. When cardinal utility was formulated in the 19th century, consumers had few choices and the rate of technological advance was slow. Under these conditions it was a reasonable assumption to assume that a consumer had learned his preferences by the time he became an adult consumer. Today consumers face a very large number of alternatives and frequently encounter products that have new features or are completely new. Under such conditions they learn their preferences as part of the item search. The important question is to what extent is it efficient for consumers to learn their preferences.

Chapter 6: Repeated Item Search: Forecasting

Consumers in considering their alternatives need to forecast the future performance of an alternative in its intended use. When consumers have developed stable preferences over specific alternatives, this forecast is encapsulated in the utility function.

For frequently purchased goods such as food, consumers can forecast the future performance and learn their preferences by a sequential trial and error (STE) strategy that is a strategy in which consumers sequentially try different alternatives until preferences are formed. We investigate how students use this strategy to choose which restaurants to frequent for lunch.

The longer the time period between purchases and the greater the rate of technological change, the less useful a STE strategy becomes for forecasting and the less the value of prior consumption. With the rapid rate of technological change and the proliferation of goods and services in the marketplace, consumers must develop strategies for forecasting the performance of alternatives with which they may have had little experience.

As consumers have limited ability to test most products, consumers must gather data from others including media ads, data supplied by the sellers and manufacturers, product reviews by current users and experts. We review the development of data sources first in newspapers, magazines and now the Internet. How much data should a consumer acquire to forecast? It is not “perfect information” because this concept is not easily definable in that the potential limit of data a consumer could acquire and process is determined by the Heisenberg uncertainty principle. Given that acquiring and processing data has real costs, it is readily apparent that consumers acquire and process a truly minuscule fraction of the data that could be provided to them. The information value of data is a function of its processing cost, reliability and capacity to discriminate among alternatives.

In forecasting beyond consumption experience, consumers use a wide variety of procedures that we demonstrate using digital cameras as an example.

Chapter 7: Repeated Item Search: Choice

A typical consumer item search has the following steps:

1. Goal and start set
2. Several set decision steps
3. Evaluation of specific alternatives in the final set
4. Selection of preferred item or items.

With repeated searching the number of alternatives in the start set decreases and in some case it can decrease to one in which case an item search has been reduced to a replacement operation. The amount of System 2 effort involved in making the various steps decreases over time and steps are combined.

Over time a consumer develops a variety of types of item searches for different types of goods that vary greatly depending on the frequency of purchase, the cost, the type of goods, and the rate of technological change. There is also tremendous variation in item search for the same type of product among consumers.

Consumers achieve search efficiency through repeated searches by acquiring a great volume of consumer knowledge about market organization and goods and services. The acquisition of this knowledge starts in early childhood and while prosaic, is extensive. In repeated searches there is no point in remembering preferences over specific alternatives that will be replaced by new products by the time of the next search for that good. An important factor in consumer search efficiency is that consumers learn decision rules and preferences over sets and attributes that will be useful in future shopping. We demonstrate this factor with a study of students’ search for jeans.

Chapter 8: Budgeting

An optimal solution of budgeting considering every possible bundle is H intractable. Even allocating money into alternative accounts is a quadratic process. For example, there are 5050 possible allocations in the case of allocating $100 into three accounts in $1 increments. How do consumers obtain H tractable heuristics to solve the budgeting problem?

In order to understand budgeting we conducted several surveys of students who lived in apartments. At our university most students live in a...

Table of contents

• Cover Page
• Consumer Optimization Problem Solving
• Title Page
• Copyrights
• Acknowledgements
• Table of Contents
• 1. Introduction
• 2. Computational Complexity
• 3. Ordering
• 4. Computational Complexity: Decision Rules
• 5. Repeated Price Search
• 6. Repeated Item Search: Forecasting
• 7. Repeated Item Search: Choice
• 8. Budgeting
• 9. How Close to Optimal?
• 10. Improving Consumer Performance
• Appendix A CC of the Discrete Two-Stage Budgeting Problem
• Bibliography
• Index