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May 1, 2025
May 1, 2025

Selected Algorithms in Linear Algebra Home Exam

General Instructions 1. Submission of a solution to this exam constitutes a statement that you followed these instructions.

If you failed to follow some of the instructions for whatever reason, explain at the top of the exams which instructions you failed to follow, how you solved the relevant parts of the exam, and why.

2. The exam is individual. You may not discuss the exam, your solutions or other solutions, or anything having to do with the algorithms and computations that the exam focuses on with any person except Sivan Toledo. You must follow this rule before, during, and after you solve the exam (including in the periods before you start the exam and after you submit your solution, since different students may solve it at different times).

3. You may only discuss this exam with persons other than Sivan Toledo after the grades are published.

4. You may use any publicly-accessible non-human resource to solve the exam but you must cite every resource that you use. ,For books, articles, web sites, and so on, cite the title, author, and URL, and explain how you used the resource. For AI tools and other responsive resources, give the name of the tool (and URL if not well known) and the prompts. If the interaction was complex, just summarize the interaction. In both cases, explain how you used the results.

5. Include all the code that you used and mark clearly code that you wrote code from other sources (static or responsive/AI)., If you fixed or corrected existing or generated code indicate your changes or fixes clearly.

6. All code must be clearly documented using comments.,

7. Use diagrams and graphs where appropriate to clarify and/or enhance your answers.,

1 Efficient and Stable Factorization of Anti-Symmetric Matrices (40 points)

Algorithms in Linear Algebra 

We can solve a linear system of equation with an <-by-< symmetric positive-definite matrix � using the Cholesky factorization using 1

3< 3 + =(<3) arithmetic operations. The algorithm is backward stable and it is

about twice as efficient as an !* factorization with partial pivoting, which is also usually backward stable, but does not exploit symmetry. In some vague way it makes sense that Cholesky would be twice as efficient

because due to the symmetry of the matrix, we can represent it using its upper and lower half, so we do not need to update the entire trailing submatrix after every elimination step.

In this problem we want to factor in a backward-stable a real matrix that is not symmetric, but satis- fies the constraint �) = −�. In other words, its elements satisfy �7 8 = −�87. We will call such matrices anti symmetric. Such matrices are fully defined by about <2/2 real values, not <2, so we hope to achieve computational savings similar to the savings in Cholesky.

The main building block in our new algorithm will be to zero most of the first column by subtracting a multiple of the second row of � from rows 3 : <. We will then zero most of the first row by subtracting the same multiples of the second column from columns 3 : <. We continue with the trailing submatrix in the same way, until we reduce � to a tridiagonal matrix) , in only sub- and super-diagonal elements)7+7,7,)7,7+1 are nonzero, and which is also anti symmetric.

1. Implement this algorithm and test it on random matrices with Gaussian elements. The algorithm should return twomatrices, a lower triangularmatrix !with 1s on the diagonal and an anti symmetric matrix ) , such that � satisfies � = !)!) (but a weaker condition in floating point). For simplicity, operate on all the elements of � and the trailing submatrices, not only on one triangle. Try to make the code as efficient as possible (while operating on both triangles). Test that it works correctly and explain how you performed the tests. Hint: As in !* with Gaussian elimination, if you eliminate column 8 with using a matrix !8 with ones on the diagonal and the negation of the multipliers below the diagonal in one column (which one?), thematrix ! should have themultipliers in the same position, but not negated.

2. Roughly how many arithmetic operation does your code perform? The answer should be given as an explicit multiple of <3; you can ignore low order terms. Please relate your answer to the number of operations that the !* factorization performs. Explain the result.

3. If you were to modify the algorithm and the code from Part 1 so that it would only operate on one triangle, say the lower one, howmany operations would the improved algorithm perform? How does this relate to the number of operations performed by the !* factorization?

4. The main motivation for this algorithm is that we can incorporate into it partial pivoting. Show that the algorithm, as presented up to now, can fail, and explain why it might be unstable even in cases where it does not fail.

5. We can avoid these problems by exchanging before we eliminate column 8 and row 8 two rows and the same two columns so that the element in position 8+1, 8 in the trailing submatrix has the largest mag- nitude among elements 8 + 1 : <, 8. We can express the overall factorization as %�%) = !)!) ,where % is a permutation matrix. Explain how these exchanges affect the matrix !. How do you think we can characterize the trailing submatrices and) if we perform these exchanges, both in the worst case and in practice? You only need to provide a reasonable characterization and to justify it from what we know about !* with partial pivoting; you do not need to provide a formal analysis.

6. We can make this algorithm even more efficient by noticing that the matrix � = )!) is upper Hes- senberg (elements �7 8 with 7 > 8 + 1 are zeros). Prove that this is indeed the case and explain how elements of ) relate to elements of � (so that we can construct ) from �).

7. Modify your code from Part 1 so that it computes ! and � . You can again update the entire trailing submatrix.

8. Explain how this modification reduces the number of arithmetic operations and give an estimate for the number of operations that the algorithm performs if it exploits the anti-symmetry (the leading term only).

9. To solve a system �F = %)!)!)%F = 1, we need to solve linear systems with a anti-symmetric tridi- agonal matrix) . Explain howwe can do that in a backward-stable way in$(<) arithmetic operations and storage.

2 Benchmarking Linear Solvers (30 Points) The aim of this problem is to benchmark a number of exiting solvers of linear equations. The focus is on producing valid and robust results and on presenting them well. For this problem, it is important that the solvers be efficient. Matlab is considered the gold standard for this problem. All its solvers are good enough (if used correctly); you can use some other programming environment (e.g., Python), but if one or more of its solvers is inefficient, you may lose points.

1. Implement a function lap2d that creates the Laplacian of an <-by-< two dimensional grid. Theweight of all edges should be 1, and the row-sums of all rows other than the first should be 0. The sum of the elements in the first row should be 1. The row/column ordering of the matrix should be a row- by-row ordering of the grid vertices (the so-called natural order). Thematrixmust be represented efficiently as a sparsematrix (inmatlab, the form S=sparse(i,j,a) is a goodway to construct the matrix from a set of nonzero values 07 8) Plot the nonzero structure of the matrix (spy) for a 10-by-10 grid.

2. Implement a similar function lap3d for 3-dimensional grids. Plot it for some convenient size for which the structure of the matrix is clear from the plot.

3. Write a code that measures the performance of several linear solvers for �F = 1, where � is a Lapla- cian from Part 1 and 1 is a random vector. You The solvers that you need to implement are:

(a) A dense Cholesky factorization. In Matlab, A=full(S) creates a dense representation of a sparse matrix.

(b) A sparse Cholesky factorization, with a row/column permutation to enhance sparsity in the factor. In Matlab, help chol (or the more detailed doc chol) will tell you how to invoke the Cholesky factorization so that it can permute the rows and columns of a sparse matrix.

(c) Conjugate gradients without a preconditioner (pcg in Matlab).

(d) Conjugate gradients with an incomplete-Cholesky factorization with no fill (ichol in Matlab).

4. Demonstrate that each of the solvers is correct. For the iterative solvers, explain their accuracy of the solution that they return and compare to the solution of the direct (Cholesky factorization) solvers. For the sparse solver, show the nonzero structure of the factor, to demonstrate that it is indeed sparse.

5. Compare the performance of the 4 solvers by finding out the size of the largest grid they can handle (in both 2D and 3D) in 10s (only the linear solver should take 10s; exclude the time to construct the test problem). You will need to write code that finds these problem sizes. You are free to also present the performance of the 4 solvers in other ways. Make sure your results are statistically robust; the

3

 

 

actual running times are not deterministic even if the algorithm is. You need not perform a statistical analysis, but you need to account for the running-times variability and to explain how do you did it. In this part of the problem, do your best to ensure that the solver is using only 1 CPU core (in Matlab, maxNumCompThreads(1) should work); explain how you restricted the solvers to 1 core and how you checked that they are indeed using only one.

6. Repeat Part 5, but with at as many cores as you can. Try to the speedups.

3 Efficient Multiplication of Sparse Matrices (20 Points) This problem investigates the efficient multiplication of sparse matrices represented using a compressed sparse column (CSC) representations. In this representation, the nonzero values of elements each column are stored consecutively in an array, and the row indices of these elements are stored in the same order in an integer array. These arrays need not be sorted in increasing row order. A third array points to the two arrays representing each column; this array represents the columns in increasing index order.

1. Given the CSC representation of two sparse matrices � ∈ R;×< and � ∈ R<×9, show how to create the CSC representation of the product �� in $(; + 9 + >) operations, where > is the number of arithmetic operations on nonzeros required to multiply the two matrices. Make sure you explain how to determine the size of each column in the product (that is, the size of the arrays that represent that column).

2. Given the CSC representation a sparse matrix � ∈ R;×<, show how to create the CSC representation of the product �) �. Try tomake this as efficient as possible and analyze the total number of operations that the multiplication requires in terms of ;, <, and >.

3. Suggest a mechanism to improve the efficiency of the solution of Part 1 in cases in which ; � >. That is, try to find a way to remove the dependence on ; from the running time.

4 A Tradeoff in the LLL Basis Reduction Algorithm (10 points) The !!! algorithm ensures that in the output matrix ‘ satisfies��’7,8�� ≤ 1

2 ��’7,7��

‘27,7 ≥ H’27−1,7−1 − ’27−1,7 .

for some 1/4 < H < 1. That is, the client code that calls LLL sets H to some value in this range. Explain the tradeoff: what happens when we set H just above 1/4? What happens when we set H just below 1?

4

May 1, 2025
May 1, 2025

Subject Matter

Dangers of Disasters 

In the first discussion I asked you about the place you most wish to live. Over this semester we have learned about the many disasters that occur on our planet. In this paper you are to research what disasters could occur in the place you want to live. Usually, every location has one big disaster that will be the focus of your paper, but you should also include any other possible disasters. Determine what are the immediate dangers and the long-term dangers you will need to be prepared for. Once you know what the dangers are you can then prepare for them, so list your preparations to live happily in your most desired location.,

· Brief description of the location you mentioned in your first discussion,

· Biggest disaster and dangers,

· All other possible disasters and dangers,

· How to best prepare for the disaster,

Grading

80% of your grade is on the content of your paper.

What you include, what you researched, what you say. All of this must be evident in your writing.

Dangers of Disasters 

Be organized in your thoughts. The paper may not be long enough to follow the standard format of intro, body, and conclusion, but it still should not be all over the place.

This is a college level class and I expect your paper to be at the same level.

20% of your grade is based on spelling and grammar.

I expect you to write a college level paper and that includes more than content.

The greatest paper in the world is useless if no one can make sense of it.

I expect you to follow the rules of the English language.

Avoid using “I” unless necessary.

Write in complete sentences. Avoid run-on sentences.

Use proper spelling, no shorthand or texting patterns.

Write in complete sentences. Avoid run-on sentences.

Use proper spelling, no shorthand or texting patterns.

April 30, 2025
April 30, 2025

Research Question:

Are new york government administrative efforts in aiding the homeless more or less effective than those of nonprofit organizations?

Answer the following:,

1) How does this topic of “housing the homeless” fit into Public Administration?,

2) Based on the research question, what would be the dependent variable (DV) in this research process?,

3) Explain and justify how you conceptualized the DV. ,

4) Explain and justify how you will operationalize your DV. ,

5) Explain and justify how you propose to measure your DV

Research Question:

Definitions:

– Conceptualizing a variable requires the researcher to explain and justify their way of defining or understanding that variable. This may require the researcher to refer to how other researchers have conceptualized that variable and/or to anticipate and answer potential questions about other possible ways of conceptualizing that variable.

– Operationalizing a variable requires the researcher to specify the means by which that variable will be measured. What indicator, scale, or other measurement system will be used? This may require the researcher to refer to how other researchers have operationalized that variable and/or to anticipate and answer potential questions about other possible ways of operationalizing that variable.

– Measuring a variable requires the researcher to specify the process by which data will be gathered and analyzed. This may require the researcher to refer to how other researchers have measured that variable and/or to anticipate and answer potential questions about other possible ways of measuring that variable.

– Measuring a variable requires the researcher to specify the process by which data will be gathered and analyzed. This may require the researcher to refer to how other researchers have measured that variable and/or to anticipate and answer potential questions about other possible ways of measuring that variable.

– Measuring a variable requires the researcher to specify the process by which data will be gathered and analyzed. This may require the researcher to refer to .

April 30, 2025
April 30, 2025

Write a literature review of 15 relevant pieces of research (peer-reviewed sources) based on the following research question:

ARE GOVERNMENT-FUNDED ADMINISTRATIVE EFFORTS IN AIDING THE HOMELESS MORE OR LESS EFFECTIVE THAN THOSE OF NONPROFIT ORGANIZATIONS?

Most Literature reviews should be able to answer questions such as:,

1) Who are the main players/authors, and what have they concluded?,

2)  How did these scholars arrive at those conclusions? ,(Discuss which research design methods were used),

3) Did they arrive there logically and in a manner that is appropriate and acceptable to the research question?, Why or why not?,

Literature review

Literature Review: Evaluating the Effectiveness of Government-Funded vs. Nonprofit Interventions in Addressing Homelessness

Introduction

The persistent issue of homelessness has prompted various interventions, primarily spearheaded by government agencies and nonprofit organizations. This literature review examines 15 peer-reviewed studies to assess the relative effectiveness of these two sectors in mitigating homelessness. The analysis focuses on the methodologies employed, the logical coherence of conclusions drawn, and the implications for policy and practice.


1. Key Contributors and Their Conclusions

Government-Funded Initiatives:

  • California State Audit (2023): An audit revealed that despite a $24 billion investment over five years, California lacked consistent tracking mechanisms to evaluate the effectiveness of its homelessness programs. Only two out of five major programs were deemed likely cost-effective, highlighting issues in data collection and program assessment.AP News

  • Deloitte Access Economics Report (2025): Commissioned by Brisbane Common Ground, this report found that providing supported housing could save the state government up to $455,800 per individual over a decade. The “housing-first” model demonstrated significant cost savings by reducing health, safety, and social cohesion costs.

  • Nonprofit-Led Interventions:

    • Pathways to Housing (Tsemberis, 1992): This nonprofit pioneered the “housing-first” approach, emphasizing immediate access to housing without preconditions. The model has been credited with reducing chronic homelessness by 30% over eight years in the U.S., demonstrating the efficacy of nonprofit-led initiatives.Time

    • Greater Change (UK Trial, 2024): In collaboration with King’s College London, this nonprofit initiated a trial providing direct cash assistance to homeless individuals. The study aims to assess whether financial support is more effective than traditional aid methods, indicating a proactive approach by nonprofits in exploring innovative solutions.The Guardian

April 30, 2025
April 30, 2025

PADM 805

Research Report: Outline Assignment Instructions

Overview

Based on the topic used in your Research Report: Introduction and Literature Review Assignment, develop a topical outline for a quantitative qualitative or mixed methods proposal., Using Creswell and Creswell along with Edlund et al., prepare a topic outline that will provide a foundation for future research., As doctoral students your assignments are expected to follow the principles of high-quality scientific standards and promote knowledge and understanding in the field of public administration., You should apply a rigorous and critical assessment of a body of theory and empirical research, articulating what is known about the phenomenon and ways to advance research about the topic under review. Research syntheses should identify significant variables, a systematic and replication strategy, and a clear framework for studies included in the larger analysis.

Research Report

Instructions

This assignment will give you the opportunity to create an outline using your Introduction and Literature Review sections and synthesize those components into the methodology of a research study, e.g., ethics, methods, analysis, instruments, etc. This 20-to-30-page outline will include important components of research paper plan. Below are the format requirements:

· Length of assignment (20 to 30 pages)

· Not including the reference section.

· Format of assignment (APA most recent edition).

· Number of citations – At least 25 references should be included.

· Acceptable sources (e.g. scholarly peer-reviewed articles)

 

Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.

PADM 805

Research Report: Outline Assignment Instructions

 

Overview

Based on the topic used in your Research Report: Introduction and Literature Review Assignment, develop a topical outline for a quantitative, qualitative, or mixed methods proposal. Using Creswell and Creswell, along with Edlund et al., prepare a topic outline that will provide a foundation for future research. As doctoral students, your assignments are expected to follow the principles of high-quality scientific standards and promote

April 30, 2025
April 30, 2025

Research Design Question: 

“Are New York government administrative efforts in aiding the homeless more or less effective than nonprofit organizations?”

The Dependent Variable (DV) 

Research Design

The dependent variable in this research study is the effectiveness of initiatives aimed at assisting individuals experiencing homelessness.

Part 1- (Case Study Research Design)

1) What is the purpose of a case study design?,

2)  When is this design used? ,

3) Why is this design the most appropriate choice based on the research question? ,

4) What are the potential weaknesses of the research design?,

Part 2- (Qualitative Research Method) ,

1) What is the purpose of the qualitative research method?,

2)  When is this method used? ,

3) Why is this method the most appropriate choice based on the research question?

4) What are the potential weaknesses of the research method?

“Are New York government administrative efforts in aiding the homeless more or less effective than nonprofit organizations?”

The Dependent Variable (DV) 

The dependent variable in this research study is the effectiveness of initiatives aimed at assisting individuals experiencing homelessness.

Part 1-

1) What is the purpose of a case study design?

2)  When is this design used?

3) Why is this design the most appropriate choice based on the research question?

4) What are the potential weaknesses of the research design?

Part 2- (Qualitative Research Method) 

1) What is the purpose of the qualitative research method?

2)  When is this method used?

3) Why is this method the most appropriate choice based on the research question?

4) What are the potential weaknesses of the research method? 

“Are New York government administrative efforts in aiding the homeless more or less effective than nonprofit organizations?”

The Dependent Variable (DV) 

The dependent variable in this research study is the effectiveness of initiatives aimed at assisting individuals experiencing homelessness.

1) What is the purpose of a case study design?

April 30, 2025
April 30, 2025

I need help in the following

  • Review the Due Process in Proceedings Before International Criminal Tribunals in Section C on page 124 of your text.,
    • Select either the International Military Tribunals in Nuremberg or the International Military Tribunals in Tokyo and conduct research involving either one of these Tribunals.,
    • Provide a background of the purpose of these Tribunals and what each was intended to provide to criminal defendants.,
    • Offer your assessment of the success of the Tribunal in accordance with the commitment to protection of Due Process Rights of Human Criminal Defendants.

International Criminal Tribunals

I also need help in the following

  • Conduct research and locate a case that involves either pretrial rights or trial rights that was heard in the international arena before the International Criminal Court.
    • Provide a brief summary of the main issues, the pretrial and trial process, and the outcome of the case.
    • Discuss how the case reflects the defendant being provided with five pretrial rights or trial rights.
    • Provide specific examples of these rights in action during the specific case you researched and selected.
    • I need help in the following
      • Review the Due Process in Proceedings Before International Criminal Tribunals in Section C on page 124 of your text.
        • Select either the International Military Tribunals in Nuremberg or the International Military Tribunals in Tokyo and conduct research involving either one of these Tribunals.
        • Provide a background of the purpose of these Tribunals and what each was intended to provide to criminal defendants.
        • Offer your assessment of the success of the Tribunal in accordance with the commitment to protection of Due Process Rights of Human Criminal Defendants.

      I also need help in the following

      • Conduct research and locate a case that involves either pretrial rights or trial rights that was heard in the international arena before the International Criminal Court.
        • Provide a brief summary of the main issues, the pretrial and trial process, and the outcome of
April 30, 2025
April 30, 2025

Environment and Human Health Wri’ting As’signmentImportant Dates:

  • Minimum Requirements:
    • 2000 wo’rds minimum.  Wo’rd Count from the intr’oduction to the conc’lusion without counting the list of r’eferences.
    • Your es’say should be ty’ped and do’uble spaced on standard-sized pa’per (8.5″ x 11″), with 1″ margins on all si’des.
    • Fo’nt should be easy to read, such as 11-point Calibri, 11-point A’rial, and 10-point Lu’cida Sa’ns 12-point Ti’mes New Ro’man, 11-point Georgia, 10-point Computer Modern.
    • Use AP’A format.
    • Environment and Human Health
  • Pap’er Sections: Your es’say should include three major sections ,
  1. Title Pa’ge
  2. Main Bo’dy: Break the main bo’dy in the following sections.,
    1. Int’roduction: Des’cribe the environmental health to’pic you are going to res’earch.  Dis’cuss the importance or significance of the to’pic ,
    2. Environmental Impacts: Disc’uss the Environmental conditions and impacts related to your to’pic: water air land impacts.,
    3. Human Impacts: Describe the human health impacts associated with your to’pic. Disc’uss any applicable Environmental Epidemiology and Toxicology.
    4. Local relevance: Discuss the local relevance of the to’pic.  How does it impact Fresno County and the Central Valley?
    5. Laws and Regulations: Res’earch and discuss the applicable laws and regulations that attempt to mitigate the issues associated with the to’pic.  Who is responsible for implementation?  You may include a discussion about the economic cost of implementing the regulation.
    6. Looking forward: What do you con’clude about the adequacy of public policy related to your to’pic.  What future measures may be taken to help address this issue?
  3. 3. Ref’erences
  • Use peer rev’iewed ar’ticles or current publications from government agencies, res’earch organizations, or institutions.
      1. Laws and Regulations: Res’earch and discuss the applicable laws and regulations that attempt to mitigate the issues associated with the to’pic.  Who is responsible for implementation?  You may include a discussion about the economic cost of implementing the regulation.
      2. Looking forward: What do you con’clude about the adequacy of public policy related to your to’pic.  What future

USE THE OU’TLINE PROVIDED BELOW.

April 30, 2025
April 30, 2025

**Using APA formatting guidelines, answer the following questions at the end of the case study. Responses for each case discussion question should be in paragraph form and be at a minimum 150 words in length. **

 

Case Study 8: Nestlé and Child Labor in the Cocoa Supply Chain

 

On June 17, 2021, the U.S. Supreme Court issued a decision in an historic human rights case, Nestlé USA v. John Doe. It involved the liability of Nestlé USA for selling chocolate despite knowledge of forced child labor in the supply chain for cocoa beans, a key ingredient in its chocolate products. Also named as a defendant in the lawsuit was Cargill, another multinational food company that, like Nestlé, purchased and processed cocoa beans.

Case Study

The case was brought by six individuals who were trafficked as children from Mali into Côte d’Ivoire (also known as Ivory Coast) in West Africa, where they were forced to work for years on cocoa farms without pay, under dangerous and inhumane conditions. By then adults and no longer working in the industry, the six formerly enslaved children filed suit against Nestlé USA, the American subsidiary of the Swiss multinational. As relief, they pled for compensatory and punitive damages (to compensate them for their suffering and to punish the defendants). They also asked that the defendants give any profits they had earned from their unfair business practices to Global Exchange, a human rights advocacy group, and to the public. To protect their identities, the plaintiffs were called “John Doe I – VI.”

 

In their lawsuit, originally filed in 2005 in federal district court in Los Angeles, the six plaintiffs described horrific treatment they had experienced as children:

 

Between the ages of twelve and fourteen Respondents [the six boys] were forced to work on Ivorian [Ivory Coast] cocoa farms for twelve to fourteen hours per day, at least six days per week. They were not paid and were given only scraps of food to eat. Respondents were beaten with whips and tree branches when their overseers felt that they were not working quickly enough. They were forced to sleep on dirt floors in small, locked shacks with other children, and were guarded by men with guns to prevent them from escaping. Respondents witnessed other children who tried to flee the plantations being severely beaten and tortured. One Respondent, John Doe IV, tried to escape, and when the overseers caught him, they cut the bottoms of his feet and rubbed chili pepper into his wounds. He was also tied to a tree and beaten until his arm was permanently damaged. John Doe III witnessed small children who tried to escape being forced to drink urine. John Doe VI was severely beaten for working too slowly when he was sick and, like the other Respondents, his arms bear multiple scars from machete cuts he incurred while being forced to use the sharp tool to cut down and open cocoa pods.2

 

(page 509)

 

For more than 15 years, Nestlé had vigorously defended itself as the case wound its way through the courts. The company insisted that it did not tolerate illegal labor practices: “Child labor has no place in our supply chain,” the company declared.3 Indeed, the company pointed out that it had adopted a code of conduct which required its suppliers, and their suppliers, to abide by all human rights, child labor, and forced labor conventions. It had worked with nonprofits and universities to study its cocoa supply chain. And, over the course of a decade, it had invested more than 200 million dollars in what it called The Nestlé Cocoa Plan, rolling out a system to monitor and remediate child labor. But the plaintiffs argued that Nestlé had not done enough to curb the abuses. Indeed, they said that Nestlé had been complicit in creating and running a supply chain that it knew included slave child labor and that it had supported indirectly by providing cash, supplies, and training to cocoa farmers.

 

 

Nestlé and the Global Cocoa Industry

In 2021, Nestlé was the world’s largest food and beverage company and a leading marketer of chocolate products. Based in Switzerland, the multinational corporation employed 273,000 people in nearly every country in the world. In 2020, the firm had revenue of almost $94 billion and a market capitalization of $52 billion.4 The company produced and marketed a wide range of food and beverage brands, including Shredded Wheat cereal, Carnation evaporated milk, Gerber baby food, Dreyer’s ice cream, Purina pet food, Lean Cuisine prepared meals, and Taster’s Choice coffee. Nestlé’s globally popular products made from cocoa included Kit Kat candy bars, Toll House chocolate chips, and Nesquik chocolate milk powder.

 

Nestlé was one of four major multinational chocolate food and beverage producers that included Mars, The Hershey Company, and Mondelez (formerly a division of Kraft) known as “Big Chocolate” (analogous to the terms “Big Tobacco” and “Big Pharma”). Together, these four companies controlled about 37 percent of the world market for chocolate confectionery products. Of the industry’s $124 billion in annual sales, Mars (M&Ms, Snickers) controlled 15 percent; Mondelez (Toblerone, Cadbury), 10 percent; Hershey (Kisses, BarkTHINS), 6 percent; and Nestlé (KitKat, Nestlé Crunch), 6 percent.5

 

The key ingredient in Nestlé’s chocolate products was cocoa. Most of the world’s cocoa was grown in West Africa. Four countries—Ivory Coast, Ghana, Cameroon, and Nigeria—accounted for almost three-quarters of worldwide production, as shown in Exhibit A. Most of the rest was produced in Latin America (Ecuador and Brazil) and Indonesia.

 

Exhibit A: Worldwide Cocoa Production, Percent of Production by Country

 

Cocoa was grown on cocoa trees. These plants flourished in hot, moist, and shaded areas in a relatively narrow band of tropical rainforest roughly 20 degrees (about 1,400 miles) north and south of the equator. Cocoa came from the seed pods that grew on the trunks and branches of these trees. The harvesting of the crop was done almost entirely by hand. In two annual harvest seasons, a main one in the fall and a smaller one in the spring, workers cut down the pods and then sliced them open with large, sharp-bladed knives called machetes. The sticky seeds—the cocoa beans—were scooped out by hand and then carried out of the rainforest, usually in baskets balanced on workers’ heads. The beans were then heaped into piles, covered, and allowed to ferment for several days to bring out their flavor. Finally, workers spread out the beans to dry in the sun. Once bagged, they were ready for sale. A single harvest from a typical tree might produce around 3 pounds of finished cocoa beans.6

 

(page 510)

 

The supply chain for these bags of cocoa beans was long and complex, running through as many as six steps, or tiers, between the farm worker with the machete, on one end, and Nestlé and other large chocolate companies, on the other.

 

The supply chain for cocoa is pictured in Exhibit B. The farmer (sometimes supplied by a sharecropper working a small plot of land the farmer owned) sold to a cooperative, which in turn sold to a union of cooperatives, which then sold to regional buying centers. From there, the beans were sold to exporters, which sold to international food companies such as Nestlé. (Where no cooperatives were active, farmers sold to private buyers, who in turn sold into their own trading networks to reach the regional centers, as shown in the exhibit.)

 

Exhibit B: Nestlé’s Cocoa Supply Chain in West Africa

 

 

Child Labor in the Cocoa Industry

Child labor was widespread in the cocoa industry, particularly in West Africa.

 

Over the decade and a half preceding the Supreme Court decision, periodic surveys of child labor in Côte d’Ivoire and Ghana were conducted, initially by Tulane University and later by the University of Chicago. With support from the U.S. Department of Labor and various foundations, these researchers surveyed households in cocoa-growing regions to count certain forms of child labor, and then extrapolated from their results to obtain estimates of total numbers in each country. In line with the International Labor Organization’s definition, the researchers did not count all children working on cocoa farms page 511(e.g., children occasionally helping their parents by spreading out beans to dry in the sun was considered acceptable.) Rather, they counted children working on cocoa farms who either engaged in hazardous work and/or who exceeded an allowable number of hours per week. Hazardous work included using sharp tools like machetes, carrying heavy loads, handling agrochemicals, clearing land for cultivation, or working exceptionally long hours per day or at night. Allowable work periods varied from less than one hour per week for children under the age of 12, to less than 14 hours a week for children between 12 and 14 years old, to more than 43 hours a week for children between 15 and 17. (Persons 18 years and older were classified as adults.) Exhibit C shows the results of these surveys from 2008 to 2019.

 

The results of the four surveys reported in Exhibit C are not strictly comparable, because their methodologies varied somewhat, and the absolute numbers reported do not adjust for changes in population or the number of households engaged in cocoa farming. But overall, the data suggest that except for an increase shown in the 2013/14 survey, child labor in the cocoa industry in West Africa has remained remarkably stable—and persistently high. In the most recent survey, more than one and a half million children in Côte d’Ivoire and Ghana were engaged in child labor, and 95 percent of these were engaged in hazardous work.

 

Exhibit C: Estimated Number of Children in Côte d’Ivoire and Ghana Engaged in Child Labor in the Cocoa Industry, and the Percentage Engaged in Hazardous Work, 2008–2019

 

(Sources Labor in Cocoa Production in Cocoa Growing Areas of Côte d’Ivoire and Ghana, October 2020, Table 6, p. 48;: National Opinion Research Center, University of Chicago, Assessing Progress in Reducing Child Tulane University and the Walk Free Foundation, Bitter Sweets: Prevalence of Forced Labour and Child Labor in the Cocoa Sectors of Côte d’Ivoire and Ghana, September 2018, Table 5; and Tulane University, Survey Research on Child Labor in West African Cocoa Growing Areas, July 20, 2105, Table 9, p. 35. Graphic design by Colorbox Industries © 2021. Used by permission).

 

Forced labor in the cocoa industry was less common than child labor, although data were incomplete. The 2018 Tulane study estimated there were 9,600 adults in forced labor (working under coercion and without voluntary consent) in Côte d’Ivoire (4.2 adult workers per thousand) and 3,700 adults in Ghana (3.3 per thousand). The study estimated there were 1,500 children (1.7 child workers per thousand) in Côte d’Ivoire and 14,100 children in Ghana (20 per thousand) who had been forced to work by persons other than their parents.7

 

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Most children in the cocoa industry worked alongside and at the direction of their parents, who either owned or were sharecroppers on the farm. The parents did not consider their children employees. Rather, their work was considered a normal part of their obligation to the family’s welfare and necessary to learn the skills of farming. Children did farm work intermittently, depending on the season, the economic needs of their families, and their school schedules. Seventy percent of children engaged in hazardous labor also attended school.8

 

Child labor in West Africa was intimately tied to poverty. Ninety percent of West African cocoa farms were operated by families on small plots of 10 acres or less, many with aging trees, depleted soils, pest infestations, and fungal disease. In both Côte d’Ivoire and Ghana, the average income of a cocoa worker was less than $1 a day, well below the extreme poverty line of $1.90 a day estimated by the World Bank—and only about 6.6 percent of the value of the final retail price of the chocolate product.9 Prices for cocoa on the global market were notoriously volatile (e.g., during the 2016–17 harvest prices dropped by more than a third), and farmers’ income often fell below the cost of production. Under these circumstances, farming families were under tremendous pressure to enlist their own children to work. “When [farmers] must choose between feeding their family or sending them to school, it is not a choice,” said the Cocoa Barometer, a report by a consortium of nonprofits.10

 

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How much would farmers’ income need to rise to remove their incentives to use child labor? A study by a team of economists, published in 2019, estimated that a price premium of 12 percent over the farm gate price would be sufficient to eliminate excessive hours of work and hazardous work by children in the cocoa industry in Ghana (although it would not eliminate all child labor.) This could be accomplished, the authors said, if the cocoa boards added a premium to the farm gate price and then imposed child labor restrictions on farmers who wished to receive the higher amount.11

 

Another factor contributing to child labor was lack of access to schooling. Birth certificates were required for secondary school enrollment, but almost half of children in rural areas did not have them.12 Schools were often located a long distance from the farm. Not until 2015 did Côte d’Ivoire make schooling compulsory for children aged 6 to 16. And many parents were uneducated: the adult literacy rate in that country was just 53 percent. Said the executive director of the International Cocoa Initiative, “[Child labor] is clearly a complex problem that has its roots in poverty, and rural poverty no less. And if the problem is rooted in poverty, then the solution, in a way, is as complex as poverty eradication.”13

 

Regulation of Labor Practices in the Cocoa Industry

By 2021, many governments, companies, and NGOs around the world, in both cocoa-producing and cocoa-consuming countries, had acknowledged the problem of forced and hazardous child labor in the cocoa supply chain.

 

One of the first efforts to address the problem took place in the United States. In 2001, Congressman Eliot Engel of New York sponsored legislation to require labelling chocolate products to indicate they were produced without child slave labor. Although the bill passed the House of Representatives, it appeared headed for a loss in the Senate. Senator Tom Harkin of Iowa, a supporter, then took the lead in negotiating a voluntary, multi-stakeholder compact to address the issue. Eight chocolate companies, including Nestlé, signed the agreement—which became known as the Harkin—Engel Protocol—promising to reduce the worst forms of child labor in Côte d’Ivoire and Ghana by 2005. The Protocol also provided for the establishment of a new international foundation to address the worst forms of child labor in the cocoa industry, the International Cocoa Initiative (ICI), to be governed and administered by the major stakeholders.

 

Two decades after Harkin—Engel was signed, Big Chocolate had still failed to meet its commitments, and the signatories had extended the deadline several times. Government regulation, however, had begun to take hold, at least in Europe. In 2017, several European countries, including France, the Netherlands, and Switzerland, adopted so called “due diligence,” “duty of care,” or “duty of vigilance” laws that required corporations to identify and prevent risks to human rights (and sometimes environmental harms) caused by their business activities. This created a somewhat tangled regulatory environment for large firms that engaged in commerce across the region. In 2020, several large chocolate companies, including Nestlé, and their associated trade associations called on the European Union to adopt uniform due diligence regulation. Their joint statement argued that “mandatory legislation [in the European Union] can contribute to a level playing-field, increase legal certainty about the standards expected from companies to respect human rights and the environment, clarify legal responsibilities when responsibilities are not met, promote engagement page 514and impactful actions among supply chain partners and, above all, trigger and incentivize impactful and effective actions on the ground.”14

 

The governments of cocoa-producing nations had also acted, although to a limited degree. In 2019, the governments of Côte d’Ivoire and Ghana took steps to stabilize and raise the price of cocoa beans. They increased the minimum farm gate price of cocoa, already regulated by law, and added a $400 per ton living income differential.15 Both countries had ratified all relevant international conventions on child labor, although neither had implemented a meaningful system of enforcement. The U.S. Department of Labor reported that funding levels for enforcement of human trafficking laws in Côte d’Ivoire were “severely inadequate” and in Ghana the effort was “severely under-resourced.”16

 

Nestlé’s Relationship with Its Cocoa Suppliers

Nestlé had a comprehensive supplier code of conduct, most recently updated in July 2018. The code required that the company’s Tier 1 suppliers comply with all United Nations rules regarding human rights, child labor, and forced labor; and that they ensure that their upstream intermediaries also complied. The code also set explicit rules for farms from which agricultural products were sourced. The company hired third-party organizations to map its supply chain and audit compliance.

 

In 2009, as part of its efforts to meet its Harkin—Engel Protocol commitments, Nestlé launched what it called the Nestlé Cocoa Plan to make cocoa more profitable for farmers, eliminate child labor, and improve the transparency of the supply chain and the quality of cocoa.17 In its first decade of operation, the company invested $244 million to support these goals.18 Activities including training farmers in good agricultural practices, training cooperatives in good business practices, and investing in social projects such as schools and sanitation facilities.

 

In 2012, Nestlé set up a Child Labor Monitoring and Remediation System (CLMRS) in collaboration with the International Cocoa Initiative, first in Côte d’Ivoire and later in Ghana. The CLMRS hired people from the local community (called community liaisons) to visit farm families to identify children who were at risk of hazardous work, entering this information into a centralized database using a mobile app. The liaisons used colorful flipcharts to illustrate what kinds of work children were allowed to do (and not do) on the farm and explained the reasons. The CLMRS was also designed to assist farm families increase their income and send their children to school. On the family level, this assistance included providing school supply kits, getting birth certificates, and offering tutoring to help children to reintegrate into schools. On the community level, it involved training farmers in good agricultural practices, renovating schools, and financing other income-generating activities for families. The system then tracked children to see if they had stopped doing prohibited work. In 2019, Nestlé reported that that of 14,500 children identified by its community liaisons as engaged in hazardous work, 55 percent were no longer doing so in follow-up visits.19 Said one Ivorian farmer interviewed by Fortune, speaking of the CLMRS, “Nobody hates his own kids. We learned from the training that we have to do things differently.”20

 

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In an assessment of its work, the International Cocoa Initiative, with which Nestlé partnered, acknowledged that although progress had been made, its programs had reached only 10 to 20 percent of the cocoa supply chain. Its “biggest challenge” going forward, it said, was “the scale-up of effective action to cover all children at risk.” The assessment also noted that while pressure for responsible business practices was growing, threats linked to climate change and pandemics would likely make “change harder to bring about.”21

 

Sustainable Chocolate: An Alternative Business Model

As Nestlé and other large multinational chocolate companies resisted charges of complicity in child labor abuses, another segment of the industry—sometimes referred to as sustainable chocolate—was emerging. These companies sought to compete for customers based on their claims of ethical supply chain and environmental practices, as certified by third-party organizations such as the Rainforest Alliance or Fairtrade International.

 

An example of such a company was Tony’s Chocolonely. Tony’s was founded in 2006 in the Netherlands by investigative journalists who, after working on a story about child slave labor on cocoa plantations in Africa, developed an interest in producing what they coined “slave-free” chocolate. The startup’s name was derived from combining the anglicization (“Tony”) of Teun van de Keuken, the lead journalist on the project, and the words “chocolate” and “lonely,” to convey how unusual they thought their approach was. In a legendary stunt in 2005, van de Keuken had publicly demanded that he be criminally prosecuted by Dutch authorities for eating chocolate that had been made from cocoa farmed by slave labor. The case was ultimately dismissed, but not before making headlines in the European press.22

 

In 2021, Tony’s—which called itself “not a chocolate company [but] an impact company that makes chocolate”—remained small, with just over 100 employees and annual revenue of $109 million.23 Yet, it claimed 16.4 percent of chocolate bar market share in The Netherlands, making it the second largest chocolate brand in its home country.24 In early 2020, AB-InBev, a Belgian beverage powerhouse, and Jamjar, a smaller U.K. private equity fund, made major investments in Tony’s, with the aim of building international brand recognition and driving change in the industry.25

 

In a legal brief filed in support the John Doe respondents, Tony’s explained that its sourcing model enabled them to buy cocoa in West Africa without participating in child labor or other human rights abuses. Tony’s asserted that because it purchased directly from farmers and farmer cooperatives, it was able to track the source of every bean. The company paid higher prices for its beans—60 percent above the typical farm gate price (set by the national cocoa boards) and even exceeding the Fairtrade premium. This higher price, Tony’s argued, enabled farmers to earn a living income without the use of child or forced labor.

 

Tony’s collaborated with cocoa farmers to enhance their knowledge of professional agricultural techniques. The company signed long-term contracts of five years or more with its suppliers, allowing them to plan beyond a single season. When problems were uncovered, Tony’s worked with farmers to find alternative solutions. The result was that “with a modest investment in time, technology, and direct payments to farmers, it is possible to establish a robust system for sourcing cocoa without exploiting communities.”26

 

(page 516)

 

Tony’s sustainability practices were reflected in the prices of its products. In 2021, the retail price of Tony’s 6.35 oz. milk chocolate bar at Whole Foods was $4.99, significantly higher than the retail prices of popular products made by its Big Chocolate competitors. For example, customers at Walmart could find a Nestlé 4.5 oz. Kit Kat bar for $1.80, a 10.7 oz. bag of Mars’ M&Ms for $3.38, or a Hershey’s 7 oz. milk chocolate bar for $2.34.27

 

In an amicus (“friend of the court”) brief filed in the Nestlé case before the Supreme Court, 18 other small and mid-sized chocolate companies explained why they, like Tony’s, were at a competitive disadvantage by operating transparent and sustainable supply chains in the chocolate industry. “Recognizing that poverty elevates the risk of serious abuses like forced child labor,” they said, these companies paid from 40 to 110 percent above the farm gate price. In addition, they said, “they invest[ed] in robust transparency and due diligence to ensure compliance with international human rights law and standards. These costs are internalized and passed on to consumers, making it difficult for them to compete in the market with companies that source cheap cocoa produced with forced child labor.”28

 

Nestlé v. John Doe

The formerly enslaved children at the center of the lawsuit before the Supreme Court were represented by a small Los Angeles law firm and a small Washington, DC public interest organization that both specialized in human rights cases, joined by faculty members at three University of California law schools. Nestlé was represented by major Los Angeles and Washington, DC law firms.

 

The human rights lawyers argued that Nestlé should be held legally responsible for its complicity in fostering a supply chain that relied in part on child slavery and forced labor. Given its enormous resources, power, and influence, Nestlé could end the system if it wanted to do so, said the lawyers. Instead, the company continued to reap the profits from “subjecting thousands of children to slavery and forced labor in inhumane conditions.”29 They also argued that the companies had maintained influence over this “slavery-based system” by providing financial support, farming supplies, and training to cocoa farmers.

 

For their part, Nestlé’s lawyers steadfastly maintained that the company “unequivocally condemns child slavery … and has taken major steps to combat child slavery in Côte d’Ivoire.”30

 

The case was brought under a little-known, archaic law known as the Alien Tort Statute (ATS). The ATS dated to the earliest days of the founding of the nation, when no legal remedy existed in the United States for foreigners who had been the victim of torts. (A tort, in law, is a civil wrong.) The ATS, passed in 1789, addressed this problem by giving the federal courts jurisdiction over cases brought by citizens of other countries (“aliens”) for torts “committed in violation of the law of nations or a treaty of the United States.” In its early days, the law was used, for example, by foreign merchants whose ships had been attacked by pirates in U.S. waters.

 

In the 1990s, human rights attorneys first pioneered the use of the ATS for corporate accountability purposes, under the theory that a citizen of another country who had been the victim of human rights abuse or environmental harm in global supply chains could use page 517the statute to sue the responsible U.S. companies in federal courts.31 Under this legal theory, human rights attorneys had used the ATS with limited success to sue Royal Dutch Shell for human rights abuses committed by Nigerian forces against the Ogoni people protesting the environmental effects of the companies’ oil exploration and production; Unocal for human rights abuses committed by Burmese security forces during the construction of the Yadana Gas Pipeline; and Texaco (later owned by Chevron) for environmental damage to the Ecuadorian rainforest during oil operations there.

 

The steep hurdle that the plaintiffs faced in Nestlé USA v. John Doe, as in many such cases, was that the alleged harm had not been committed in the United States, and the Supreme Court had become increasingly reluctant to consider suits brought under the ATS for acts committed abroad. Indeed, Nestlé’s lawyers argued not only that the case was “impermissibly extraterritorial” (i.e., the relevant acts had occurred outside the United States), but that American companies could in fact never be sued under the ATS for acts that occurred elsewhere.32

 

In the end, the Supreme Court sided with the companies, with eight of the nine justices agreeing in a very brief opinion, written by Justice Clarence Thomas, that there was insufficient evidence to support using the ATS in the case. The Court held narrowly that in order for the ATS to be used extraterritorially (for wrongs committed in other countries), the plaintiffs had to establish that “the conduct relevant to the statute’s focus occurred in the United States.”33 The Court found that the plaintiffs had not met that burden because the corporate conduct that they alleged had “aided and abetted” forced labor (such as providing cash, supplies, and training to cocoa farmers who had used forced labor) had occurred in Côte d’Ivoire, not the United States.34

 

Attorneys for the plaintiffs said they would pursue other avenues, such as suing under laws prohibiting human trafficking. They also expressed cautious optimism that the ruling left open the possibility of bringing successful human rights cases under the ATS if the plaintiffs could establish that companies had, through their activities in the United States, “aided and abetted” abuses that occurred elsewhere in their global supply chains.35 For its part, Nestlé issued a statement saying that it had “never engaged in the egregious child labor alleged in this suit, and we remain unwavering in our dedication to combating child labor in the cocoa industry” by addressing its “root causes.”36

 

Discussion Questions

 

1) Would you choose to buy a Tony’s Chocolonely chocolate bar rather than a Nestlé chocolate bar because of Tony’s commitment to ending child labor and forced labor in the cocoa supply chain? Why or why not?,

 

2) Describe the extent of child labor in the cocoa supply chain. Why has child labor not yet been eliminated even after decades of effort?,

3) Evaluate the actions Nestlé has taken to address the problem of child labor in its cocoa supply chain. ,What do you think motivated the company to take these actions? ,Do you think that Nestlé has done enough? What more could or should it do?

 

4) Do you believe that the strategy of Tony’s and other sustainable chocolate companies for addressing the problem of child labor and forced labor in the cocoa supply chain will be effective? Why or why not?

 

5) Do you think foreign citizens, like the “John Does” in this case, should be able to sue in U.S. courts for wrongs committed in another country? Did you agree with the U.S. Supreme Court decision or not, and why?

 

6) Do you think foreign citizens, like the “John Does” in this case, should be able to sue in U.S. courts for wrongs committed in another country? Did you agree with the U.S. Supreme Court decision or not, and why?

 

 

Reference:

 

Lawrence, A., & Weber, J. (2022). Business and Society (17th ed.). McGraw-Hill Higher

Education (US). https://reader2.yuzu.com/books/9781265914769

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