F1000Research F1000Research 2046-1402 F1000 Research Limited London, UK 10.12688/f1000research.167325.1 Research Article Articles Moderate regulations are optimal for NFP program expense allocations: Findings from the combination of mechanism design and k-means clustering

[version 1; peer review: 1 approved with reservations]

 Mizutani Fuminobu Conceptualization Formal Analysis Funding Acquisition Investigation Methodology Project Administration Visualization Writing – Original Draft Preparation https://orcid.org/0000-0003-1306-8891 a 1 Uehara Yuko Investigation Supervision Validation Writing – Review & Editing https://orcid.org/0009-0005-8204-2339 2 Department of Business Administration, Kanto Gakuin University, Yokohama, 2310016, Japan College of Sustainability and Tourism, Ritsumeikan Asia Pacific University, Beppu, 8748577, Japan fuminobu@kanto-gakuin.ac.jp

No competing interests were disclosed.

 26 8 2025 2025 14 827 20 8 2025 Copyright: © 2025 Mizutani F and Uehara Y 2025 This is an open access article distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background

The context of this study is the ethical dilemma faced by not-for-profit organizations’ (NFPs’) executives. This study examines the ways in which regulators determine the degree to which expense allocations should be limited or prohibited, whereas there is a lack of consensus in the literature. California has moderate regulations on the expense allocation of NFP programs. These regulations can influence those of other states and foreign countries.

 Methods

Actual data can provide clues on how to resolve disagreements. Through the adoption of a combination of mechanism design and k-means clustering, this study explains how regulators can optimize regulations on NFP program expense allocations.

 Results

The k-means clustering results were calculated. There were 966 cases in the first cluster and 37 in the second cluster. The cluster center of the first cluster was 9,343, and the cluster center of the second cluster was 160,581. The required number of repeats was 12.34%, which is]the breakpoint ratio for sanctions to be imposed.

 Conclusions

One method to achieve this goal is to intentionally limit the scale of imposed sanctions on expense allocations while maintaining some necessary sanctions to maintain mutual trust within the donation market. While the findings here contradict the views of some rating organizations, they are consistent with prior academic literature.

 Game Theory Program Expense Allocation K-Means Clustering California NFP (Not-for-Profit Organization) Air Force Office of Scientific Research FA2386-23-1-4008 This work was supported by the Air Force Office of Scientific Research under award number FA2386-23-1-4008. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Introduction

As a case in the educational collection of the University of Texas at Austin, not-for-profit organizations (NFPs) often confront ethical dilemmas in terms of fundraising ( Drumwright, 2022). Program expense allocations by executives of NFPs tend to be inflated and are prone to manipulation. Of course, mutual trust between executives and contributors is an element of governance for NFPs ( Pilon and Brouard, 2025). Program expense allocations may violate this trust, similar to financial misconduct in profit-oriented entities ( Honigsberg, 2020). However, there may be another reason NFP executives are considering even though expense allocation may harm mutual trust. For example, some NFPs aim to secure greater contributions by overstating their programme expense ratios. Accounting standards allow for some discrepancies between executives, and under certain circumstances, they are able to legally report inaccurate expense allocations. The context of this study is the ethical dilemmas faced by NFP executives.

This study examines the ways in which regulators determine the extent to which expense allocations should be limited or prohibited, whereas there is a lack of consensus in the literature. Prior literature mainly focuses on how regulators can prevent inflated expense allocation outright. Actual data can provide clues on how to resolve disagreements. The paper also aims to illustrate how to combine mechanism design and classical computer science problems, ex. K-means clustering can be useful for research accounting for NFPs. Its focus is to interpret the public sector’s decisions, such as that of California’s governor and attorney, through game theory.

Rating organizations such as CharityWatch have criticized the expense allocations of NFPs, and the public sector has periodically tried to regulate them. Notably, California Assembly Bill 1181 aimed to regulate allocation broadly. In a detailed explanation, CharityWatch expressed regret that this bill was vetoed by the governor ( CharityWatch, 2023). The governor indicated that the bill could “pose burdensome implementation challenges for the charities impacted by its provisions” ( Senate Judiciary Committee, 26:2021). Similarly, the attorney generally halted sanctions on NFPs in California ( Bonta, 2019). Subsequently, he became a federal health secretary. The Department of Health and Human Services had the tightest relationship with NFPs in all federal agencies ( WSJ, Jan. 13, 2021). It can be assumed that he rescued NFPs from burdensome implementation challenges, which is consistent with the governor’s actions. It is doubtful that complete prevention of inflated expense allocations is the best economic policy. For example, all three NFPs with expense allocations listed in the first paragraph of Bonta (2019) are humanitarian organizations. These organizations may have beneficiaries whose lives are in danger or have special fundraising needs.

This study adopts game theory as a framework. The contributors are principals and executives are agents. Game theory provides a convenient framework for the analysis of this problem, as it is necessary for executives to gauge how contributors react to their actions.

The presumption is that states and countries have similar regulations as in California. According to the ABA (American Bar Association), California is the leading state for the MNCA (Model Nonprofit Corporation Act) ( Nonprofit Organizations Committee, 2022). All U.S. states have Financial Accounting Standards Board (FASB) accounting standards for NFPs. Contemporary Japan has similar regulations for NFPs to California, although it has different regulations elsewhere. Notably, Japan has Specified Non-Profit Judicial Person (NPO) accounting standards, which are based on FASB’s accounting standards.

The remainder of this paper is organized as follows: Section 2 presents the prior literature. Section 3 builds on this theory. Section 4 explains the methodology of this study. Section 5 presents the results of the study. Section 6 extends the discussion. Finally, Section 7 concludes the study.

 Prior literature

Prosocial activities are a common topic in finance. For example, Walker et al. (2023) wrote about finance for these types of activity. There is also an extensive literature on expense allocation. Dang and Owens (2020) indicated that approximately 25% of British NFPs are financially misreported. Cyr et al. (2022) indicate that regulations influence how executives of Canadian NFPs recognize expense allocations. Ling and Roberts (2023 and 2025) and Allen et al. (2024) explain expense allocations in the U.S. and ways to prevent inflated expense allocations. There is prior literature on the limitations of the contributors. Caviola et al. (2020) revealed that contributors have limited ability to understand the effectiveness of NFPs. According to Yang and Northcott (2021), one method for regulators to build public trust is to investigate public concerns about “wrongdoing” at NFPs. Chan and Zhang (2021) focused on sanctions for misreporting NFPs.

Some prior studies cast doubt on the current accounting norms of NFPs. Burkart et al. (2018) argue that financial transparency does not always increase the utility of stakeholders surrounding NFPs, indicating that rating organizations sometimes lead the push for transparency. Mitchell (2017) insists that some financial norms paradoxically hamper NFPs, although his focus is slightly different from that of this study. A reduction in the flexibility of NFPs reduces their efficiency. Burkart et al. (2018) and Mitchell (2017) are consistent with Muller (2018) in criticizing not only program expense ratios, but also various metrics. Goncharenko and Khadaroo (2020) warned that accounting regulations may restrict NFP activities based on Russian law.

The financing of humanitarian organizations is a significant factor when examining NFPs. Tariq et al. (2023) assert that the funding of humanitarian organizations is not only insufficient but also volatile.

Bénassy-Quéré et al. (2019) explain the shapes of economic policy and describe it as a succession of trade-offs. Regulators were also included in the public sector. Fowler (2023) depicted the ambiguity of the public sector as a double-edged sword and showed practical trade-offs. The concept of trade-offs is discussed in Section 6 of this paper.

Rasmusen (2007) uses textbook game theory, which includes explanations of agency theory. The players’ utility is frequently considered. Financial reporting is also within the scope of this study. In addition, the labor market is discussed by dividing the supply side into “serious” and other applicants. K-means clustering is a classic statistical method. For example, Kopec (2019) explained k-means clustering in a recent study. Hsu et al. (2021) adopted k-means to analyze the finances of NFPs but did not combine k-means with game theory.

There is ambiguity as to whether inflated expense allocations are deliberate falsification, and these distorted expenses are often lawful and may even be justifiable in some circumstances. Sandel (2010) separated lies from other kinds of misinformation and suggested that certain falsehoods are more justifiable than lies. Finlayson (2005) describes psychologist Kohlberg’s theory as influenced by philosopher Habermas, which posits that even though laws must usually be complied with, sometimes they ought to be disobeyed.

 Theory

Decisions by executives at NFPs rely on expected decisions by contributors to NFPs; therefore, game theory is a suitable framework for analysis. NFPs’ expense allocations can be regarded as an issue in the mechanism design for messages. Regulators can influence financial reporting as messages from NFPs through mechanism design. NFP executives want to be trusted by contributors through their messages (financial reporting), even though their financial reporting has sometimes been manipulated.

The NFPs mentioned here have program expense ratios, both in actual terms and in terms of fundraising needs. Program expense allocations are unnecessary for NFPs with good program expense ratios and NFPs without fundraising requirements. Notably, if an NFP is a humanitarian organization and the utility of its executives reflects the utility of its beneficiaries whose lives are at risk, fundraising success strongly influences the utility of executives. The von Neumann–Morgenstern utility is often adopted in game theory. Thus, this study adopted this utility.

Symbols mean here:

p: population of contributors

r c: ratio of serious contributors

r s: ratio to be imposed sanctions

a: dummy variable if serious contributors contribute

b: dummy variable if non-serious contributors contribute

d i: average contribution amount by a serious contributor

d j: average contribution amount by a non-serious contributor

Under conditions in which there are no sanctions by regulators, donation revenue can be formulated as follows: pr c d i a + p ( 1 − r c ) d j b = donation revenue a = { 1 if True , 0 if False . b = { 1 if True , 0 if False .

If an NFP’s financial reporting is honest, a simple formula is: pr c d i 1 ・ 1 + p ( 1 − r c ) d j ・ 0 = donation revenue

Generally, contributors want financial transparency from the NFPs. As such, even serious contributors who are eager to see an NFP reach their goals will not approve of inflated expense allocation. If serious contributors do not allow these types of expense allocations and there are no sanctions by regulators, the manipulated financial report that brings donation revenue is as follows: pr c d i ・ 0 + p ( 1 − r c ) d j ・ 1 = donation revenue

Under the assumption that the funding of humanitarian organizations is volatile, after sanctions by regulators are introduced: r s ・ { pr c d i ・ 1 + p ( 1 − r c ) d j ・ 1 } + ( 1 − r s ) { pr c d i ・ 0 + p ( 1 − r c ) d j ・ 1 } = donation revenue

If the actual data show (5) as a positive value, there is a negative incentive to allocate expenses. Thus, there is no space for expense allocation and no regulations are necessary. ( 2 ) – ( 3 ) = r c d i − d j + r c d j

If (5) is not a positive value, an NFP decides whether to manipulate following (6). ( 2 ) – ( 4 ) = p ・ { r c ・ d i − ( 1 − r s ) ・ ( 1 − r c ) ・ d j } . A NF P ′ s decision making = { manipulate if ( 2 ) < ( 4 ) can not decide if ( 2 ) = ( 4 ) report honestly if ( 2 ) > ( 4 )

It is useful to calculate how (7) is achieved using the actual data. Of course, there may be differences between an individual NFP and a third sector as a whole. However, even a simplified analysis will bring a blueprint to the third sector. r c d i − ( 1 − r s ) ( 1 − r c ) d j = 0

If r s is sufficiently low, regulators can easily prevent all inflated expense allocations. Since there are frequently these types of expense allocations by NFPs all over the U.S., including California, it can be assumed that regulators intentionally keep regulations on NFPs moderate. However, if r s is high, there is a different presumption concerning regulators. However, if they decided to impose these sorts of sanctions on all inflated expense allocations, the cost for regulators would be prohibitive, and they simply could not prevent all misstatements.

 Methods

It is well known that the total amount of contribution in the U.S. and the U.K. is large. While ample statistical data exist concerning the financial statements of NFPs in both countries, raw data for contributors are rare. However, there are raw data for contributors with large sample sizes in Japan, which have been paying attention to the legal system for NFPs in California since the last part of the 20th century.

The Japan Fundraising Association provides a dataset of Japanese contributors for each fee. The dataset was used as the data source for this study. The association collected statistical data through the Nationwide Survey on the Reality of Donations (Zenkoku Kifu Jittai Chosa). Because only anonymized datasets are provided by the association, IRB review is unnecessary for this study.

How processed by summing up various categories of contributions, consistency with Giving USA was brought to each sample of this dataset ( IUPUI Lilly Family School of Philanthropy, 2023). This is the sum of NQ2_1_8 and NQ2_1_19 for the numbering of the dataset. Because the annual income of each respondent is recorded only as a range and not as a precise figure, the annual income of each respondent is substituted by the midpoint of each respondent’s annual income category. Samples that did not make any contribution can be assumed to be not or only slightly influenced by the culture of the U.S. donation market. Then, the setting up of k-clustering was completed by removing samples that did not make any contributions. Next, Equation (5) was calculated. Finally, if (5) is not a positive value, (6) is calculated.

Computer applications

Setting up the above steps are preceded by a spreadsheet. IBM SPSS, which is popular in the social sciences, is a statistical application used for counting and k-means clustering. The input for the number of clusters was two. The mathematical application used for calculations and building a figure from the formula is Wolfram|One, which is reliable.

 Results

The descriptive statistics of the processed dataset are shown in Table 1 (n = 1,003).

Descriptive statistics.
Variable Mean SD Min Max
Annual income (in 10,000 JPY) 500.15 353.4370 0 1,400
Contribution (in JPY) 14,921.90 35,329.72 5 500,000

Source: Japan Fundraising Association, 2022.

The results of the k-means clustering were calculated. There were 966 cases in the first cluster and 37 in the second cluster. The cluster center of the first cluster was 9,343, and the cluster center of the second cluster was 160,581. The number of repeats required was 12. r c = 37 / 1,003 r c d i − d j + r c d j = 37 / 1,003 ・ 160 , 581 − 9,343 + 37 / 1,003 ・ 9,343

The above result was negative. Thus, manipulation is a dominant strategy for an NFP when there are no sanctions.

Decremental donation revenue was calculated using the formula below, as shown in Figure 1. The x-axis represents r s and the y-axis represents the decreasing amount. r c d i − ( 1 − r s ) ( 1 − r c ) d j = 37 / 1,003 ・ 160,581 − ( 1 − r s ) ( 1 − 37 / 1 , 003 ) 9,343

Relationship between expense allocations and sanctions.

When r s = 1,027,947/3,008,446, (7) is achieved.

 Discussion

The scarcity of serious contributors is consistent with the findings of Caviola et al. (2020). In addition, consistent with Cyr et al. (2022), there is space for mechanism design by regulators.

Regulators could hypothetically use sanctions to prevent all inflated expense allocations, an amount that is less than approximately 34% of all expense allocations, which appears to be an achievable goal (7). In the real world, there are frequent expense allocations by NFPs across the U.S., including California. Thus, regulators who recognize the goals of NFPs intentionally adopt moderate regulations. This is not because of potential costs for regulators, but because of the burdensome implementation challenges for NFPs. This result is consistent with the decisions made by California’s governor and the attorney general, as described in the Introduction. Regulatory decisions can be interpreted from the perspective of mechanism design.

Some sanctions are necessary to maintain mutual trust within the donation market, and maintaining the market is the point of decision. However, regulators do not want to impose sanctions on all inflated expense allocation. To achieve the objectives of NFPs, fundraising through inflated expense allocation is sometimes required. As Burkart et al. (2018) and Mitchell (2017) warned about some normative goals, complete prevention would harm the beneficiaries of some NFPs. Bénassy-Quéré et al. (2019) also explained that regulators are confronted with trade-offs.

Allowing inflated expense allocations is a possible option. Through imperfect sanctions, regulators make NFPs navigate through a series of obstacles. In terms of obstacles for NFPs, humanitarian organizations are particularly volatile and have imminent fundraising needs, as Tariq et al. (2023) state. According to Sandel (2010) and Finlayson (2005), it can be assumed that there is a space where these types of imperfect sanctions are permitted.

The California governor’s and attorney general’s decisions seem less than optimal for preventing all inflated expense allocations, but optimal in terms of maximizing the utility of NFPs stakeholders, including beneficiaries.

 Conclusions

By theorizing mechanism design and k-means clustering, it is indicated that regulators choose moderate regulations on the expense allocations of NFPs. Such regulations appear to force NFPs to navigate obstacles and optimize the utility of NFP stakeholders, including beneficiaries. For example, California’s governor and attorney general appear to have done so. The findings here contradict some rating organizations but are consistent with prior academic literature. Because there is debate among regulators on how to tailor the obstacles for NFPs in the prior literature, this finding for actual data can contribute to the literature.

Other studies adopting classic computer science problems may provide further insights into accounting for NFPs. The limitation of this study is the extent to which the findings fit. It is somewhat unclear whether the findings apply sufficiently to cases other than California, or in states or countries influenced by California.

 Ethical approval

This paper did not involve in any human subject experiments and did not need ethical approval of the institutional review board (IRB).

 Data availability

Data were collected from a spreadsheet file of a third party, “the Japan Fundraising Association.” We do not have the right to share this spreadsheet file. The contract between the association and the authors legally prohibits sharing of raw data. The IRB of the first author’s affiliated university does not say anything about sharing of this spreadsheet. This association’s URL is https://jfra.jp/en/for 2025. Entering a contract with this association through its email address info@jfra.jp and purchasing is required to access the full data. The cost of purchasing a pass is 110,000 in JPY. The latest data for Jun. 2025 are available for 2020.

 Acknowledgements

The authors would like to thank b-cause Inc. for their English proofreading service.

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Mak. 2020;15(4):509–516. 10.1017/S1930297500007452 Chan EW Zhang X : Understanding and deterring misreporting in nonprofits: The joint effects of pay level and penalty type. Account. Rev. 2021;96(4):157–177. 10.2308/TAR-2019-0620 CharityWatch: You cannot rely on the government to protect you from bad charities. CharityWatch;2023. Reference Source Cyr D Landry S Fortin A : Management of charitable program expense ratios in the charity sector. Aust. Account. Rev. 2022;32(1):106–123. 10.1111/auar.12346 Dang CT Owens T : Does transparency come at the cost of charitable services? Evidence from investigating British charities. J. Econ. Behav. Organ. 2020;172:314–343. 10.1016/j.jebo.2020.02.020 Drumwright ME : Full disclosure: Manipulating donors, The Science of Everyday Ethics: Make Easy, Useful, and Fun. University of Texas at Austin;2022. Reference Source Finlayson JG : Habermas: A Very Short Introduction. Oxon: Oxford University Press;2005. 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Manag. 2021;37(4):367–384. 10.1111/faam.12283 10.5256/f1000research.184431.r409635 Reviewer response for version 1 Mohd Noor Nurul Hidayana 1 Referee https://orcid.org/0000-0003-2262-2524 Faculty of Administrative Science and Policy Studies, Universiti Teknologi MARA, Seremban, Negeri Sembilan, Malaysia

Competing interests: No competing interests were disclosed.

 10 9 2025 Copyright: © 2025 Mohd Noor NH 2025 This is an open access peer review report distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. recommendation approve-with-reservations

The title does not reflect the content in the manuscript. Why moderate regulations? Why not strong or comprehensive regulations?

Abstract: “California has moderate regulations on the expense allocation of NFP programs.” – I don’t understand the purpose of this statement in your study. Why refer to California and not other countries/states? The statement is irrelevant.

The findings statement is difficult to understand for a layperson. Please paraphrase the sentence. Make sure the findings are understandable.

Introduction section:

“As a case in the educational collection of the University of Texas at Austin, not-for-profit organizations (NFPs) often confront ethical dilemmas in terms of fundraising (Drumwright, 2022).” Why open your sentence with these statements? The authors do not elaborate on cases that happen at the University of Texas at Austin. You cannot expect all readers to be aware of this case. The readers come from diverse backgrounds and countries.

Please define NPOs and elaborate on their nature, challenges faced by NPOs, and their governing bodies.

Since the study is among NPOs in Japan. Please discuss NPOs from the Japanese context. This is important since the NPO nature varies between each country.

Please discuss the identified research gaps.

Please highlight the significance of the study.

Please list your research objectives or research questions.

The authors made a presumption about California; however, the empirical evidence and facts are not strongly justified.

 Literature review

The accountability of the NPO concept needs to be discussed.

The use of game theory is not critically justified.

Regulations used in Japan are not stated and explained.

The LR section is poorly constructed and needs more explanation.

Please avoid referring to obsolete empirical studies.

 Methodology

The methodology section is poorly constructed and academically written.

Please explain population and sample selection, research methodology used (either quantitative or qualitative), sampling techniques, database reference, validity, and reliability of data collection.

 Findings

Please explain your table and figure briefly.

The findings are too narrow; please include more significant findings.

 Discussion – needs more explanation, please support your findings with past studies. Please include a discussion of theoretical and practical implications.

Is the work clearly and accurately presented and does it cite the current literature?

Partly

If applicable, is the statistical analysis and its interpretation appropriate?

Partly

Are all the source data underlying the results available to ensure full reproducibility?

Partly

Is the study design appropriate and is the work technically sound?

No

Are the conclusions drawn adequately supported by the results?

Yes

Are sufficient details of methods and analysis provided to allow replication by others?

No

Reviewer Expertise:

nonprofit and organisational management, entreprenuership, social work, and youth studies

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

Mizutani Fuminobu Business Administration, Kanto Gakuin University, Yokohama, Japan

Competing interests: N/A

 22 12 2025

Thank you very much for reading our first version and commenting. Your comments are helpful for us.

The preface in the review report

Point 1: Response:  The title was changed to focus on HOs. Besides, we added explanations that HOs are not only for contributors but also for beneficiaries.

Point 2:  Response: We added explanations on the relationship between California and Japan from the past to present.

Point 3: Response:  We revised the section 6, especially 6.1 of the main text.

“Introduction section” in the review report

1: Response:  Drumwright (2022) is cited only to fascinate readers including university students as described in the section 1, though both of the authors had travel experiences to Texas.

2: Response:  We added explanations based on Gee et al. (2023).

3: Response:  We added explanations as the mention related to Point 2. Japanese regulations on NFPs have been influenced from California since 1990s.

4: Response:  ​​​​​​​We wrote the research gap in 3.1 of the main text, based on the section 2.

5: Response:  ​​​​​​​We highlighted the significance in the first paragraph of the section 7 and make the second paragraph of that section supplemental.

6: Response:  ​​​​​​​We directly wrote the research objective in 3.1 of the main text.

7: Response:  ​​​​​​​The response is same with 3.

“Literature review” in the review report

1: Response:  ​​​​​​​We discussed the accountability in 2.3 of the main text, citing prior literature.

2: Response:  ​​​​​​​We justified based mainly on Viljoen et al. (2021) and Koster et al. (2022).

3: Response:  ​​​​​​​We added explanations in the section 1.

4: Response:  ​​​​​​​The section 3 is revised by adding sentences and correcting a typo in a formula.

5: Response:  ​​​​​​​We eliminated two research articles from the references.

“Methodology” in the review report

1: Response:  ​​​​​​​The section 4 is revised.

2: Response:  ​​​​​​​We added descriptions in 4.2. Related to the database reference, we inserted another table.

“Findings” in the review report

1: Response:  ​​​​​​​We added brief explanations.

2: Response:  ​​​​​​​Sentences on findings increased. Please view 6.1 of the main text.

“Discussion” in the review report

Response:  We cited past studies and practical documents in 6.2 and 6.3 of the main text.