Leadership Gap in Selection and Practice

• Leadership gap is a discrepancy between the stated leadership values and the leaders actually selected, recognized, or enabled in practice.
• It manifests as distorted promotion pipelines, under-specified roles, and inefficiencies in signaling and coordination across various disciplines.
• Empirical research across fields—from agile transformation to physics—highlights the need for transparent, equitable selection and adaptive governance.

Searching arXiv for recent and relevant papers on “leadership gap” and adjacent formulations. The leadership gap denotes a family of mismatches between the leadership a system says it values and the leadership it actually selects, recognizes, enables, or sustains. In the literature, the term does not have a single universal definition. In physics, it names the divergence between the leaders institutions need for excellence and fairness and the leaders actually selected through opaque or cronyistic processes. In agile transformation, it refers to the difference between what “agile leaders” are implicitly expected to accomplish and what process-focused frameworks actually specify. In project management, it identifies a gap between abstract leadership theory and empirical evidence about which concrete leader behaviors improve project efficiency. In human-AI systems, it appears as a misrecognition problem: visible human authority can persist after decision-shaping power has shifted elsewhere. In formal political and coordination models, the gap is a wedge between socially efficient leadership and leadership behavior distorted by incentives or information structure (Barzi et al., 2022, Gren et al., 2020, Ćwiąkała et al., 7 Oct 2025, Jadad, 30 Apr 2026, Bandyopadhyay et al., 2022, Kyriazis et al., 2023).

1. Major meanings of the concept

Across domains, the concept is best understood as a set of structurally related but analytically distinct problems. Some versions concern selection: who gets leadership roles and by what criteria. Others concern specification: what leadership work is actually required but left undescribed. Others concern realization: whether potential leadership capacity is converted into effective direction. Still others concern recognition: whether authority is located where organizations believe it is.

Domain	Leadership-gap formulation	Representative source
Physics	Mismatch between needed leaders and actually selected leaders	(Barzi et al., 2022)
Agile transformation	Mismatch between expected agile leadership and framework specification	(Gren et al., 2020)
Scrum team maturation	Deliberate lack of leadership creating space for role transfer	(Spiegler et al., 2018)
Project management	Gap between leadership theory and measurable project behaviors	(Ćwiąkała et al., 7 Oct 2025)
Human-AI teaming	Gap between visible human control and actual decision-shaping authority	(Jadad, 30 Apr 2026)
Electoral conflict	Gap between second-best policy and politically induced hawkish policy	(Bandyopadhyay et al., 2022)

This suggests that the term is not restricted to leader scarcity. It also covers distorted promotion pipelines, hidden authority, under-specified roles, inefficient signaling equilibria, and unrealized leadership capacity. A plausible implication is that “leadership gap” functions less as a single variable than as a comparative diagnosis: it marks a discrepancy between a normative or functional benchmark and an observed organizational or strategic outcome.

2. Selection, meritocracy, and representation

One influential formulation ties the leadership gap to failures of meritocracy, equity, and inclusion. In physics, equal opportunity is treated as central to meritocracy: opportunity and leadership should go to the people most qualified by performance, not on the basis of arbitrary or irrelevant attributes. The leadership gap is therefore the mismatch between the leaders physics institutions need to achieve excellence and fairness and the leaders actually selected through current processes. The argument is explicitly not that excellence and equity compete; rather, equity is part of excellence, and underrepresentation on a scale “far worse than could be expected” under a functioning meritocracy is treated as evidence that actual practices do not match the field’s ideals. High-level leadership matters especially because such positions have an outsized impact on culture, hiring and promotion norms, responses to misconduct, retention, and whether underrepresented groups feel welcome and supported (Barzi et al., 2022).

Gender-focused work places the gap at multiple pipeline stages. In a large multinational manufacturing firm, women in lower-level positions were 27.4% less likely to apply for promotions than men under the preferred hierarchy-based definition, and the gap was concentrated at the first step into leadership rather than among employees who already held leadership roles. The paper attributes this not mainly to confidence or success beliefs, but to a specific design feature of many early-career promotions: having to take responsibility over a team. Among employees already in leadership, 75% identified taking on responsibility over a team as the most salient change when first promoted, and survey evidence showed that women were 36% less likely to want responsibility over a team in five years and 13% less likely to choose a hypothetical position with team responsibility (Haegele, 2024).

A different diagnosis appears in the legal profession, where the gap is modeled through supply and demand rather than application behavior. Using data from 327 law firms and 248,628 lawyers, the study argues that a 30% candidate-pool requirement such as the Mansfield Rule may be mathematically infeasible if the relevant leadership pipeline does not contain enough underrepresented lawyers. In the full dataset, leadership positions comprised 136,539 lawyers; women in leadership were 38,342 (28%) and minorities 14,981 (11%). For firms with more than 751 lawyers, white female leadership supply had 18% fill capacity and minority leadership supply 15%, both below the 30% threshold. The paper’s claim is not that diversity initiatives are useless, but that percentage-based slate rules can create the appearance of progress while the underlying structural shortage remains unresolved (Dimeglio, 2023).

Qualitative studies of women in software engineering leadership shift the emphasis from entry and supply to lived legitimacy and authority. One study of three women in leadership or management roles in the same technology company in Brazil derived 23 codes grouped into 7 themes: Permission to Occupy Technology Spaces, Recognition and Equal Opportunities, Need to Go Above and Beyond, Mental Wear and Tear, Drama and Stereotypes, Obstacles and Fears, and Hire and Education for Diversity. The leadership gap here is not a lack of leadership ability but a workplace in which women leaders face a higher proof burden, structural sexism, male protectionism, stereotype-driven credibility loss, and extra diversity labor (Kohl et al., 2021).

3. Developmental and distributed leadership

Another line of work treats the leadership gap as a problem of role under-specification in maturing teams. In agile transformation, organizations often appoint managers, Scrum Masters, project managers, or other staff as “agile leaders” without giving them a clear definition of what leadership should comprise when building agile teams. The empirical claim is that process-focused frameworks under-describe the actual work leaders must perform. The studied practitioners were not merely passive facilitators: with less mature or newly formed teams, they provided explicit guidance, stopped unhelpful discussion patterns, assigned tasks when volunteering did not work, enforced basic Scrum routines, and explained the meaning of agile practices. The paper organizes this gap around three challenge categories that are not explicitly mentioned in more process-focused agile frameworks: Team maturity, Team design, and Culture and mindset. It links these to Tuckman’s developmental model and to Wageman’s sequence in which the leader must first be a designer, then a midwife, and only later a coach (Gren et al., 2020).

Within Scrum-specific research, the phrase acquires a more technical meaning. The leadership gap is defined as “a lack of leadership which provides the opportunity for a team to take on a leadership role.” Rather than a failure, the gap is a productive vacancy in which a formal role holder retreats far enough for team members to claim and be granted leadership functions. In a Grounded Theory study of 53 practitioners from 29 teams at Robert Bosch GmbH, Scrum Masters initially performed nine leadership roles: Method Champion, Disciplinizer on Equal Terms, Coach, Change Agent, Helicopter, Moderator, Networker, Knowledge Enabler, and Protector. As teams matured, many of these roles were gradually transferred to team members. The enabling environment was characterized by communication on equal terms, psychological safety, transparency, shared understanding, shared purpose, self-efficacy, trust, and freedom (Spiegler et al., 2018).

These studies reject a common simplification according to which self-organization means immediate leader withdrawal. The agile-transformation evidence states that if leaders try to be only facilitators “from day one,” they can hamper the team’s development. The Scrum-maturation evidence similarly describes a staged movement from centralized to distributed leadership, not an abrupt disappearance of leadership. A plausible implication is that mature self-organization is often the outcome of deliberate, temporally calibrated leadership rather than its absence.

4. Leadership, execution, and performance

In project management, the leadership gap is framed as a lack of empirical evidence connecting leadership theory to observable project behavior. A quantitative questionnaire study of 100 respondents used 16 closed questions, ordinal coding (Yes = 1, Varies = 0.5, No = 0), and Spearman rank correlation because the data were ordinal. The most positively evaluated behaviors were providing constructive feedback (87% Yes, mean 0.915, median 1), ensuring role clarity (86% Yes, mean 0.915, median 1), encouraging initiative and independent problem-solving (85% Yes, mean 0.919, median 1), and communicating goals and outcomes effectively (84% Yes, mean 0.900, median 1). The key bivariate result was a statistically significant but weak positive correlation between constructive feedback and teams achieving project goals, with $\rho = 0.286$ and $p = 0.004 < 0.05$. The broader ranking placed Constructive feedback at 0.28, Clear roles at 0.27, Communication at 0.25, and Delegation at 0.21, ahead of more weakly correlated items such as Conflict management (0.10) and Decision involvement (0.05) (Ćwiąkała et al., 7 Oct 2025).

Open-source software development offers a different operationalization. Leadership is not defined by title but by coding centrality: the lead developer is the developer with the highest number of commits, or temporally the one with the largest cumulative share of commits up to a trimester. Across repositories, the most active developer authors more than half of all commits, while the second-ranked developer typically contributes about 10–20%. Unevenness is measured by relative effective team size,

$\frac{2^{H}}{N},$

where $H$ is the binary entropy of the commit distribution and $N$ is team size; smaller values mean more uneven work distribution. Repositories with more heterogeneous workload distributions were more successful, with Spearman correlations of at least $\rho = -0.28$, $p<0.001$ for stars and at least $\rho = -0.11$, $p<0.001$ for downloads. Leadership change occurred in 618 repositories, about 10% of the analyzed set, and 92% of those experienced only one such change. Using matched controls, the paper found that leadership change was associated with faster success growth, including $\Delta_{t=0} = 0.05$ and $p = 0.004 < 0.05$0 for stars (Betti et al., 2024).

Context-sensitive work on female-led software projects complicates any simple style-performance equation. In a longitudinal multiple case study of 13 software development projects, LPC scores ranged from 47 to 109 with a median of 67, and no direct relationship was found between LPC leadership style and objective project performance: $p = 0.004 < 0.05$1, $p = 0.004 < 0.05$2, $p = 0.004 < 0.05$3. Instead, performance relationships appeared elsewhere. Objective team performance and team communication showed $p = 0.004 < 0.05$4, $p = 0.004 < 0.05$5; perceived leadership and perceived task management showed $p = 0.004 < 0.05$6, $p = 0.004 < 0.05$7; and leadership style and customer involvement showed $p = 0.004 < 0.05$8, $p = 0.004 < 0.05$9, suggesting a potential association between human-oriented leadership in low customer-involvement settings and task-oriented leadership in high customer-involvement settings (Nguyen-Duc et al., 2017).

Taken together, these results indicate that leadership gaps in execution are often behavioral and situational rather than purely dispositional. Clear feedback, role clarity, communication, workload concentration, turnover timing, and project context recur as stronger explanatory factors than abstract labels alone.

5. Strategic, informational, and dynamical mechanisms

Several formal models show that the leadership gap can arise even when leader quality is not the primary problem. In a coordination model with one leader and $\frac{2^{H}}{N},$0 followers, the leader observes the state perfectly and moves first, while followers receive private noisy signals $\frac{2^{H}}{N},$1. The leader’s action generates a signaling effect, but followers also face a miscoordination effect because they worry about what other followers will do. The central result is a cutoff $\frac{2^{H}}{N},$2: efficient leadership is the unique $\frac{2^{H}}{N},$3-rationalizable outcome if and only if follower signals are sufficiently noisy, $\frac{2^{H}}{N},$4. If followers are too well informed, leadership may fail: followers can rationally refuse to follow even when the leader’s action reveals that $\frac{2^{H}}{N},$5 is efficient, and the leader may “choose the undesirable action in the first place” because she fears followers will play against her. The paper therefore argues that leadership effectiveness depends on follower information structure, not only on how well informed the leader is (Kyriazis et al., 2023).

In political conflict, the gap is modeled as hawkish drift. Citizens elect a leader who chooses how much land to retain, $\frac{2^{H}}{N},$6, under re-election incentives. Leaders differ in ideology $\frac{2^{H}}{N},$7 and ability $\frac{2^{H}}{N},$8, conflict costs satisfy $\frac{2^{H}}{N},$9, $H$0, $H$1, and the baseline uses $H$2 and

$H$3

Because higher ability lowers conflict cost, hawkish behavior can signal competence. The political equilibrium cutoff $H$4 weakly exceeds the second-best cutoff $H$5, and when office rents $H$6 are high the two can diverge sharply. Under the condition $H$7, more hawkish politicians find it easier to satisfy the reelection cutoff, so hawkish politicians may have a reelection advantage. The leadership gap here is the strategic wedge between socially efficient settlement and the policy chosen by office-seeking leaders (Bandyopadhyay et al., 2022).

Network and communication models generalize the idea beyond formal office. In a neuro-inspired communication model, leadership emerges from repeated activation, adaptive attention weights, credibility scores, inertia $H$8, score sensitivity $H$9, and noise $N$0. The same local rules can generate laissez-faire, participative or democratic, autocratic, hidden leadership, and successive leadership scenarios. Leadership is therefore modeled not as an imposed title but as a dynamical consequence of attention redistribution and credibility accumulation (Allahverdyan et al., 2017). In a separate dynamic alliance model, unequal alliances governed by parameter $N$1 produce a distinctive power-vacuum regime: at intermediate inequality, one leader is present at a time but is rapidly replaced after losing status. At $N$2 and $N$3, the average leader persisted for about 7000 time steps in simulations run over 2 million time steps, demonstrating substantial turnover without leaderlessness (Bryden et al., 2019).

These models complicate a common misconception that leadership gaps are simply deficits of individual competence. The formal results instead show gaps generated by electoral signaling, follower precision, local communication rules, alliance inequality, and coordination structure.

6. Measurement, governance, and intervention

Recent work also formalizes leadership gaps as problems of measurement and governance design. In a directed organizational graph $N$4, the Average Forest (AF) measure defines leadership as expected marginal contribution across all maximal spanning forests. For a maximal forest $N$5, player $N$6’s marginal contribution is

$N$7

and AF averages this quantity over all maximal forests. The associated productivity measure is

$N$8

with the key identity

$N$9

If the digraph is quasi-strongly connected, productivity reaches $\rho = -0.28$0; otherwise, the structure leaves value unrealized. This makes the leadership gap measurable as a mismatch between potential leadership capacity encoded in organizational structure and the productive value actually realizable through feasible hierarchies (Flores et al., 31 Jul 2025).

In human-AI systems, governance difficulties are framed through a five-position spectrum: Pure Human, Centaur, Co-equal, Minotaur, and Pure AI. The relevant question is not who nominally signs off, but who frames the problem, generates options, challenges them, redirects the work, decides, and remains answerable for the result. The central risk is misrecognition: leaders may keep a human-centered story in place after decision-shaping authority has shifted elsewhere, or believe oversight remains meaningful when it has become “ceremonial.” The framework adds co-adaptability, defined as the capacity of a configuration to adjust and become stronger under changing conditions as participants learn, recalibrate, and remain effective together over time. Here the leadership gap is a decoupling of influence, answerability, and visible authority (Jadad, 30 Apr 2026).

Intervention-oriented scholarship emphasizes process redesign. In physics, the proposed remedy is to replace informal and opaque leadership selection with best practices from Industrial-Organizational Psychology: conduct a job analysis; advertise broadly through societies such as the National Society of Black Physicists, National Society of Hispanic Physicists, National Technical Association, and SACNAS; build diverse search committees; train committees on bias; use a pre-agreed rubric; eliminate low-value steps; use reliable assessment tools; use structured interviews, which are described as “two to three times less reliable” when unstructured; use anonymized qualification statements; use an unforeseen EDI case study; and think carefully about confidentiality of candidate names. The paper’s central claim is that leadership selection is a leverage point for changing culture: if leadership is chosen through opaque, biased, or cronyistic practices, institutions will not become equitable or excellent (Barzi et al., 2022).

Across these literatures, the leadership gap is therefore not reducible to the absence of leaders. It can describe distorted selection, broken promotion rungs, under-specified developmental work, unrealized network capacity, hidden authority, inefficient signaling equilibria, or symbolic oversight. What unites these cases is a recurring discrepancy between formal narratives of leadership and the mechanisms that actually determine who leads, how leadership operates, and with what consequences.