Corruption persists globally, yet most mathematical models oversimplify it. This study introduces a seven-compartment fractional-order model capturing chronic entrenchment and relapse. Memory effects reveal societal inertia: past experiences buffer rapid moral decline but make recovery slow once corruption takes hold. Prevention emerges as the most effective and cost-efficient strategy, outperforming treatment alone. Combining prevention with targeted treatment creates synergy, reliably reducing corruption below the endemic threshold. These findings provide policymakers a quantitative basis for prioritizing transparency and ethics education while focusing rehabilitation on breaking the chronic-relapse cycle.
Recent advances in polarization research highlight the rise of identity polarization - the fusion of political ideology with demographic and cultural identities into exclusionary partisan mega-identities. Building on models of homophily and interpersonal influence, this paper proposes a social consolidation model to formalize how multi-dimensional identity alignment conditions interaction opportunities and drives opinion dynamics. Agents are situated in synthetic populations with parametrically correlated positions across dimensions (e.g. ideology, race, education). Interaction occurs through similarity-based reinforcement and compromise, but varying levels of consolidation systematically alter network structure and opinion evolution. Simulations reveal that, depending on the level of consolidation, identical micro-mechanisms yield divergent outcomes - from consensus in loosely aligned populations to entrenched polarization in consolidated ones - recasting polarization as an emergent property of network ecology.
This study focuses on the relationship between NIMBY (Not In My Backyard) facility siting and the population distribution. We model a city as a continuous interval in one-dimensional space and examine two factors affecting location decisions: social welfare, which aggregates residents' single-dipped utility from the facility location, and siting feasibility, which captures the tendency to locate facilities in low-density areas. Our theoretical analysis demonstrates that social welfare is maximized at the city's edge under typical assumptions on the utility function. We introduce a composite objective function to examine how these factors interact. The findings are partially confirmed by Japanese data, which show that municipal solid waste facilities tend to be located near the boundary of municipalities and in low-density areas.
Quantifying intergenerational changes in educational homophily is challenging when education level of marriageable individuals is generation-specific. To address this challenge, the literature proposed various indicators. We argue that suitable indicators should meet several analytical criteria. However, our main criterion is empirical in nature: suitable indicators, when computed from data on American couples born after 1930, should exhibit a U-shaped trend at the national level and for the majority of the US states. A cardinal homophily indicator constructed with the NM-method, based on an old forgotten and recently reinvented ordinal indicator, is one of the few indicators that meets the criteria.
This paper explores how minority group size moderates the effect of employer prejudice on hiring discrimination. We propose a simple job search model in which prejudiced employers retain hiring discretion but are legally required to offer equal pay to all workers. Our analysis suggests that employers are more likely to exclude smaller minority groups from employment; however, as the minority population increases, employment discrimination diminishes and may even vanish. We further show that this result persists even when employer prejudice varies across firms and intensifies with minority group size.
