Survey Evidence on Conditional Norm Enforcement

We discuss survey evidence on individuals' willingness to sanction norm violations – such as evading taxes, drunk driving, fare dodging, or skiving off work – by expressing disapproval or social exclusion. Our data suggest that people condition their sanctioning behavior on their belief about the frequency of norm violations. The more commonly a norm violation is believed to occur, the lower the individuals' inclination to punish it. Based on an instrumental variable approach, we demonstrate that this pattern reflects a causal relationship.Norm Enforcement, Sanctioning, Social Norms, Survey Evidence

Survey Evidence on Conditional Norm Enforcement

We discuss survey evidence on individuals' willingness to sanction norm violations - such as evading taxes, drunk driving, fare dodging, or skiving o work - by expressing disapproval or social exclusion. Our data suggest that people condition their sanctioning behavior on their belief about the frequency of norm violations. The more commonly a norm violation is believed to occur, the lower the individuals' inclination to punish it. Based on an instrumental variable approach, we demonstrate that this pattern reflects a causal relationship.Norm Enforcement; Sanctioning; Social Norms; Survey Evidence

Observation- and Modelling of Morphodynamics in Sandy Coastal Environments

The topic of sandy coast morphodynamics involves the mutual influences of coastal topography, local sedimentology, the driving meteorological and hydrodynamic boundary conditions, flora and fauna, and the activities of human beings: The latter as direct actors through coastal constructions and other interventions, as indirect actors through possible contributions to global change, but also as receiving agents - as living individuals confronted with the forces of the sea. The general aim of coastal research is to gain an as comprehensive as possible understanding of the different systems and their interaction in order to be able to evaluate their current state, assess their stability, explain past changes (in the geological record), and predict future developments under different conditions. Such systems dynamics involve a large bandwidth of spatial and temporal scales: from the microscopic interaction of turbulent fluid motions with single particles to meso-scale tidal dynamics of subaqueous bedforms to macro-scale seasonal adaptations of beach profiles or the meandering of tidal channels, to the mega-scale evolution of shorelines and shelf systems over decades to centuries. The process of understanding involves a continuous feedback of observations, abstractions, mathematical formulations, model development (ranging from conceptual models to mathematical formulations of processes, and to complex, process-based numerical modelling systems), and the testing of models on the basis of observations, new abstractions, and so forth. In the case of the morphodynamics of sandy coasts, the interaction of the physical processes involved in hydrodynamics, sediment dynamics, and their mutual adjustment to changing bed topographies seem most relevant, although biogeochemical processes play a (commonly underrated) additional role. This discourse presents an extended summary of the current state in the continuous process of gaining knowledge on coastal morphodynamics. It focuses on the dynamics of tidal channels and their main roughness elements: subaqueous compound bedforms. Methodological approaches involved are field measurements and numerical modelling, which are introduced and discussed

Poset Ramsey Number R(P, Qn). I. Complete Multipartite Posets

A poset $(P′,≤_{P′})$ contains a copy of some other poset $(P,≤_P)$ if there is an injection $f:P′→P$ where for every $X,Y∈P, X≤_PY$ if and only if $f(X)≤_{P′}f(Y)$. For any posets $P$ and $Q$, the poset Ramsey number $R(P, Q)$ is the smallest integer $N$ such that any blue/red coloring of a Boolean lattice of dimension $N$ contains either a copy of $P$ with all elements blue or a copy of $Q$ with all elements red. A complete ℓ-partite poset $K_{t1,…,tℓ}$ is a poset on $∑^ℓ_{i=1}t_i$ elements, which are partitioned into $ℓ$ pairwise disjoint sets $A^i$ with $|A^i|=t_i, 1≤i≤ℓ$, such that for any two $X∈A^i$ and $Y∈A^j$, $X<Y$ if and only if $i<j$. In this paper we show that $R(K_{t1,…,tℓ, }Q_n)≤n+\frac{(2+on(1))ℓn}{logn}$

Poset Ramsey number R(P,Qn)R(P,Q_n). III. Chain Compositions and Antichains

An induced subposet $(P_2,\le_2)$ of a poset $(P_1,\le_1)$ is a subset of $P_1$ such that for every two $X,Y\in P_2$, $X\le_2 Y$ if and only if $X\le_1 Y$. The Boolean lattice $Q_n$ of dimension $n$ is the poset consisting of all subsets of $\{1,\dots,n\}$ ordered by inclusion. Given two posets $P_1$ and $P_2$ the poset Ramsey number $R(P_1,P_2)$ is the smallest integer $N$ such that in any blue/red coloring of the elements of $Q_N$ there is either a monochromatically blue induced subposet isomorphic to $P_1$ or a monochromatically red induced subposet isomorphic to $P_2$. We provide upper bounds on $R(P,Q_n)$ for two classes of $P$: parallel compositions of chains, i.e.\ posets consisting of disjoint chains which are pairwise element-wise incomparable, as well as subdivided $Q_2$, which are posets obtained from two parallel chains by adding a common minimal and a common maximal element. This completes the determination of $R(P,Q_n)$ for posets $P$ with at most $4$ elements. If $P$ is an antichain $A_t$ on $t$ elements, we show that $R(A_t,Q_n)=n+3$ for $3\le t\le \log \log n$. Additionally, we briefly survey proof techniques in the poset Ramsey setting $P$ versus $Q_n$.Comment: 20 pages, 23 figures. Merged with arXiv:2205.0227