Averaging Lorenz curves

A large number of functional forms has been suggested in the literature for estimating Lorenz curves that describe the relationship between income and population shares. The traditional way of overcoming functional-form uncertainty when estimating a Lorenz curve is to choose the function that best fits the data in some sense. In this paper we describe an alternative approach for accommodating functional-form uncertainty, namely, how to use Bayesian model averaging to average the alternative functional forms. In this averaging process, the different Lorenz curves are weighted by their posterior probabilities of being correct. Unlike a strategy of picking the best-fitting function, Bayesian model averaging gives posterior standard deviations that reflect the functional-form uncertainty. Building on our earlier work (Chotikapanich and Griffiths, 2002), we construct likelihood functions using the Dirichlet distribution and estimate a number of Lorenz functions for Australian income units. Prior information is formulated in terms of the Gini coefficient and the income shares of the poorest 10% and poorest 90% of the population. Posterior density functions for these quantities are derived for each Lorenz function and are averaged over all the Lorenz functions.     

On the Compatibility of Organizational Behavior Management and BACB Certification

The number of practicing behavior analysts who hold Behavior Analyst Certification Board (BACB) certification has substantially increased in the past decade. Some have mistakenly interpreted the BACB’s certification requirements as being specific to the autism and intellectual disabilities practice area. We present key BACB requirements, describe how they are practice-area neutral, and provide specific examples of their relevance to organizational behavior management.     

Can formula apportionment really prevent multinational enterprises from profit shifting? The role of asset valuation,intragroup debt,and leases

The European Commission has been supporting a transition from a system of separate accounting to formula apportionment. After its 2011 draft directive was rejected by the Council, the Commission presented two new draft directives in October 2016, one stipulating rules for a common tax base and another the terms for consolidation and apportionment. The aspired system of unitary taxation is considered more resistant to profit shifting and assumed to reduce compliance costs. However, there are also doubts about the extent, to which such a system will eradicate tax-planning activities of MNEs. Other concerns have arisen about the practical issue of enforcing uniform rules for asset valuation throughout the member states. We use a dynamic model of tax accounting based on neoclassical investment theory and effective tax rates to determine to what extent formula apportionment mitigates the efficiency of typical profit-shifting strategies. We focus on the roles of transfer pricing and intragroup debt financing (through loans and leases) under both separate accounting and formula apportionment. We also take into account a possible leeway for inconsistent valuation. Our results show that instead of eliminating tax planning strategies, the proposed system might simply induce a shift from manipulating reported profits to influencing the apportionment key. Inside the European Union, the CCCTB may be able to render thin capitalisation rules and transfer pricing documentation redundant. However, formula apportionment invites for new forms of tax planning. It is therefore essential to give credit to these new kinds of tax incentives when implementing a system of unitary taxation.     

CCR or BCC: what if we are in the wrong model?

The CCR model by Charnes et al. (Eur J Oper Res 2:429–444, 1978) together with the BCC model by Banker et al. (Manag Sci 30:1078–1091, 1984) are the most popular approaches of measuring efficiency among a group of decision making units, DMUs, in data envelopment analysis, DEA. The right choice of a DEA model—CCR or BCC—often, if not always, is a difficult decision. To evaluate a DMU’s efficiency for both models might be helpful, but it does not always capture the essential issues at stake. In this paper we propose a comparative analysis of both concepts: How does activity scaling under constant BCC-efficiency influence CCR-efficiency. And inversely, how does BCC-efficiency behave when activity scaling under constant CCR-efficiency is applied. Such findings of mutual effects improve a DMU’s ability to reassess upsizing and downsizing of activities. Moreover, it allows for exact calculations of the resulting economic effects, and these effects give new insights beyond classical DEA. Finally, scale efficiency turns out to be the ideal concept to control these activity changes, rather than just CCR- or BCC-efficiency. We use a little numerical example to emphasize advantages of the new concept and sketch the new findings for a theater scenery.     

Coaching as a Packaged Intervention for Telemarketing Personnel

Prior literature indicates that although the sales function of an organization is a critical element for its success, there is a lack of research on specific actions managers can take to influence sales subordinates. The purpose of the present study was to assess the effects of a coaching package combined with incentives on sales performance for telemarketing personnel in an organizational setting. Following the implementation of the coaching package, there was a substantial increase in critical behaviors performed, pending sales set, and final sales completed by all telemarketers.     

Uniqueness of equilibria in atomic splittable polymatroid congestion games

We study uniqueness of Nash equilibria in atomic splittable congestion games and derive a uniqueness result based on polymatroid theory: when the strategy space of every player is a bidirectional flow polymatroid, then equilibria are unique. Bidirectional flow polymatroids are introduced as a subclass of polymatroids possessing certain exchange properties. We show that important cases such as base orderable matroids can be recovered as a special case of bidirectional flow polymatroids. On the other hand we show that matroidal set systems are in some sense necessary to guarantee uniqueness of equilibria: for every atomic splittable congestion game with at least three players and non-matroidal set systems per player, there is an isomorphic game having multiple equilibria. Our results leave a gap between base orderable matroids and general matroids for which we do not know whether equilibria are unique.     

Optimization problems with color-induced budget constraints

In 1984, Gabow and Tarjan provided a very elegant and fast algorithm for the following problem: given a matroid defined on a red and blue colored ground set, determine a basis of minimum cost among those with k red elements, or decide that no such basis exists. In this paper, we investigate extensions of this problem from ordinary matroids to the more general notion of poset matroids which take precedence constraints on the ground set into account. We show that the problem on general poset matroids becomes -hard, already if the underlying partially ordered set (poset) consists of binary trees of height two. On the positive side, we present two algorithms: a pseudopolynomial one for integer polymatroids, i.e., the case where the poset consists of disjoint chains, and a polynomial algorithm for the problem to determine a minimum cost ideal of size l with k red elements, i.e., the uniform rank-l poset matroid, on series-parallel posets.     

Approximation strategy-proof mechanisms for obnoxious facility location on a line

In the facility location game on a line, there are some agents who have fixed locations on the line where an obnoxious facility will be placed. The objective is to maximize the social welfare, e.g., the sum of distances from the facility to all agents. On collecting location information, agents may misreport the locations so as to stay far away from the obnoxious facility. In this paper, strategy-proof mechanisms are designed and the approximation ratio is used to measure the performances of the strategy-proof mechanisms. Two objective functions, maximizing the sum of squares of distances (maxSOS) and maximizing the sum of distances (maxSum), have been considered. For maxSOS, a randomized 5/3-approximated strategy-proof mechanism is proposed, and the lower bound of the approximation ratio is proved to be at least 1.042. For maxSum, the lower bound of the approximation ratio of the randomized strategy-proof mechanism is proved to be 1.077. Moreover, a general model is considered that each agent may have multiple locations on the line. For the objective functions maxSum and maxSOS, both deterministic and randomized strategy-proof mechanisms are investigated, and the deterministic mechanisms are shown to be best possible.     

On tree representations of relations and graphs: symbolic ultrametrics and cograph edge decompositions

Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g. in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics define an edge-colored complete graph that allows to represent the topology of this graph as a vertex-colored tree. Here, we are interested in the structure and the complexity of certain combinatorial problems resulting from considerations based on symbolic ultrametrics, and on algorithms to solve them.This includes, the characterization of symbolic ultrametrics that additionally distinguishes between edges and non-edges of arbitrary edge-colored graphs G and thus, yielding a tree representation of G, by means of so-called cographs. Moreover, we address the problem of finding “closest” symbolic ultrametrics and show the NP-completeness of the three problems: symbolic ultrametric editing, completion and deletion. Finally, as not all graphs are cographs, and hence, do not have a tree representation, we ask, furthermore, what is the minimum number of cotrees needed to represent the topology of an arbitrary non-cograph G. This is equivalent to find an optimal cograph edge k-decomposition \(\{E_1,\dots ,E_k\}\) of E so that each subgraph \((V,E_i)\) of G is a cograph. We investigate this problem in full detail, resulting in several new open problems, and NP-hardness results.For all optimization problems proven to be NP-hard we will provide integer linear program formulations to solve them.     

Bounds on the domination number of a digraph

A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S is adjacent from at least one vertex in S. The domination number of D, denoted by \(\gamma (D)\), is the minimum cardinality of a dominating set of D. The Slater number \(s\ell (D)\) is the smallest integer t such that t added to the sum of the first t terms of the non-increasing out-degree sequence of D is at least as large as the order of D. For any digraph D of order n with maximum out-degree \(\Delta ^+\), it is known that \(\gamma (D)\ge \lceil n/(\Delta ^++1)\rceil \). We show that \(\gamma (D)\ge s\ell (D)\ge \lceil n/(\Delta ^++1)\rceil \) and the difference between \(s\ell (D)\) and \(\lceil n/(\Delta ^++1)\rceil \) can be arbitrarily large. In particular, for an oriented tree T of order n with \(n_0\) vertices of out-degree 0, we show that \((n-n_0+1)/2\le s\ell (T)\le \gamma (T)\le 2s\ell (T)-1\) and moreover, each value between the lower bound \(s\ell (T)\) and the upper bound \(2s\ell (T)-1\) is attainable by \(\gamma (T)\) for some oriented trees. Further, we characterize the oriented trees T for which \(s\ell (T)=(n-n_0+1)/2\) hold and show that the difference between \(s\ell (T)\) and \((n-n_0+1)/2\) can be arbitrarily large. Some other elementary properties involving the Slater number are also presented.