Sensitivity of fluvial sediment source apportionment to mixing model assumptions: A Bayesian model comparison

Mixing models have become increasingly common tools for apportioning fluvial sediment load to various sediment sources across catchments using a wide variety of Bayesian and frequentist modeling approaches. In this study, we demonstrate how different model setups can impact upon resulting source apportionment estimates in a Bayesian framework via a one-factor-at-a-time (OFAT) sensitivity analysis. We formulate 13 versions of a mixing model, each with different error assumptions and model structural choices, and apply them to sediment geochemistry data from the River Blackwater, Norfolk, UK, to apportion suspended particulate matter (SPM) contributions from three sources (arable topsoils, road verges, and subsurface material) under base flow conditions between August 2012 and August 2013. Whilst all 13 models estimate subsurface sources to be the largest contributor of SPM (median ∼76%), comparison of apportionment estimates reveal varying degrees of sensitivity to changing priors, inclusion of covariance terms, incorporation of time-variant distributions, and methods of proportion characterization. We also demonstrate differences in apportionment results between a full and an empirical Bayesian setup, and between a Bayesian and a frequentist optimization approach. This OFAT sensitivity analysis reveals that mixing model structural choices and error assumptions can significantly impact upon sediment source apportionment results, with estimated median contributions in this study varying by up to 21% between model versions. Users of mixing models are therefore strongly advised to carefully consider and justify their choice of model structure prior to conducting sediment source apportionment investigations

The allocation between EU member states of seats in the European Parliament

This note contains the recommendation for a mathematical basis for the apportionment of the seats in the European Parliament between the Member States of the European Union. This is the unanimous recommendation of the Participants in the Cambridge Apportionment Meeting, held at the instigation of the Committee on Constitutional Affairs at the Centre for Mathematical Sciences, University of Cambridge, on 28–29 January 2011

The allocation between the EU member states of the seats in the European Parliament Cambridge Compromise

This Note contains the recommendation for a mathematical basis for the apportionment of the seats in the European Parliament between the Member States of the European Union. This is the unanimous recommendation of the Participants in the Cambridge Apportionment Meeting, held at the instigation of the Committee on Constitutional Affairs at the Centre for Mathematical Sciences, University of Cambridge, on 28-29 January 2011.Proportional Representation, degressive proportionality, apportionment, European Parliament. Classification

Linear-time Algorithms for Proportional Apportionment

The apportionment problem deals with the fair distribution of a discrete set of $k$ indivisible resources (such as legislative seats) to $n$ entities (such as parties or geographic subdivisions). Highest averages methods are a frequently used class of methods for solving this problem. We present an $O(n)$-time algorithm for performing apportionment under a large class of highest averages methods. Our algorithm works for all highest averages methods used in practice.Comment: 13 pages, to appear in ISAAC 201

Corporate Income Taxation of Multinationals in a General Equilibrium Model

This paper contributes to the discussion on Separate Accounting versus Formula Apportionment in the corporate income taxation of multinational enterprises (MNEs). The innovation of the analysis is that we consider a general equilibrium tax competition model with an endogenously determined world interest rate. Under the principle of Separate Accounting, it turns out that corporate tax rates may be inefficiently low or high, while under Formula Apportionment corporate tax rates are always inefficiently low. These results are true independent of whether the number of countries is small or large. They reverse the insights obtained by previous studies under the assumption of an exogenously given world interest rate.corporate income tax, Separate Accounting, Formula Apportionment

Corporate tax harmonization in the EU

This paper explores the economic consequences of proposed EU reforms for a common consolidated corporate tax base. The reforms replace separate accounting with formula apportionment as a way to allocate corporate tax bases across countries. To assess the economic implications, we use a numerical CGE model for Europe. It encompasses several decision margins of firms,such as marginal investment, FDI decisions, and multinational profit shifting. The simulations suggest that consolidation does not yield substantial welfare gains for Europe. The variation of effects across countries is large and depends on the choice of the apportionment formula. Consolidation with formula apportionment does not weaken incentives for tax competition. Tax competition instead offers a rationale for rate harmonisation, in addition to base harmonisation.

A note on apportionment methods

This paper investigates the suitability of apportionment methods based on the idea of preserving the coalition function of the simple game represented by the populations of the states. The results show that an apportionment method which satisfies desirable properties such as population monotonicity, house monotonicity, etc., does not exist. A classification of simple voting games via winning coalitions is also given.apportionment methods, simple games, winning coalitions

Tax Competition with Formula Apportionment: The Interaction between Tax Base and Sharing Mechanism

The EU Commission is advocating a common consolidated tax base for the corporate income tax, accompanied by a revenue sharing mechanism based on formula apportionment. We analyse tax competition in such a regime, focussing on the interaction between the definition of the tax base and the apportionment method. Tax competition leads to suboptimally low tax rates if and only if the investment elasticity of the tax base is lower than the investment elasticity of the apportionment factor. For any apportionment method a change in the definition of the tax base can turn a race-to-the-bottom in tax competition into a race-over-the-top.tax competition, formular apportionment, corporate income tax

Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System

Political parties in Northern Ireland recently used a divisor method of apportionment to choose, in sequence, ten cabinet ministries. If the parties have complete information about each others' preferences, we show that it may not be rational for them to act sincerely by choosing their most-preferred ministry that is available. One consequence of acting sophisticatedly is that the resulting allocation may not be Pareto-optimal, making all the parties worse off. Another is nonmonotonicty—choosing earlier may hurt rather than help a party. We introduce a mechanism that combines sequential choices with a structured form of trading that results in sincere choices for two parties. Although there are difficulties in extending this mechanism to more than two parties, other approaches are explored, such as permitting parties to making consecutive choices not prescribed by an apportionment method. But certain problems, such as eliminating envy, remain.Proportional Representation, apportionment, divisor methods, Sincere and Sophisticated Choices, Envy Free Allocations, Sports Drafts