Network models and biproportional rounding for fair seat allocations in the UK elections

Systems for allocating seats in an election offer a number of socially and mathematically interesting problems. We discuss how to model the allocation process as a network flow problem, and propose a wide choice of objective functions and allocation schemes. Biproportional rounding, which is an instance of the network flow problem, is used in some European countries with multi-seat constituencies. We discuss its application to single seat constituencies and the inevitable consequence that seats are allocated to candidates with little local support. However, we show that variants can be selected, such as regional apportionment, to mitigate this problem. In particular, we introduce a parameter based family of methods, which we call Balanced Majority Voting, that can be tuned to meet the public's demand for local and global ``fairness''. Using data from the 2010 and 2015 UK General Elections, we study a variety of network models and implementations of biproportional rounding, and address conditions of existence and uniqueness

Multidimensional Allocation: In Apportionment and Bin Packing

In this thesis, we deal with two problems on multidimensional allocation, specifically in apportionment and in bin packing. The apportionment problem models the allocation of seats in a House of Representatives such that it is proportional to the dimensions being represented. One example is the allocation of the 435 House seats to the 50 U.S. states, which demands being proportional in the one dimension of state population. It is also common to demand proportionality in both state population and political affiliation, where we now have to allocate to two dimensions simultaneously. We begin by investigating what it means for an 1-D apportionment to be "fair", and use this to judge the various methods of apportionment that have been used throughout history. This motivates the study of divisor methods, a certain class of apportionment methods that avoid any paradoxes. We then formally tackle the problem of 1-dimensional and 2-dimensional apportionment with divisor methods through the lens of optimization. The optimization approach generalizes well to higher dimensions, but a proportional apportionment is not always possible in 3 or more dimensions. Our thesis outlines the current method for finding "approximate" apportionments and improves it in certain regimes. As for bin packing, we model the allocation of virtual machines to servers (with limited capacity) in cloud computing, with the goal of designing and analyzing efficient algorithms that optimize the expected cost of the allocation. This builds off previous work that only considered the case where the items being packed had a one-dimensional size. We extend some of those results to items with multi-dimensional size in this thesis.Undergraduat

System and Decision Sciences at IIASA 1973-1980

This report contains a brief history of the past achievements of the System and Decision Sciences Area at IIASA, and a summary of its current and future research directions. There is a comprehensive list of the scientific staff of the Area since 1973, together with a list of their publications; abstracts of the most recent reports and biographies of the scholars working in the Area in 1980 are also included

Optimization techniques for systems reliability with redundancy

Call number: LD2668 .T4 1978 K87Master of Scienc