The Complexity of Fully Proportional Representation for Single-Crossing Electorates

We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin--Courant's rule, but remains NP-hard for Monroe's rule. Our algorithm for Chamberlin--Courant's rule can be modified to work for elections with bounded single-crossing width. To circumvent the hardness result for Monroe's rule, we consider single-crossing elections that satisfy an additional constraint, namely, ones where each candidate is ranked first by at least one voter (such elections are called narcissistic). For single-crossing narcissistic elections, we provide an efficient algorithm for the egalitarian version of Monroe's rule.Comment: 23 page

Diversifying the uniform? The participation of minority ethnic personnel in the British armed services

This paper considers the pressures on the British armed services to increase the participation of minority ethnic groups and assesses recent government policy on this issue. Limited progress has been made towards the realisation of current goals, which are framed largely in terms of the concept of ‘equal opportunities’. The authors argue that while the concept of diversity appears to provide a more sociologically well founded basis for future government strategy on this aspect of service personnel policy, there remain significant obstacles to effective implementation of practical measures. These concern in particular the way in which the armed services relate to wider questions of British identity. Successfully increasing the participation of minority ethnic communities in the British armed services, we contend, entails developing a new framework for British identity and citizenship that cannot be accomplished by the armed services alone. Rather it is a responsibility of both government and wider society as a whole

Approximating the MaxCover Problem with Bounded Frequencies in FPT Time

We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N, and an integer K. The goal is to find up to K sets from S that jointly cover (i.e., include) as many elements as possible. This problem is well-known to be NP-hard and, under standard complexity-theoretic assumptions, the best possible polynomial-time approximation algorithm has approximation ratio (1 - 1/e). We first consider a variant of MaxCover with bounded element frequencies, i.e., a variant where there is a constant p such that each element belongs to at most p sets in S. For this case we show that there is an FPT approximation scheme (i.e., for each B there is a B-approximation algorithm running in FPT time) for the problem of maximizing the number of covered elements, and a randomized FPT approximation scheme for the problem of minimizing the number of elements left uncovered (we take K to be the parameter). Then, for the case where there is a constant p such that each element belongs to at least p sets from S, we show that the standard greedy approximation algorithm achieves approximation ratio exactly (1-e^{-max(pK/|S|, 1)}). We conclude by considering an unrestricted variant of MaxCover, and show approximation algorithms that run in exponential time and combine an exact algorithm with a greedy approximation. Some of our results improve currently known results for MaxVertexCover

Modelling of heat emitters embedded within third order lumped parameter building envelope model

A dynamic modelling approach for heat emitters embedded within an existing third order lumped parameter building envelope model is reported in this work. The model has been found to provide more accurate results with negligible expense of computational time compared to a conventional quasi-dynamic model. The dynamic model also is preferred over the quasi-dynamic model as it allows for modelling emitters with high thermal capacity such as under-floor heating. Recommendation for this approach is justified through a series of analyses and comparative tests for various circuit options, timesteps and control volumes

Understanding analogical reasoning : viewpoints from psychology and related disciplines

Analogy and metaphor have a long history of study in linguistics, education, philosophy and psychology. Consensus over what analogy is or how analogy functions in language and thought, however, has been elusive. This paper, the first in a two part series, examines these various research traditions, attempting to bring out major lines of agreement over the role of analogy in individual human experience. As well as being a general literature review which may be helpful for newcomers to the study of analogy, this paper attempts to extract from these literatures existing theories, models and concepts which may be interesting or useful for computational studies of analogical reasoning

Computational Aspects of Multi-Winner Approval Voting

We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show that computing the winner for proportional approval voting is NP-hard, closing a long standing open problem. As none of the rules are strategyproof, even for dichotomous preferences, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents. In many settings, we show that it is NP-hard for an agent or agents to compute how best to vote given a fixed set of approval ballots from the other agents