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This survey deals with two-sided matching markets where one set of agents (workers/residents) has to be matched with another set of agents (firms/hospitals). We first give a short overview of a selection of classical results. Then, we review recent contributions to a complex and representative case of matching with complementarities, namely matching markets with couples. We discuss contributions from computer scientists, economists, and game theorists. © 2013 World Scientific Publishing Company. ; P. Biró gratefully acknowledges financial support from OTKA grant K69027 and the Hungarian Academy of Sciences under its Momentum Programme (LD-004/2010). F. Klijn gratefully acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through Plan Nacional I+D+i (ECO2011–29847), the Government of Catalonia (SGR2009–01142) and the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075) ; Peer Reviewed

To ensure equal representation, the voting districts of a country must be more or less of the same size. Designing such voting districts, however, is not an easy task due to the fact that voting districts are encompassed in administrative regions. Since the respective share of an administrative region, i.e.\ the number of seats its entitled to based on its population, is not necessarily an integer number, it is hard to distribute the seats in a fair way. The arising fair distribution problem is called the apportionment problem. Proportionality of the allocation is the most important, but not the only factor of a fair solution. Monotonicity related difficulties, administrative and demographic issues make the problem more complex. We provide an overview of the classical apportionment methods as well as the Leximin Method - a new apportionment technique designed to comply with the recommendation made by the Venice Commission. We discuss the properties of apportionments and test the most prominent methods on real data.

One of the aims of the new electoral law of Hungary has been to define a fairer apportionment into voting districts. This is ensured by a set of rules slightly more premissive than those laid out in the Code of Good Practice in Electoral Matters of the Venice Commission. These rules fix the average size of the voting districts, require voting districts not to split smaller towns and villages and not to cross county borders. We show that such an apportionment is mathematically impossible. We make suggestions both to the theoretical approach to resolve this problem, study the properties of our approach and using our efficient algorithm and the data of the 2010 national elections we determine the optimal apportionment. We also study the expected effect of demographic changes and formulate recommendations to adhere to the rules over the long term: increase the number of voting districts to about 130, allow the number of voting districts to change flexibly at each revision of the districts and base the districts on regions rather than counties.

AbstractIn this paper we present simulations for international kidney exchange programmes (KEPs). KEPs are organised in more than ten countries in Europe to facilitate the exchanges of immunologically incompatible donors. The matching runs are typically conducted in every three months for finding optimal exchanges using hierarchical optimisation with integer programming techniques. In recent years several European countries started to organise international exchanges using different collaboration policies. In this paper we conduct simulations for estimating the benefits of such collaborations with a simulator developed by the team of the ENCKEP COST Action. We conduct our simulations on generated datasets mimicking the practice of the three largest KEPs in Europe, the UK, Spanish and the Dutch programmes. Our main performance measure is the number of transplants compared to the number of registrations to the KEP pools over a 5-year period, however, as a novelty we also analyse how the optimisation criteria play a role in the lexicographic and weighted optimisation policies for these countries. Besides analysing the performances on a single instance, we also conduct large number of simulations to obtain robust findings on the performance of specific national programmes and on the possible benefits of international collaborations.

Many countries have secured larger quantities of COVID-19 vaccines than their populace is willing to take. This abundance and variety of vaccines created a historical moment to understand vaccine hesitancy better. Never before were more types of vaccines available for an illness and the intensity of vaccine-related public discourse is unprecedented. Yet, the heterogeneity of hesitancy by vaccine types in certain segments of society has been neglected so far, even though factual or believed vaccine characteristics and patient attributes are known to influence acceptance. In this paper, we address this problem by analysing acceptance and assessment of five vaccine types using information collected with a nationally representative survey (N=1000) at the end of the third wave of the COVID-19 pandemic in Hungary, where a unique portfolio of vaccines were available to the public in large quantities. Our special case enables us to quantify revealed preferences across vaccine types since one could evaluate a vaccine unacceptable and even could reject an assigned vaccine to wait for another type. We find that the source of information that respondents trust characterizes their attitudes towards vaccine types differently and leads to divergent vaccine hesitancy. Believers of conspiracy theories were significantly more likely to evaluate the mRNA vaccines (Pfizer and Moderna) unacceptable while those who follow the advice of politicians evaluate vector-based (AstraZeneca and Sputnik) or whole-virus vaccines (Sinopharm) acceptable with higher likelihood. We illustrate that the rejection of non-desired and re-selection of preferred vaccines fragments the population by the mRNA versus other type of vaccines while it generally improves the assessment of the received vaccine. These results highlight that greater variance of available vaccine types and individual free choice are desirable conditions that can widen the acceptance of vaccines in societies.