Optimal redistricting under geographical constraints: Why "pack and crack" does not work

We show that optimal partisan redistricting with geographical constraints is a computationally intractable (NP-complete) problem. In particular, even when voter's preferences are deterministic, a solution is generally not obtained by concentrating opponent's supporters in \unwinnable" districts ("packing") and spreading one's own supporters evenly among the other districts in order to produce many slight marginal wins ("cracking").

Vertikális korlátozások - növelik vagy csökkentik a jólétet? Érvek az irodalomból = Vertical constraints - do they increase or reduce welfare? Arguments in the literature

A vertikális korlátozások témaköre a versenypolitika és -szabályozás egyik legfontosabb, de mindenképpen legtöbb vitát generáló területe. A téma magyar irodalma elsősorban elméleti kérdésekkel foglalkozik, mellőzve a konkrét iránymutatásokat a probléma kezelésére. Először röviden bemutatjuk a vertikális korlátozások indokait és hatásmechanizmusát magyarázó teoretikus irodalmat, felsorolva azok hatékonyságnövelő hatását hangsúlyozó érvrendszereket, illetve a versenykorlátozás lehetőségét tárgyaló modelleket is. Ezután bemutatjuk, hogy milyen fontos empirikus vizsgálatokat végeztek ezen elméletek vizsgálatára, és milyen következtetések vonhatóak le a tapasztalatokból. _________ The field of vertical constraints is one of the most important in competition policy and regulation, but one that generates the most debate. Hungarian literature on the subject deals primarily with theoretical questions, refraining from offering specific guidelines for handling the problem. The paper first covers briefly the causes of the vertical constraints and the Hungarian theoretical literature on its effective mechanism, listing the system of arguments that point to its effect of increasing efficiency and the models that discuss the possibility of limiting competition. The paper then presents the major empirical examinations made of these theories and the conclusions drawn from that experience.

Páros összehasonlításon alapuló pontozási eljárások monotonitása: önkonzisztencia és önkonzisztens monotonitás. Adalékok a pontozási eljárások axiomatikus tárgyalásához = Monotonicity of paired comparison-based ranking methods: self-consistency and self-consistent monotonicity. Contributions to an axiomatic analysis of scoring methods

A cikk a páros összehasonlításokon alapuló pontozási eljárásokat tárgyalja axiomatikus megközelítésben. A szakirodalomban számos értékelő függvényt javasoltak erre a célra, néhány karakterizációs eredmény is ismert. Ennek ellenére a megfelelő módszer kiválasztása nem egy-szerű feladat, a különböző tulajdonságok bevezetése elsősorban ebben nyújthat segítséget. Itt az összehasonlított objektumok teljesítményén érvényesülő monotonitást tárgyaljuk az önkonzisztencia és önkonzisztens monotonitás axiómákból kiindulva. Bemutatásra kerülnek lehetséges gyengítéseik és kiterjesztéseik, illetve egy, az irreleváns összehasonlításoktól való függetlenséggel kapcsolatos lehetetlenségi tétel is. A tulajdonságok teljesülését három eljárásra, a klasszikus pontszám eljárásra, az ezt továbbfejlesztő általánosított sorösszegre és a legkisebb négyzetek módszerére vizsgáljuk meg, melyek mindegyike egy lineáris egyenletrendszer megoldásaként számítható. A kapott eredmények új szempontokkal gazdagítják a pontozási eljárás megválasztásának kérdését. _____ The paper provides an axiomatic analysis of some scoring procedures based on paired comparisons. Several methods have been proposed for these generalized tournaments, some of them have been also characterized by a set of properties. The choice of an appropriate method is supported by a discussion of their theoretical properties. In the paper we focus on the connections of self-consistency and self-consistent-monotonicity, two axioms based on the comparisons of object's performance. The contradiction of self-consistency and independence of irrel-evant matches is revealed, as well as some possible reductions and extensions of these properties. Their satisfiability is examined through three scoring procedures, the score, generalised row sum and least squares methods, each of them is calculated as a solution of a system of linear equations. Our results contribute to the problem of finding a proper paired comparison based scoring method.

Properties of risk capital allocation methods: Core Compatibility, Equal Treatment Property and Strong Monotonicity

In finance risk capital allocation raises important questions both from theoretical and practical points of view. How to share risk of a portfolio among its subportfolios? How to reserve capital in order to hedge existing risk and how to assign this to different business units? We use an axiomatic approach to examine risk capital allocation, that is we call for fundamental properties of the methods. Our starting point is Csóka and Pintér (2011) who show by generalizing Young (1985)'s axiomatization of the Shapley value that the requirements of Core Compatibility, Equal Treatment Property and Strong Monotonicity are irreconcilable given that risk is quantified by a coherent measure of risk. In this paper we look at these requirements using analytic and simulations tools. We examine allocation methods used in practice and also ones which are theoretically interesting. Our main result is that the problem raised by Csóka and Pintér (2011) is indeed relevant in practical applications, that is it is not only a theoretical problem. We also believe that through the characterizations of the examined methods our paper can serve as a useful guide for practitioners.

Hedging under liquidity constraints

Although risk management can be justified by financial distress, the theoretical models usually contain hedging instruments free of funding risk. In practice, management of the counterparty risk in derivative transactions is of enhanced importance, consequently not only is trading on exchanges subject to the presence of a margin account, but also in bilateral (OTC) agreements parties will require margins or collateral from their partners in order to hedge the mark-tomarket loss of the transaction. The aim of this paper is to present and compare two models where the financing need of the hedging instrument also appears, influencing the hedging strategy and the optimal hedging ratio. Both models contain the same source of risk and optimisation criterion, but the liquidity risk is modelled in different ways. In the first model, there is no additional financing resource that can be used to finance the margin account in case of a margin call, which entails the risk of liquidation of the hedging position. In the second model, the financing is available but a given credit spread is to be paid for this, so hedging can become costly.