The paper presents modifi cation of four nonprobabilistic procedures of fair division of a set of indivisible goods with money: Original Knaster, Adjusted Knaster, Equal Shares and Second Prices. The purpose of modification is to adjust the aforementioned methods to the problem of division of a set of goods in a situation of unequal entitlements. Extended versions of six formal properties, namely: strong Pareto optimality, proportionality, envyfreeness, equitability, strategy-proofness and anonymity are also presented. Moreover,proofs of procedures having the same formal properties in a situation of unequal entitlements as in a situation of equal entitlements are shown.

The paper presents and compares four nonprobabilistic procedures of fair division of a set of indivisible goods with money: Original Knaster, Adjusted Knaster, Equal Shares and Second Prices. The last two are presented for the first time in the article. The analysis concerns the formal properties of thosemethods, namely: strong Pareto optimality, proportionality, envy-freeness, fairness, strategy-proofness and anonymity. Moreover, classes of situations inwhich those procedures meet aforementioned properties will be compared.

Social choice theory is essentially about the constraints upon effective mechanisms for implementing desirable states of a society or a group, given the preferences and utilities of its members. Social choice theory is also, and much more generally, a conceptual examination of normative theories of society – theories that characterize what it is for state of affairs to be better from the social point of view. Social choice methods have different aims, for example democratic decision-making, epistemic decision-making, respecting individual rights of persons and groups, just distribution of goods. They are justified by the sets of postulates, which represent different basic social values.

The dynamic development of experimental economics, in particular of experimental work in game theory, has contributed to the questioning of the basic assumptions of classical game theory: the rationality and self-interest assumption. In response, those assumptions are being modified and more realistic models of human behavior in situations which can be described as games are being developed. The article provides a short overview of the models that abandon the self-interest assumption. An account is given mostly of the distributional models (i.a. inequity aversion models, model of quasi-maximin preferences). The results of the experiments designed to test the rival distributional models of social preferences are also presented in the article, as well as of the experiments that assess to the role played by intention-based reciprocity in motivating human behavior.

Artykuł analizuje problem racjonowania, czyli podziału pojedynczego, jednorodnego i doskonale podzielnego dobra pomiędzy agentów o różnych cechach, zwanych typami. Jeśli typ agenta jest dodatnią liczbą rzeczywistą (interpretowaną np. jako „roszczenie” agenta), twierdzenie Younga mówi, że przy założeniu ciągłości, metoda racjonowania jest spójna i symetryczna wtedy i tylko wtedy, gdy posiada reprezentację w postaci ciągłej funkcji parametrycznej. Twierdzenie to zostało uogólnione w niniejszym artykule na wszystkie ośrodkowe przestrzenie typów. Kolejne wyniki charakteryzują wszystkie, nie tylko ciągłe, metody parametryczne oraz podają proste kryterium rozstrzygające, kiedy metoda binarna (zdefiniowana jedynie dla dwóch agentów) może być rozszerzona do spójnej metody zdefiniowanej dla dowolnej liczby agentów. Omówione jest też zastosowanie do wielowymiarowego problemu bankructwa, ilustrujące korzyści z uogólnienia twierdzenia Younga.