The article proposes a new type of statistical dependence. Statistical independence of this type means the identity of the frequency order of category choices in all groups. The compatibility between choices will be assessed by means of a diversity measure. A new measure of statistical dependence, its properties and interpretation will be specifi ed.

Debate regarding evidence based medicine in current state focuses on basic philosophical as-sumptions of paradigm announced in 1992 by EBM Working Group. One of the topic in this debate is clinical reasoning in light of medical decision-making. Polish literature still lacks of comprehensive presentation in this theoretical fi eld. In current article I present overview of models of clinical reasoning. I begin from the debate of rationality distinguishing two positions called meliorism and panglosianism. Next I proceed to elaboration of three models for clinical reasoning in context of meliorists position. It gives an opportunity to look closer for inferential rules of clinical decision-making and as a result may be precious perspective for future re-search and medical education.

The aim of this paper is to investigate the fi rms’ incentives to engage in process R&D under vertical industrial setting, when the raising rivals’ cost effect is present. We show that R&D investment of the downstream duopoly fi rm raises the rival’s marginal costs of production. The downstream R&D behavior can give rise to the symmetric investment games, i.e., the prisoner’s dilemma, the deadlock game and the harmony game, between downstream competitors. If the costs of the R&D investments made by the downstream fi rms are large enough, the downstream fi rms can participate in the harmony game, which results in the investment hold-up or the creation of the R&D-avoiding cartel. For more R&D-effi cient downstream fi rms, the downstream investment game can end up in the prisoner’s dilemma or the deadlock game. In the prisoner’s dilemma, both downstream fi rms invest in R&D, but such a behavior is not Pareto optimal. In the prisoner’s dilemma, greed and fear make fi rms invest in R&D. In the deadlock game, both downstream fi rms invest in R&D, and such a behavior is Pareto optimal. The R&D investments are not induced by any social tension (greed or fear).

Gerrymandering is a form of voting manipulation whereby electoral district boundaries are drawn to produce a partisan or political bias in elections. In this paper, we study partisan gerrymandering in the United States to understand its undemocratic outcomes and how the design of election institutions can promote or prevent gerrymandering. We begin with a survey of the history of gerrymandering, with a particular focus on partisan
gerrymandering. We then consider the normative standards of fairness in democracy that partisan gerrymandering may violate. Next, we present a typology of partisan gerrymandering based upon the district maps drawn in California, Pennsylvania, Massachusetts, and New Jersey for the 2012 elections. Using the partisan symmetry method, we estimate the seats/votes curves of the congressional maps used in 38 states during the 2012 elections. We find that partisan gerrymanders occur almost exclusively when politicians are given control over redistricting. This analysis implies that a political
designer, who wants to minimize gerrymandering, should not put redistricting in the hands of politicians.

We propose a simple yet new formula for estimating national seat shares and quantifying seat biases in elections employing the Jefferson-D’Hondt (JDH) method for seat allocation. It is based solely on the national vote shares and fi xed parameters of the given electoral system. The proposed formula clarifi es the relationship between seat bias on the one hand, and the number of parties and the number of districts on the other. We demonstrate that the formula provides a good estimate of seat allocations in real-life elections even in the case of minor violations of the underlying assumptions. With that aim in mind, we have tested it for all nine EU countries that employ the JDH method in
parliamentary elections. Moreover, we discuss the applications of the formula for modeling the effects of vote swings, coalition formation and breakup, spoiler effects, electoral engineering, artifi cial thresholds and political gerrymandering. By not requiring district-level vote shares, our formula simplifi es electoral simulations using the JDH method.

Winning a championship is the highest achievement in Formula 1, and multiple titles can earn one a place in the pantheon of the sport. In this article I explore whether the scoring method for selecting a champion can be considered defi nitive, and how unstable results might be when the method’s parameters are slightly changed. I have employed case studies of paradoxes and historical recreations of seasons using alternative scoring systems. Finally, I argue that the Borda count is desirable system for scoring in Formula 1,
and that building strategies by teams around particular scoring systems is a legitimate aspect of the sport.

In this article we attempt to summarize the fi ndings from a number of studies on the asymmetric dominance effect (attraction effect, decoy effect). This is a phenomenon where popularity of one of the decision alternatives increases when accompanied by a similar but inferior (dominated) option. Scientifi c research and numerous observational studies show that the attraction effect occurs in various fi elds, incl. the economy, politics, law or medicine. In the literature there are many ambiguities and contradictory theories about, for example, its determinants in the light of the dual-systems theory. It is not ntirely clear whether the phenomenon of asymmetric domination is the result of a refl ective, deliberative way of information processing or of quick and intuitive thinking. There is also no unequivocal answer to the question whether this effect is a manifestation of human irrationality or whether it is an adaptive and effective decision-making strategy in conditions of uncertainty and information noise. The article contains a broad overview of research on the effect of asymmetric dominance among people and animals. The hanges in the susceptibility to this effect across the lifespan are analysed. Finally, the paper discusses using the asymmetric dominance effect to achieve socially desirable goals as described in the theory of libertarian paternalism.

In the Polish public debate, one occasionally hears voices advocating the need for a significant change in the system of elections to Sejm, the Lower Chamber of Parliament – the objective of such changes would be to strengthen larger parties. As an example to follow, proponents of these changes cite Hungary, where the changes in electoral rules allowed the party in power to retain majority in the legislative despite reduction in popular support. Opponents of this solution see it as a manifest electoral manipulation. The aim of the present paper is to analyze how the “marginal only” changes to the structure of constituencies electing members of Sejm postulated in the political arena would affect electoral results of individual political groups and what would be the broader political consequences. The author pays particular attention to expected impact of such changes on the majority bonus for the winning party, possible government coalition variants, concentration of party system at parliamentary level and proportionality of elections. Simulation of allocation of seats in Sejm based on votes cast was prepared for three possible variants of the structure of Sejm constituencies, on the basis of historical data (for the 2011 and 2015 elections) and the predicted results of 2019 elections. Comparison of the simulated outcomes with the results obtained in the system currently in place allows to answer the main question posed.

This paper presents the results of two studies analysing the impact of procedural fairness and a sense of alienation on real tax payments in the public goods game. Study 1 showed that an unfair procedure of determining the rules of the game increases the frequency of tax evasion. In Study 2, tax evasion was associated with a sense of alienation induced in the subjects, understood as a conviction about the ineffectiveness of one’s own actions. The results of the studies presented in this paper indicate the importance of the treatment of taxpayers by the tax system as a factor infl uencing the propensity for tax fraud.

The purpose of the article is to provide a comparative analysis of two types of randomization – egalitarian and proportional – in distributive decisions, with a view to determining conditions in which they can be applied. It is argued in the article that justice reasons in favour of egalitarian randomization should be construed broadly (as embracing not only the situation of indifference – the equal satisfaction of a given criterion, but also the situations of the lack of criteria or their incommensurability), and that they are stronger than utilitarian reasons. It is also argued that the confl ict between justice ex ante and justice ex post may take an acute form only in the case of proportional randomization, which is why this type of randomization can be applied relatively rarely – only in two situations: if the distribution is repeatedly made and/or if the differences
between claims of the candidates (for a good/burden being distributed) are not substantial. Some other differences are also pointed out in the article, e.g., that while proportional randomization must always be statistical, egalitarian randomization may be at times epistemic. It is also argued that in some circumstances (e.g., in the context of the so called Number Problem) doubts may arise as to which type of randomization should be applied, and the applications of both types may prove to be equivalent.

The paper is devoted to the topic of strategic grading, which is a term that describes situations in which a judge acquires his preferred result by giving a dishonest opinion. The initial issues concern searching for the possibility of supplementing the rules of etermining the verdict of the Scottish jury in a way that prevents jurors from manipulating it and strategic grading in the context of a system of artifi cial majority used in Polish courts of criminal justice. As it is shown, the Polish system is immune to the strategic behaviour of the judges. Article puts forward a new model of grading systems which generalizes the model constructed by Balinski & Laraki, and is similar to the classical model of Moulin. The new model is based on the assumption that for any given grades
one should be able to determine how close they are. An utterly new defi nition of strategic grading is given, and the article explains why it is needed. The main goal of the article is to give a characterization of grade aggregation functions which, in the new model, are immune to the strategic grading. On the basis of the proof by Balinski and Laraki, it is shown that order functions meet this criterion. Moreover, it is proven that under some additional assumptions they are the only type of such functions.