The article examines the impact of nine counterfactual modifications to the Polish elector-al system on the results of the Sejm elections held on October 15, 2023. Scenarios analyzed include various methods of demographic seat adjustments, redistribution of overseas votes, changes to proportionality methods (D’Hondt vs. Sainte-Laguë), and changing the number of electoral districts. The issue of how deeper changes to the system may affect the strategic behavior of parties and voters is also analyzed. Results indicate that while each modification slightly alters seat distribution among parties, most changes do not significantly affect the overall balance of power in the Sejm.

This paper presents a theoretical and empirical analysis of the electoral process within Open-List Proportional Representation (OLPR) systems and introduces the 5R model (Reelection, Reanimation, Rise, Reattempt, Rookie) for examining career paths, access rules, and elite cir-culation in OLPR contexts. The theoretical section breaks down the electoral process into five stages: from candidate auto-selection, through pre-selection and list hierarchization by party leaders, to gaining votes and seat allocation. A particular emphasis is placed on differ-ences in politicians’ career paths and the strategies party leaders employ in list construction. The empirical analysis demonstrates the impact of the OLPR system on different types of parties and candidates, showing how both party structures and candidates’ career paths are influenced by this system. The study utilizes an extensive dataset of official electoral results spanning 20 years of Polish democratic elections (1990–2019), covering both general and local elections, with strong internal comparability. Thus, based on these findings, the paper intro-duces the 5R model, which can serve as a framework to interpret elite circulation, political career paths, and access rules in OLPR systems. This model serves as a foundation for future research on candidate demographics, particularly gender, age, and territorial representation.

The primacy effect has long been considered a decisive factor in determining election outcomes and has consequently developed a robust literature dedicated to studying it in different scenarios and contexts. However, existing research has offered limited insight into how the choice of voting method, particularly by-mail voting, may infl uence its impact on elections by altering how and when voters participate. This article fi rst reviews why the primacy effect exists, how researchers identify its infl uence, and its overall impact on election outcomes. It then discusses why the use of by-mail voting
should be expected to alter the primacy effect, and analyzes two works where this relationship has been explored. Their results highlight several of the issues faced when trying to examine this relationship, but also indicate that further study is warranted and likely to be fruitful.

The paper presents some consequences of using semi-open lists, including the preferential vote mechanism, in parliamentary elections in Poland. The Authors discuss whose role in assigning parliamentary seats is greater: that of party organizations’ leaders, who decide on the order of candidates on electoral lists, or that of citizens who cast preferential votes. The paper focuses in the elections in the years 2001–2011, in which, according to poll data, party voting dominated over personal voting. The results of parliamentary elections in Poland show that ballot position effects are persistently present and that people tend to vote for list leaders in their constituencies. However, a simulation of a closed-list mechanism shows that in 2001–2011, ca 20 per cent of parliamentary seats were assigned as a result of the interventionist impact of the preferential vote on the
candidate lists established by parties. The ability to vote for a specifi c candidate is rather important for Poles. The Authors also point out that the candidates from the top of party lists may obtain such good results because voters resort to simple reasoning and vote for those from the top of a list, irrespective of the nature of the list itself. (However, the effect does not seem to be very signifi cant).

: Traditional studies on political consequences of electoral systems were recognising electoral formula as the most important variable responsible for the consequences generated by a given electoral system. Meanwhile, recent studies suggest that the impact of this variable is defi nitely overrated. The article shows how the number of seats won in electoral districts affects the political parties and their candidates' chances of winning both in the proportional representation voting systems as well as in the majority and plurality ones. Using the examples of Polish parliamentary elections, the present paper both examines the thesis according to which larger electoral districts always increase proportionality and identifi es the conditions under which the thesis finds its application.

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.

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.