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 text supplements the article by S. Linder and contains information about research on the primacy effect in Poland. The subject of J. Raciborski’s analyzes were elections to national councils (local government bodies) in 1988 – the last elections before the fall of communism in Poland, elections to the Sejm in 1989 and 1991. T. Żółtak investigated the existence of the primacy effect in the elections to the Senate in 1991-2007. However, the primacy effect in the 2014 regional elections was of greatest political importance. The
strength of this effect was measured by J. Flis. Analyzes were also carried out on the effect of a candidate’s position on the party semi-open list in proportional elections. However, this is a completely different issue, as in this case the position on the list is related to the actual political weight of the candidate. In Poland, the relationship of the primacy effect with postal elections has never been studied, which results from the marginal importance of the latter, as well as the procedures used in elections, which prevent a separate analysis of the content of votes cast by post and at the polling station.

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.

Before the parliamentary elections in 2018, the ruling party in Turkey, AKP, introduced a new apparentement provision in the electoral law, which allowed parties to make electoral alliances in order to meet the electoral threshold. We claim that this was an ex post mistake. AKP’s electoral engineering was motivated by their fear that its coalition partner, MHP, would not exceed the 10% threshold. While MHP actually met the threshold in the election, the opposition party, İP, failed to do so. Thanks to the new law, the votes for İP were not wasted, as would have happened under the old law. AKP less than 50% of seats and it consequently lost the parliamentary majority. Under the old electoral law, AKP would have won the majority. We use four alternative scenarios in order to estimate the seats and evaluate the political consequences of the unsuccessful electoral manipulation

This paper proposes a correction to the Flis-Słomczyński-Stolicki (2019, 2020) formula for countries with large variation among their districts in terms of political divisions. The Flis-Słomczyński-Stolicki formula (FSS formula) estimates seat allocations under the Jefferson-D’Hondt method by using national vote shares, as well as other parameters that are often readily available. However, the FSS formula does not yield precise estimates in those countries where there are independent candidates, special rights assigned to minority parties, signifi cant variation in district sizes, or an unequal distribution of votes due to ethnic or other regional divisions. Hence, I propose dividing the national distribution of votes into regions that satisfy the assumptions of the FSS formula within their district borders. By applying the FSS formula to regions consisting of historically and politically homogenous districts, I demonstrate that the formula’s estimates become signifi cantly more precise. For instance, by applying the regional correction to the 2018 Turkish Parliamentary elections, as well as other Turkish elections between 2007 and 2015, I show that the formula with the correction in three separate regions improves the Loosemore-Hanby goodness of fi t estimates from 2.1 to 3.41 percentage points (95% CI). Thus, the correction might signifi cantly improve the estimates of the FSS formula in various countries, including Spain, Peru, and Belgium.

Why do political actors pass legislation that seemingly hurts them? Lustration laws limit access to public offi ce of the ancien regime's collaborators and hurt members of post-communist parties in East-Central Europe. So why has lustration in Poland, Hungary, and Bulgaria been passed when post-communist parties held parliamentary majorities? Why did the postcommunist party in Romania switch from no-lustration to pro-lustration after the 1992 elections? We explain this phenomenon by electoral timing and rules of rocedure in legislatures. Specifi cally, we develop an agenda-setter model with a finite number of parties, imperfect information, and multiple potential medians. Our main argument can be summarized as follows: Suppose that the Postcommunists do not introduce any lustration bill and then lose proposal power in elections. If Anti-communists come to power, they are sure to introduce a harsher bill, and the median of the legislature may prefer such a bill to a no-bill status quo. Post-communists can prevent such a scenario by implementing a mild bill themselves. If they manage to appease the new parliamentary median, they will block a harsher bill that would be implemented after they lose power. Additional results show how electoral perspectives and uncertainty affect and modify this typical scenario. We test our model with an exhaustive analysis of all cases from East- Central Europe that meet our assumptions that a Postcommunist party is in power and no lustration bill is already in force.

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.

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.

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.

The way in which an electoral system influences the party system is a salient topic discussed in political science and social choice theory. Researches in post-communist countries have so far usually been analyses of the isolated cases of the elections. Here all free parliamentary elections in this region are examined. It allows measuring the total effect of the electoral system on the party system. It was found that the consequences of some electoral institutions are different than observed in old democracies: single-member districts with majority rule may cause considerable parliament fragmentation and the consequences of mixed systems are heterogeneous and depending on their inner mechanics. It was also found that the form of the party system depends to a greater degree on the properties of the political scene than on the electoral system.

Each of the EU enlargements raised problem of new apportionment of EP seats among EU member states. Each time solution was found in the process of multilateral negotiations, but since 1970s postulates to replace repeated negotiations by impartial mathematical formula have been raised, based on some concept of ”degressive proportionality”. When in 2007 EP started works on new apportionment before 2009 elections, one of the proposed solutions was ”parabolic method” of V. Ramirez, but in October 2007 EP again accepted allotment of seats not based on a mathematical formula, on the ground that ”apportionment is a political issue and can not be solved only on the mathematical base”. The paper presents the new proposal of degressively proportional apportionment method ua. The ua method leaves to the politicians decision about strength of the degressiveness of proportionality, but after this is politically accepted, the apportionment is based only on an of impartial mathematical formula.