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 main aim of this study is to replicate the effect shown by Traczyk et al. (2018), where individuals with higher statistical numeracy, compared to individuals with lower statistical numeracy, employed a more effortful choice strategy when outcomes were meaningful. I hypothesize that participants with higher numeracy will be more likely to make choices predicted by Cumulative Prospect Theory and Expected Value theory (CPT/EV) in high-payoff problems than in low-payoff problems. Data collection was done online by appointing 73 participants. Participants’ preference, fluid intelligence, objective and subjective numeracy were measured using thirteen high and eleven low payoff choice problems, International Cognitive Ability Resource (ICAR), Berlin Numeracy Test (BNT), and Subjective Numeracy Scale (SNS), respectively. All the measures mentioned above were presented randomly. Results showed that all participants, in high-payoff condition, on average maximized EV; however, participants with high BNT scores were more likely to make choices consistent with CPT/EV predictions than individuals with low BNT scores. Furthermore, compared to less numerate participants, highly numerate participants were less likely to make choices consistent with CPT/EV predictions in low-payoff condition. Highly numerate individuals
adjusted their choice strategy by modulating their response time, indicating
their discernible sensitivity towards large asymmetry in payoff. In conclusion, the effect shown by Traczyk et al. (2018) was successfully replicated.

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.

The paper starts with the defi nitions of fi ve major voting methods that can be applied in single-member districts. Then the political consequences of single-member districts are discussed. The special attention is paid to those consequences that are considered negative and to potential ways of neutralizing them. The next section compares selected subtle effects of using simple majority rule versus alternative vote. The fi nal section reviews methods that mix proportional representation and majoritarian components.

The aim of the paper is to analyse group characteristic related to the problem of bullying, from a game-theoretical perspective. Bullying is a specific type of violence that happens in schools and it is a group phenomenon. The behaviour of bystanders can either encourage or discourage potential bullies. The paper presents a game-theoretical model of bystanders’ behaviour. It is assumed that bystanders feel morally obliged to defend the victim (internalised norm) but they also want to conform (conformity). In order to analyse the factors that can infl uence the scope of group reaction, a structurally embedded sequential coordination game was played for different initial conditions. Computer
simulations were conducted for networks of a specifi c type (Erdős–Rényi random graph). The main aim of analyses was to identify structural features of the group that can enable or block the intervention of bystanders. There is a non-linear relationship between network density and the scope of reaction. Both low and high density can make it harder for the bystanders to oppose the bully. Interactions between structural and non-structural features of the group have been observed. Depending on the strength of the internalized norm and conformity level, different structural characteristics may improve or lower the
chances of group intervention. As far as non-structural group characteristics are concerned, there is a positive relationship between the scope of group reaction and the strength of the internalized norm, whereas the level of conformity affects the chances of group intervention in a negative way.

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.

The presented research shows that consumer choice of product depends on the sequence in which products are presented. When they were presented according to decreasing prices the customer chose more expensive products than in the case of increasing prices. However this happens only in case of paying cash not voucher. In order to rule out the alternative reasons of this effect another study was conducted. Participants of the second study were randomly acquainted with 10 product brands. Then they chose one of ten products which were sorted according to their prices: decreasing or increasing.
Again, when paying cash, participants chose more expensive products when they were sorted according to decreasing prices. The results of second research suggest that the presented differences in choosing products cannot be explained by anchoring heuristic, the effect of priority, or incomplete information processing.

In fair distribution of a set of indivisible goods it is problematic to provide basic equality if the goods differ in value. One of the most popular solutions to the problems are lotteries. The paper presents seven selected probabilistic procedures: random distribution, lexicographic procedure of equal chances of satisfaction, random serial dictatorship, core from random endowments, probabilistic serial, top trading cycles from equal division and
random priority with infi nite k factor. Some of these procedures always lead to the
same result as some other procedure, therefore these procedures are equivalent. The formal features of the procedures are also analysed in the paper: ordinal efficiency, ex post efficiency, and both strong and week version of: envy-freeness, proportionality, equitability, and individual strategy-proofness.

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.

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.

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.