Nicola Maaser

Equal representation in two-tier voting systems

The paper investigates how voting weights should be assigned to differently sized constituencies of an assembly. The one-person, one-vote principle is interpreted as calling for a priori equal indirect influence on decisions. The latter are elements of a one-dimensional convex policy space and may result from strategic behavior consistent with the median voter theorem. Numerous artificial constituency configurations, the EU and the US are investigated by Monte–Carlo simulations. Penrose’s square root rule, which originally applies to preference-free dichotomous decision environments and holds only under very specific conditions, comes close to ensuring equal representation. It is thus more robust than previously suggested.

On the Democratic Weights of Nations

Which voting weights ought to be allocated to single delegates of differently sized groups from a democratic fairness perspective? We operationalize the one person, one vote principle by demanding every individual’s influence on collective decisions to be equal a priori. The analysis differs from previous ones by considering intervals of alternatives. New reasons lead to an old conclusion: weights should be proportional to the square root of constituency sizes if voter preferences are independent and identically distributed. This finding is fragile, however, in that preference polarization along constituency lines quickly calls for plain proportionality.

A note on the direct democracy deficit in two-tier voting

A large population of voters with single-peaked preferences are partitioned into disjoint constituencies. Collective decisions are taken by their representatives, one from each constituency, according to a weighted voting rule. It is assumed that each representative’s ideal point perfectly matches that of the respective constituency median and that top-tier decisions are in the voting game’s core. The resulting representative-democratic voting outcomes generally differ from those of a direct-democratic, single-tier system. The expected discrepancy varies with the voting weight allocation. It is minimized by weights proportional to constituency population sizes only if citizens differ sufficiently more between than within constituencies. Weights proportional to the square root of population sizes perform better if all citizens have independent and identically distributed ideal points.

The Mean Voter, the Median Voter, and Welfare-Maximizing Voting Weights

Representatives from differently sized constituencies take political decisions by a weighted voting rule and adopt the ideal point of the weighted median amongst them. Preferences of each representative are supposed to coincide with the constituency’s median voter. The paper investigates how each constituency’s population size should be mapped to a voting weight for its delegate when the objective is to maximize the total expected utility generated by the collective decisions. Depending on the considered utility functions, this is equivalent to approximating the sample mean or median voter of the population by a weighted median of sub-sample medians. Monte Carlo simulations indicate that utilitarian welfare is maximized by a square root rule if the ideal points of voters are all independent and identically distributed. However, if citizens are risk-neutral and their preferences are sufficiently positively correlated within constituencies, i.e., if heterogeneity between constituencies dominates heterogeneity within, then a linear rule performs better.

Mostly sunny : a forecast of tomorrow's power index research

Power index research has been a very active field in the last decades. Will this continue or are all the important questions solved? We argue that there are still many opportunities to conduct useful research with and on power indices. Positive and normative questions keep calling for theoretical and empirical attention. Technical and technological improvements are likely to boost applicability.

Power illusion in coalitional bargaining: An experimental analysis

In real world bargaining the distribution of seats or voting weights often does not accurately reflect real power. Game-theory predictions are insensitive to nominal differences. We refer to the converse idea that nominal differences matter as power illusion. We experimentally study the Baron-Ferejohn model with variation in nominal power. We find strong evidence for the existence of power illusion. Thus, attention needs to be paid to nominal power in the design of weighted voting systems.

Codecision in context: implications for the balance of power in the EU

The paper analyzes the European Union’s codecision procedure as a bargaining game between the Council of the European Union and the European Parliament. The relative influence of these institutions on legislative decision-making in the EU is assessed under a priori preference assumptions. In contrast to previous studies, we do not consider the codecision procedure in isolation but include several aspects of the EU’s wider institutional framework. The finding that the Council is more influential than the Parliament due to its more conservative internal decision rule is robust to adding ‘context’ to the basic model, but the imbalance is considerably attenuated.

Fair Representation and a Linear Shapley Rule

When delegations to an assembly or council represent differently sized constituencies, they are often allocated voting weights which increase in population numbers (EU Council, US Electoral College, etc.). The Penrose square root rule (PSRR) is the main benchmark for fair representation of all bottom-tier voters in the top-tier decision making body, but rests on the restrictive assumption of independent binary decisions. We consider intervals of alternatives with single-peaked preferences instead, and presume positive correlation of local voters. This calls for a replacement of the PSRR by a linear Shapley rule: representation is fair if the Shapley value of the delegates is proportional to their constituency sizes.

Games and Political Decisions

This chapter provides an introduction to some fundamental aspects of decision-making in committees. ‘Committee’ is used to refer to a decision-making body that comprises a small number of members (as opposed to a referendum situation), and chooses from a set of well-defined policy alternatives (in contrast to the electorate in a general election which usually chooses between candidates or party platforms). Decisions are ultimately reached by putting alternatives to a vote according to some voting rule specifying which subsets of all committee members can pass a proposal. This notion of a committee differs from everyday language where the term also applies to expert panels with advisory function, or organizational subunits that make recommendations or submit proposals to some superordinate organization.

Robust Equal Representation

This chapter investigates the robustness of square root rules for equal representation in two-tiered voting systems. When policy alternatives are non-binary and decisions are made by simple majority rule, Chap. 2 demonstrated that weight proportional to the square root of population size is approximately optimal, which may be interpreted as extending the scope of Penrose’s square root rule beyond the narrow limits of binary decision-making. However, in light of the normative character of this result, the simplifications used in the modeling of a complex real situation, such as, e.g., decision-making in the EU Council of Ministers, require special scrutiny.