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In a democratic proportional election system, it is vital that the mandates in the parliament are allocated as proportionally as possible to the number of votes the parties got in the election. We formulate an optimization model for allocation of seats in a parliament so as to minimize the disproportionality. By applying separable programming techniques, we obtain an easily solvable problem, and present a method for solving it optimally. The obtained solution is the feasible solution that has the minimal disproportionality (with the measure chosen), even in the presence of a parliament threshold, which is not always the case for the practical procedures used in many countries. We apply the approach to real life data from the last three elections in Sweden, and show that the result is better, i.e. more proportional, than what was obtained with the modified Sainte-Laguë method, which is presently used. A natural suggestion would be to use our method instead. We also consider the issue about constituencies, and suggest a procedure, based on the same kind of optimization problem, for allocating mandates in the constituencies, without changing the overall allocation with respect to parties. The numbers of mandates for the constituencies are based on the number of votes given, not on estimated numbers of inhabitants entitled to vote. This removes the need for compensatory mandates, and makes the question about sizes of the constituencies less important.

We introduce a model with strategic voting in a parliamentary election with proportional representation and uncertainty about voters' preferences. In any equilibrium of the model, most voters only vote for those parties whose positions are extreme. In the resulting parliament, a consensus government forms and the policy maximizing the sum of utilities of the members of the government is implemented.

I consider the decision of a parliament that might change the electoral system for the forthcoming elections from plurality rule to proportional representation. Parties are office-motivated. They care about winning and about the share of seats obtained. I consider two di¤erent scenarios of how parties in the government share the spoils of office: Equally or proportionally to their share of seats. If the government is formed by a single party and parties expect that each party will obtain the same share of votes in the next election the electoral rule will never be changed. That is, for a change to occur the government should be formed by a coalition. I ?nd that a change is more likely to occur when the number of parties is larger and also when the spoils of o¢ ce are shared equally among the members in the governing coalition. I extend these results to analyze the decision of a change from a less proportional rule to a more proportional one.

This article shows that for a single-vote electoral system for a representative body to treat all voters and all parties equally, it must produce results essentially identical to list proportional representation (PR). Democratic theory has often been agnostic concerning representative institutions. Different institutions have been compared in terms of behavioral outcomes rather than axiomatic properties. Building on van der Hout (Annual meeting of the Public Choice Society, San Diego, 2002) result, we show that for an electoral system to completely respect the principle of liberal political equality and popular sovereignty, its results must be equivalent to those of list PR.

There has been a longstanding debate about the link between political representation and health. In this article, I provide novel evidence that electoral reforms that shifted from a majoritarian to a proportional system of voter representation generated substantive health benefits for the general population. Using the exemplary case of Switzerland, I first show that the spread of proportional representation between 1890 and 1950 increased political participation and gave the working class, represented by left-wing parties, greater weight in the political process. Consistent with theories of the electoral system, proportional representation increased public investments, esp. in basic education, with few effects on redistribution or total spending. Based on comprehensive archival mortality statistics since 1890, I then demonstrate that the observed shifts in representation and public finances were associated with substantial declines in child mortality by 15% and in mortality from infectious diseases, the major killer of the time, by 10-15%.

In a democratic proportional election system, it is vital that the mandates in the parliament are allocated as proportionally as possible to the number of votes the parties got in the election. We formulate an optimization model for allocation of seats in a parliament so as to minimize the disproportionality. By applying separable programming techniques, we obtain an easily solvable problem, and present a method for solving it optimally. The obtained solution is thus the feasible solution that has the minimal disproportionality (with the measure chosen), in contrast to the heuristic procedures used in many countries. We apply the approach to real life data from the last three elections in Sweden, and show that the result is better, i.e. more proportional, than what was obtained with the "adjusted odd number rule", which is presently used. A natural suggestion would be to use our method instead. We also consider the issue about constituencies, and suggest a procedure, based on the same kind of optimization problem, for allocating mandates in the constituencies, without changing the overall allocation with respect to parties. In our approach, the numbers of mandates for the constituencies are based on the number of votes given, not on estimated numbers of inhabitants. This removes the need for fixed and equalization mandates, and also makes the question about sizes of the constituencies less important.

The paper presents the problem of choosing the representatives in an assembly when the whole electoral region is subdivided into electoral districts. Because of the two dimensions, geographical (districts) and political (parties), the problem is called bi-apportionment. Often the allocation of seats to districts is pre-determined and furthermore distorted ---meaning that the ratios of the number of assigned seats to population size vary significantly across districts. The paper surveys proposed bi-apportionment methods with a focus on the conflict that may arise between party-proportional representation under district distortions.

The paper presents the problem of choosing the representatives in an assembly when the whole electoral region is subdivided into electoral districts. Because of the two dimensions, geographical (districts) and political (parties), the problem is called bi-apportionment. Often the allocation of seats to districts is pre-determined and furthermore distorted ---meaning that the ratios of the number of assigned seats to population size vary significantly across districts. The paper surveys proposed bi-apportionment methods with a focus on the conflict that may arise between party-proportional representation under district distortions.

The paper presents the problem of choosing the representatives in an assembly when the whole electoral region is subdivided into electoral districts. Because of the two dimensions, geographical (districts) and political (parties), the problem is called bi-apportionment. Often the allocation of seats to districts is pre-determined and furthermore distorted ---meaning that the ratios of the number of assigned seats to population size vary significantly across districts. The paper surveys proposed bi-apportionment methods with a focus on the conflict that may arise between party-proportional representation under district distortions.

The paper presents the problem of choosing the representatives in an assembly when the whole electoral region is subdivided into electoral districts. Because of the two dimensions, geographical (districts) and political (parties), the problem is called bi-apportionment. Often the allocation of seats to districts is pre-determined and furthermore distorted ---meaning that the ratios of the number of assigned seats to population size vary significantly across districts. The paper surveys proposed bi-apportionment methods with a focus on the conflict that may arise between party-proportional representation under district distortions.

The paper presents the problem of choosing the representatives in an assembly when the whole electoral region is subdivided into electoral districts. Because of the two dimensions, geographical (districts) and political (parties), the problem is called bi-apportionment. Often the allocation of seats to districts is pre-determined and furthermore distorted ---meaning that the ratios of the number of assigned seats to population size vary significantly across districts. The paper surveys proposed bi-apportionment methods with a focus on the conflict that may arise between party-proportional representation under district distortions.

The purpose of this article is to ensure free, fair and credible election by adopting electoral reformation, switch from `Winner Take All" (WTA) to Proportional Representation (PR) system. In Bangladesh the election process and election result both have been questioned. Nevertheless, election is one of the key components in ensuring democracy. Particularly the free, fair and credible election is one of the basic and crucial prerequisites and elements of democratic government and governance. Bangladesh, we found an under developed political culture, lack of democratic political organizations, institutions and practices in true sense. All these indicators have been almost failed to institutionalize democracy in Bangladesh. In this backdrop, this paper attempts to explain that, a switch from the current Winner Takes All (WTA) system to Proportional Representation (PR) system can reshape the election system by keeping consistency, because of the fact that the democracy means the rule of the majority but the minority can't be uprooted as well as Proportional Representation (PR) method can help stabilize democracy in Bangladesh.

We introduce incomplete information to a multiparty election under proportional representation: each voter knows her preferences and votes strategically to maximize her payoffs, but is uncertain about the number and the preferences of the other voters. Parties are assumed to be purely office motivated and, hence, the resulting governments are always minimum winning. In this framework we prove a) generic existence of equilibria where only two parties receive a positive fraction of the votes and therefore lead to single-party governments and b) generic inexistence of equilibria that lead to coalition governments. That is, contrary to common wisdom, a proportional rule is found not to promote sincere voting and to be favorable towards single-party governments. The existence of two-party equilibria that lead to single-party governments is robust to parties having ideological concerns.

In their article 'Liberal political equality implies proportional representation', which was published in Social Choice and Welfare 33(4):617–627 in 2009, Eliora van der Hout and Anthony J. McGann claim that any seat-allocation rule that satisfies certain 'Liberal axioms' produces results essentially equivalent to proportional representation. We show that their claim and its proof are wanting. Firstly, the Liberal axioms are only defined for seat-allocation rules that satisfy a further axiom, which we call Independence of Vote Realization (IVR). Secondly, the proportional rule is the only anonymous seat-allocation rule that satisfies IVR. Thirdly, the claim's proof raises the suspicion that reformulating the Liberal axioms in order to save the claim won't work. Fourthly, we vindicate this suspicion by providing a seat-allocation rule which satisfies reformulated Liberal axioms but which fails to produce results essentially equivalent to proportional representation. Thus, the attention that their claim received in the literature on normative democratic theory notwithstanding, van der Hout and McGann have not established that liberal political equality implies proportional representation.

Pork barrel spending is typically attributed to the strategic behavior of political elites hoping to be electorally rewarded by voters residing in their districts. Such behavior is expected to depend on the incentives imposed by the electoral system. We estimate the causal effect of local representation in a closed list proportional representation system where individual candidates have no clear electoral incentive to favor their hometown. Using data from Norwegian regional governments, we still find a hometown bias. We document that municipalities with a representative on the regional council from the same party as the governor tend to obtain more funding for local investments. In an extension we show that citizens also tend to vote more often for parties with a governor candidate from their own hometown, consistent with an expectation of particularistic benefits. Both effects are driven by municipalities with below median population size.