Picture of person typing on laptop with programming code visible on the laptop screen

World class computing and information science research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

The Department also includes the iSchool Research Group, which performs leading research into socio-technical phenomena and topics such as information retrieval and information seeking behaviour.


Evaluating competing criteria for allocating parliamentary seats

Rose, Richard and Bernhagen, Patrick and Borz, Gabriela (2012) Evaluating competing criteria for allocating parliamentary seats. Mathematical Social Sciences, 63 (2). pp. 85-89. ISSN 0165-4896

Full text not available in this repository. Request a copy from the Strathclyde author


In an established parliament any proposal for the allocation of seats will affect sitting members and their parties and is therefore likely to be evaluated by incumbents in terms of its effects on the seats that they hold. This paper evaluates the Cambridge Compromise’s formula in relation to compromises between big and small states that have characterised the EU since its foundation. It also evaluates the formula by the degree to which the Compromise departs from normative standards of equality among citizens and its distribution of seats creates more anxiety about the risks of losses as against hypothetical gains. These political criteria explain the objections to the Cambridge Compromise. However, the pressure to change the allocation of seats is continuing with EU enlargement and the arbitrary ceiling of 751 seats imposed by the Lisbon Treaty. European institutions have been created through treaties between states that have equality under international law regardless of population. However, gross inequalities in population between European Union (EU) member states–Germany is more than 200 times bigger than Luxembourg–have resulted in the votes assigned states in the European Council, the EU’s chief decision-making body, being unequal between legally equal states. The allocation of seats in the first chamber of national parliaments normally allocates seats to constituencies in proportion to population consistent with the norm of political equality of electors. The European Parliament (EP) has departed from the norm of the equality of Europe’s citizens by giving a disproportionate number of seats to smaller states. The result, in the words of a document of the Committee on Constitutional Affairs (2010, 39), ‘is really no more than a political fix’ involving party, national and personal interests. Moreover, there is a recurring problem of patching up the fix, because the Parliament is required to review the allocation of seats before each quinquennial EP election. In the early stages of reviewing the allocation of seats for the 2014 EP election, the EP’s Committee on Constitutional Affairs commissioned a Symposium of Mathematicians in Cambridge to identify a formula that would be ‘impartial to politics’ and ‘eliminate the political bartering which has characterised the distribution of seats so far’ (Grimmett, 2012, 1). The convenor, Grimmett (2012, 3), describes these terms of reference as calling for ‘a principled and fresh approach unprejudiced with respect to particular Member States or political groups and free of influence from historical positions’. The result is the aptly named Cambridge Compromise, which allocates seats taking into account both the claims of the EU’s member states (equal treatment in the Base) and population (Proportionality). The tightly focused terms of reference of the Constitutional Affairs Committee are notable for criteria that are excluded. The emphasis on a fresh approach free of historical commitments ignores positive theories that emphasise that established institutions only alter incrementally through path-dependent adjustments from a given starting point ( [Braybrooke and Lindblom, 1963] and [Pierson, 2004]). Whatever the impartial intent of a formula, rational choice theories (e.g. Knight et al., 2008) predict that politicians will evaluate proposals for changes according to the anticipated effect they will have on their interests as Members of the European Parliament (MEPs) or of an EP Party Group. EU rules for approving changes in the allocation of EP seats are consistent with the Pareto optimal principle that a change should only occur if it is possible to make at least one beneficiary better off without making any others worse off, because the re-allocation of seats between countries requires the unanimous approval of member states as well as approval by a majority of MEPs. Both positive and normative theories of democracy (see e.g. Dahl, 1989) emphasise the importance of equality; individuals should not only have the right to vote but also that votes should be cast and counted on the basis of ‘one person, one vote, one value’. While political criteria were exogenous to the recommendations of the Cambridge group, they have been central in the deliberations of MEPs elected under the existing allocation of seats and belonging to Party Groups that vary in the countries from which they draw their members. Instead of evaluating the apportionment of seats according to internal properties of a formula, Members of the European Parliament (MEPs) apply consequentialist criteria: How does it affect the existing allocation of seats to my country and to my Party Group? Hence, this article takes the allocation of seats in the current Parliament as the base line and makes political criteria endogenous. Since different mathematical formulas can have different consequences, the Cambridge Compromise is compared with the partisan allocation of seats with a square root formula as well as with the status quo.