4) Fair voting in parliamentary elections

posted Jul 1, 2011, 3:18 AM by Ecmi Milano   [ updated Jul 8, 2011, 12:00 AM ]

Instructor: Phil Knight 

Most countries in Europe use some form of proportional representation (PR) as a means of allocating members of parliament at both local and national level. The UK has joined in recently and a number of elections (e.g., European, Scottish) use forms of PR; although there is strong resistance to bringing it into the election for members of parliament (MPs) to Westminster, as the recent referendum on the Alternate Vote system indicates. Currently, UK elections are fought on the first past the post (FPTP) system. In a multi-party election, this can skew results significantly. For example, in the 2001 general election, the Labour party won 65% of the seats but only 40% of the votes. Conversely, in 2010 the Liberal Democrats received 23% of the votes but only 9% of the seats.FPTP is also alleged to be responsible for effectively disenfranchising many voters, as the demographics of some constituencies means that they almost never change hands. For example, Gower, Normanton and Makerfield have elected Labour MPs without exception since 1906. Voters in these areas know that there is almost no chance of their vote making a difference, turnout can be very low. A similar problem in Switzerland led to a successful legal case by a disgruntled voter, and a canny lawyer may be able to use Human Rights legislation to alter the voting system elsewhere.One of the main objections to PR for UK parliamentary elections is that it breaks the link of MPs with individual constituencies: as well as being members of a party, MPs have traditionally represented the interests of individual voters in the towns or districts they have been elected to.The task here is to devise a model of PR to solve the problems of a FPTP system while retaining a constiuency link. Ideally, the system should be straightforward to implement and not subject to anomalous allocation of representatives. In particular, it should be able to accommodate the nationalist parties in the UK which have strong regional representation. The applicability of any proposed system outside of the UK should be investigated.

Preferred mathematical background: Some exposure to linear algebra. Preferrably some numerical analysis: numerical linear algebra and optimisation would be helpful but not essential. Some discrete mathematics would be helpful, too.