There is near-universal agreement among electoral specialists that the crucial determinant of an electoral system's ability to translate votes cast into seats won proportionally is the district magnitude; i.e., the number of members to be elected in each electoral district. Under a single-member system such as First Past The Post (FPTP), Alternative Vote (AV) or the Two-Round System (TRS), there is a district magnitude of one; voters are electing a single representative. Under a multi-member system, by contrast, there will by definition be more than one member elected in each district. Under any proportional system, the number of members to be chosen in each district determines, to a significant extent, how proportional the election results will be.
The systems, which achieve the greatest degree of proportionality, will utilise very large districts, because such districts are able to ensure that even very small parties are represented in the legislature. For example, a district in which there are only three members to be elected means that a party must gain at least 25 percent +1 of the vote to be assured of winning a seat. A party, which has the support of only ten percent of the electorate, would not win a seat, and the votes of this party's supporters could therefore be said to have been wasted. In a nine-seat district, by contrast, ten percent +1 of the vote would guarantee that a party wins at least one seat. This means not only that the results are more proportional, but that there is also more chance that small parties will be able to be elected. The problem is that as districts grow larger - both in terms of the number of seats and often, as a consequence, in their geographic size as well so the linkage between an elected member and their constituency grows weaker. This can have serious consequences in societies where local factors play a strong role in politics, or where voters expect their member to maintain strong links with the electorate and act as their 'delegate' in the legislature.
Because of this, there has been a lively debate about the best level of district size. Most scholars agree, as a general principle, that district magnitudes of somewhere between three and seven seats per district tend to work quite well, and there is also general agreement that odd numbers like three, five, and seven work better in practice than even numbers, particularly in a two-party system. But this is only a rough guide, and there are many situations where a higher number may be both desirable and necessary to ensure satisfactory representation and proportionality. In many countries, the electoral districts follow pre-existing administrative divisions, perhaps state or provincial boundaries, which means that there may be a wide variation in their size. Numbers at the high and low ends of the spectrum tend to deliver more extreme results. At one end of the spectrum, a whole country can form one electoral district, which normally means that the quota for election is extremely low and even very small parties can gain election. In the Netherlands, for example, the whole country forms one district of 150 members, which means that election results are extremely proportional, but also means that parties with extremely small vote shares, even less than one percent, can gain representation, and that the link between an elected member and a geographic area is extremely weak, see The Netherlands.
At the other end of the spectrum, PR systems can be applied to situations in which there is a district magnitude of only two. A system of List PR is applied to two-member districts in Chile, for example, and as the Chilean case study indicates, this delivers results which are quite disproportional, even though a proportional formula is used, because only two parties can gain representation in each district, see Chile: Proportionality or Majoritarianism?. This has tended to undermine the benefits of PR in terms of representation and legitimacy.
Both of these polarized examples serve to underline the crucial importance of district magnitude in any system of proportional representation. It is arguably the single most important institutional choice when designing a PR electoral system, and is also of crucial importance for a number of non-PR systems as well. The Single Non-Transferable Vote, for example, delivers semi-proportional results despite its lack of a proportional electoral formula, precisely because it is used in multi-member districts, see Single Non-Transferable Vote. Similarly, the Single Transferable Vote when applied to single-member districts becomes the Alternative Vote, which retains some of the advantages of STV but not its proportionality, see Single Transferable Vote and see Alternative Vote. In majoritarian systems, as district magnitude increases, proportionality is likely to decrease. To sum up, when designing an electoral system, the district magnitude is in many ways the key factor in determining how the system will operate in practice, the extent of the link between voters and elected members, and the overall proportionality of election results.
