Disproportionality across Electoral Systems

Disproportionality across Electoral Systems

     When electoral engineers design an electoral system they are faced with myriad options for doing so. From First-Past-The-Post (Single Member Plurality (SMP)), to open-list Proportional Representation, to Mixed-Member Proportional systems, there are numerous ways to design an electoral system.  With each electoral system there are pros and cons. For example, FPTP systems are notorious for their disproportionate results and “pluralitarian” governments, whereas PR systems are, as the name suggest, much more proportional. Proportionality, the difference between a party’s share of votes and share of seats in parliament, is one of the most important metrics that one must consider when comparing electoral systems.

     So, which electoral systems offer the least and highest amounts of disproportionality? Political Scientists have long noted the extremely disproportionate results that arise in FPTP systems.  In the most recent election in the United Kingdom for example, the Tories won a majority of seats in parliament, while only receiving 37% of the vote nationally. In some cases, under the FPTP system, the party which receives the most votes can actually end up in the minority of parliament! Another example of how FPTP leads to high degrees of disproportionality is the case of the United Kingdom Independence Party, and its performance in the 2015 election. Here, UKIP received about 13% of the national vote, but only received one seat in parliament (1/650^th of parliament). This stands in sharp contrast to the performance of the Scottish National Party, which received 56 seats in parliament on less than 5% of the national vote! To summarize, UKIP received almost three times as many votes as the SNP, but the SNP received 56 times the representation in parliament. Such disproportionality is a direct result of the electoral system in place. If the system were perfectly proportional, then UKIP would have almost three times the representation as the SNP, rather than the current situation of 56 to 1 in favor of the SNP.

     The primary measure of proportionality in comparing electoral systems is the Gallagher Index of Proportionality. This index goes from zero—meaning no disproportionality—to 100, meaning complete disproportionality (which, in reality could never occur in a democracy). Essentially, the higher the number, the more disproportionate the results of an election are. Using the Gallagher Index of Proportionality (GIP), I have compared thirteen countries across four general types of electoral systems. These four electoral systems are as follows: FPTP, Closed-List PR, Open-List PR, and Mixed systems. I have selected three countries from each of these electoral system categories, with the exception of FPTP, from which I have selected four countries. I then took the average of the GIP scores for the elections during years 1990-2011 (inclusive). The results are unsurprising, with the FPTP systems having higher rates of disproportionality, with the exception of the United States, which has relatively low levels of disproportionality, especially considering the fact that it has an FPTP electoral system.

     The sample average differences across systems are quite in line with expectations, with Open-List PR system having the least amount of disproportionality, FPTP systems having the highest amounts, and Mixed and Closed-List PR systems in between. The sample average of GIP scores can be seen in Table 2. The results are more striking at the national, rather than system-level. Some notable examples of extremely high or low disproportionality are the United States, South Africa, and the Netherlands.  The United States stands out among its FPTP peers with its relatively low rate of disproportionality, with an average GIP score of 3.55 (See Table 1). This is likely a result of the “psychological effect” of Duverger’s law, in which voters respond to the “wasting” of votes by voting strategically for a party which has a realistic chance of winning an election. South Africa has the most proportional results of any country in the sample, with an average GIP score of 0.3 (See Table 1). All of the mixed systems in my sample have relatively large amounts of disproportionality when compared to PR systems, but this is what one would expect given that these systems contain Single Member Districts.

     If one considers the democratic principle of “one person, one vote”, then it is clear that Proportional Representation is the most “democratic” of electoral systems. FPTP systems, with their systemic problem of wasted votes, lead to the most disproportionate outcomes, like the example of UKIP and the SNP noted earlier. Mixed systems try to strike a balance between the regional/personal nature of SMDs and the proportionality of PR. Some countries, like New Zealand, have reformed their electoral systems to achieve higher degrees of proportionality. If proportionality was the only metric that mattered when it came to choosing electoral systems, then all of them would be some variation of PR. But other factors must be taken into consideration, such as religious and/or ethnic differences, geography, and even tradition. That is why there is such variation within and across electoral systems.

    

Table 1: Average Disproportionality of Election Results across Electoral Systems 1990-2011 (inclusive)

Country	Electoral System	Average Disproportionality 1990-2011 (inclusive)
Canada	FPTP	12.20
India	FPTP	7.42
United Kingdom	FPTP	15.93
USA	FPTP	3.55
Israel	Closed-PR	2.12
Spain	Closed-PR	5.70
South Africa	Closed-PR	0.3*
Denmark	Open-PR	1.34
Finland	Open-PR	3.26
Netherlands	Open-PR	1.02
Germany	Mixed	3.70
New Zealand	Mixed	2.69**
Italy	Mixed	6.13

 *South Africa 1994-2011.

**New Zealand 1996-2011.

Table 2: GIP Sample Averages

Type	GIP Sample Average
FPTP	9.78
Closed-PR	2.71
Open-PR	1.87
Mixed	4.17

Bibliography:

Carey, John M, and Simon Hix. 2011. “The Electoral Sweet Spot: Low-Magnitude Proportional Electoral Systems.” American Journal of Political Science 55(2): 383–397.

Gallagher, Michael and Mitchell, Paul. The Politics of Electoral Systems. Oxford University Press. Print. 2005.

Gallagher, Michael. 1991. “Proportionality, Disproportionality, and Electoral Systems.” Electoral Studies 10(1): 33–41.