The mathematics of elections 2

In my article The mathematics of elections, I argued that Singapore's use of Group Representation Constituencies (GRC) [1] is anti-democratic as this electoral scheme tends to disenfranchise those of minority political persuasions. This comes about because, given the homogenising effect of large numbers, GRC voting results fall into a narrow bell curve. GRCs tend to produce electoral outcomes rather similar to each other; votes cast for the opposition are diluted everywhere.

Single-member constituencies (SMC) on the other hand, permit more graininess. Local issues and socio-economic profiles unique to a district are more likely to retain prominence given smaller electoral sizes. The result, I argued, is that election outcomes for SMCs reveal a more spread-out bell curve: Some districts vote strongly for the ruling party, others strongly favour the opposition.

A comment by Shaox pointed out a weakness of the first article: It seemed to rely only on the 2006 election. With merely 9 SMCs and 7 GRCs, there aren't enough data points to convince.

I have now looked at the data for the last 4 general elections, and calculated the standard deviations for this larger data set.

 
Single-member constituencies

Between 1991 and 2006, 48 single-member constituencies saw contests. For each constituency, I calculated the deviation of the percentage vote obtained by the ruling People's Action Party (PAP) from the mean of SMCs for that election. The data can be seen in footnote 2. 

The largest negative deviation suffered by the PAP was -30.5% in Potong Pasir in 1991. The largest positive deviation the PAP enjoyed was +18.6% in Tanglin, in the same general election. 

As a set, the standard deviation was 12.7 percentage points, making a spread from -2SD to +2SD of about 50 percentage points. In my earlier article, I had guessed that it might be about 40 percentage points.

Expansion of the data set gave rise to a problem: Eight of these 48 contests were not 2-sided affairs -- a possible complication to the analysis. There was 1 three-sided contest (Bukit Timah) in 2001, another (Bukit Gombak) in 1997 and 5 of them (Bukit Merah, Bukit Timah, Chua Chu Kang, Jurong and Tanglin) in 1991. There was even a four-sided contest (Chua Chu Kang) in 1997.

One possible way to deal with these was to remove them from the data set. However, since voter behaviour in Singapore tends to be one of deciding whether to be for or against the PAP,  and since in all these cases, the extra opposition candidates never polled more than 8 percent -- with the exception of Chia Shi Teck, the Independent candidate in the 4-sided contest, who polled 14 percent -- I felt that I could leave them in without serious deleterious effect. This especially as the deviations I was calculating referred to PAP vote-share.

 
Group Representation Constituencies

Between 1991 and 2006, 21 GRCs saw contests. The largest negative deviation the PAP experienced was -11.0% in Cheng San, 1997, against the Workers' Party. The best positive deviation was +14.2% in Marine Parade, 1991, when then-Prime Minister Goh Chok Tong and his team were challenged, not by any of the main opposition parties, but by the marginal-to-the-point-of-laughable Singapore Justice Party.

With this (still inadequate) data set, the standard deviation was 6.2 percentage points. The spread therefore from -2SD to +2SD would be 25 percentage points. In my earlier article, I had estimated it to be in the region of 20 percentage points.

These 21 GRCs pile up more narrowly around the mean:

Expanding the data set for GRCs to encompass 4 general elections also gave rise to a problem: In 1991, the GRCs were all 4-man districts, but by 2006, they were all 5- or 6-man districts. We need to bear in mind that we're not exactly comparing like with like over the years.

 
Conclusion

The data from the last 4 general elections support my thesis that GRCs have a homogenising effect on election results. The scheme therefore reduces diversity in political representation and effectively disenfranchises a significant number of voters who cast their votes for opposition candidates. 

SMCs permit this diversity to a greater extent.

The extreme skewing of Singapore's electoral map to leave only about 10% of the electorate in SMCs, with the vast bulk in GRCs is in essence an anti-democratic scheme. It is unjustifiable.

© Yawning Bread 

Footnotes

1. Group Representation Constituencies are super-large constituencies assigned as many as 6 seats in parliament. Political parties field teams of candidates and voters are asked to vote for the team they prefer. Election results take the form of winner-takes-all.
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2. Raw data:

Addenda

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