'12' the correct number of (3-Memb) GRCs for Singapore.

'12' the correct number of (3-Memb) GRCs for Singapore.
Ans: 12.2164 (3men GRCs, min 1 minority each).
i.e. 12 - if U round to nearest whole number.

Balancing the facts that:
i) Singapore is a multiracial country where non-Chinese are a minority- and thus the unique need to 'ensure parliamentary minority representation' this despite the largest minority population group in Singapore professing to not "believe in being spoon-fed or being too dependent on government help" in 'The Malays in Singapore – no crutch mentality'[LKSblog, 28Jul2010].
ii) "Singaporeans want greater say when it comes to political activities like policy making as compared to ten years ago." [AsiaOne, 02Aug2010].

Both the numbers of GRCs as well as the MPs per GRC ought to be kept to a minimum- the maximum number of candidates per GRC being 3, so as not to disrupt democratic elections as GRCs are an overly partisan way of conducting elections- which the ruling PAP has roundly admitted both in PM Lee's admission about his paranoia against any parliamentary opposition: "What is the opposition's job? It's not to help the PAP do a better job", which ended with "I'm going to spend all my time thinking what's the right way to fix them, to buy my supporters votes, how can I solve this week's problem and forget about next year's challenges?" [YouTube/@1m10s] as well as SM Goh's admission weeks later that: "'Without some assurance of a good chance of winning at least their first election, many able and successful young Singaporeans may not risk their careers to join politics,' Mr Goh said" [ST 26June2006].

The following calculation seeks to determine what the correct number of GRCs for Singapore should be, keeping in mind both these concerns:
Wherein:
- X is the number of GRCs; (84 - 3X) being the number of SMCs.
- Where the total number of seats in parliament is 84 (yr 2001 to current).
- Where the number of seats per GRC is 3 and the number of minority MPs per GRC is one; (to keep the maths simple- i.e. 5mem GRCs w min. 2 minority MPs only serve to complicate matters unnecessarily- unless U do it across the board and have 6 GRCs of 5 MPs each etc).
- Where the minority population % in Singapore is 25.8% (dtd 2009- Sing-stat).
- Where the 'efficiency of ensuring minority population' is = [X / (84 x 0.258)]
- Where the 'efficiency' of upholding pure SMC parliamentary seats is defined by [(84 - 3X) / 84].

Solving for x:
[X / (84 x 0.258)] = [(84 - 3X) / 84]
84X = (84 - 3X)(84 x 0.258) = (84 - 3X)(21.672) = 1820.440 - 65.016X
84X + 65.016X = 1820.440
X = 1820.440 / 149.016 = 12.2164

When X =12.2164, the efficiency of maintain minority rep. = efficiency of maintaining SMCs= [X / (84 x 0.258)] = [(84 - 3X) / 84] = 56.3700%.

When X =12.2164, the number of SMCs= [84 - 3(12.2164)]= 47.3508= 48 (rounded to the nearest multiple of 3/ based on optimal no. of GRCs).

Conclusion:
Since at par, 12 GRCs only ensures 55.3710% minority representation [{X / (84 x 0.258)} = 55.3710%] , there remains a short fall of up to 9 minority MPs; this is where PM Lee's coincidentally good 'foresight' comes to play- "With the changes, Parliament can have up to nine NCMPs, up from six.”: [CNA 26 April 2010]- giving PM Lee the prophetic honour, if indeed the minority representation after elections remains at the unlikely low of 12/84, of installing the max number of NCMPs (9) (the no. of minority MPs becoming {12 + 9} = 21)- albeit to balance racial imbalances rather than as a stop gap measure for current GRC related partisan parliamentary imbalances.

References:
- 'Group Representation Constituencies (GRCs)': "The GRC system was established in 1988 to ensure that the minority racial communities in Singapore will always be represented in Parliament. .. " [Elections Department Singapore](last accessed 23Aug2010).
- 'The Malays in Singapore – no crutch mentality': "Berita Harian Singapore editor Guntor Sadali: 'We do not believe in being spoon-fed or being too dependent on government help. In other words, we do not have a crutch mentality.'" [LKSblog, 28Jul2010]
- 'Singaporeans want more say': "Singaporeans want greater say when it comes to political activities like policy making as compared to ten years ago." [AsiaOne, 02Aug2010].
- 'The GRC Election System Fair Representation of the People?': "With almost NINETY PERCENT of Singaporeans living in HDB Flats, and the "Racial Ratio of Tenants" allowed to occupy each block (including resale flats) subject to HDB-Government Approval and Control, is it still necessary to have the GRC system to ensure a fair representation of "Minority Races" in Parliament?"~ 'Atobe' [SGforums 17Dec2002].
- 'GRCs make it easier to find top talent: SM': "'Without some assurance of a good chance of winning at least their first election, many able and successful young Singaporeans may not risk their careers to join politics,' Mr Goh said" ; with hosting site footnote: "In Singapore, a Group Representation Constituency is a super-sized constituency where 5 or 6 candidates from the same party have to stand for election as a team. Voters vote for the party, not for individuals, thus weak candidates can still win a seat in Parliament by riding the coattails of stronger candidates."- [ST 26June2006]
- 'PM Lee says countries worldwide respect and admire Singapore's proven system': "What is the opposition's job? It's not to help the PAP do a better job... ...I'm going to spend all my time thinking what's the right way to fix them, to buy my supporters votes, how can I solve this week's problem and forget about next year's challenges?" [CNA:03May2006][YouTube/@1m10s]
- 'GRCs to shrink, but they will stay': "Prime Minister Lee Hsien Loong told Parliament yesterday there should not be too many six-member GRCs, as this makes it harder for voters to identify with the whole slate of MPs." [ST, 28May2009].
- 'Parliament amends Constitution to change NCMP & NMP schemes' “The NCMP position is a unique feature of Singapore politics. … With the changes, Parliament can have up to nine NCMPs, up from six.”: [CNA 26 April 2010].
- 'Betrayal of the original intent of the GRC system of elections. (By SMC minimization)' Facts and figures from (Table1) Yeo Lay Hwee. “Electoral Politics in Singapore”, [Chart wiki: Constituencies of Singapore], [Chart wiki: Ethnic composition (%) of resident population], ~B.C.: [A1forums, 25Aug2010].

Additional References:
- 'Having more single seats will help the PAP': "..many citizens are unhappy that some MPs entered Parliament by piggybacking on party heavyweights through the GRC format. The PAP should consider having more SMCs so that more of their fresh candidates can prove their worth by winning a seat on their own steam.": [ST, 4Feb2010]
- 'SG Elections.com': "an award-winning website that houses the most comprehensive archive of Singapore election results available." [link].
- 'Singapore: Drawing Districts to Ensure Super-Majorities in the Parliament': [aceproject (?date?)]
- 'All eyes on whether PAP will stay in power on Nomination Day' : "We want to have a First World parliament for Singapore, so we need to have a First World government and a First World opposition. If you want us to treat you as gentlemen, argue on the merits of your policy and our policy. Take it to a higher level and we will treat you accordingly and respond accordingly," Lee Kuan Yew,. [CNA, 24 April 2006]

Postscript:
At 12x GRC (3memb), 48x SMC, the efficiencies of assurance of minority rep vs SMC integrity are 55.3710% vs 57.1429% respectively .=================================================
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