Implementing Proportional Representation within the GRC System

While it may not be popular to support the existence of GRCs, there are administrative arguments for the grouping of constituencies into GRCs in Singapore. However, the current implementation of the administrative grouping is poor. Parliamentary Elections for GRC seats are akin to a high stakes game where large fractions constituents of constituents will be disenfranchised. (e.g.: in a 55% - 45% result, 45% of the constituents are not represented by the team they voted for.)

Now, unless candidates from political parties are of such atrociously low quality as to be unable to work together with each other, there is a strong case for the use of Proportional Representation in Singapore. Having representatives from various political parties ensure that each constituents can be represented by the party they believe in (if that party has sufficient support for at least one representative to enter parliament).

Who Gets How Many Seats

In a Proportional Representation system for GRCs, voters vote for parties. There are various variants of Proportional Representation, but we shall adopt one where each party selects which of its candidates take the seats It wins. This variant is selected to address the legacy of race in Singapore politics. But before getting to that, an important aspect of implementing Proportional Representation should be dealt with.

The chief issue with Proportional Representation where there are small numbers of seats (less than 7, for instance) is how to allocate seats to parties in response to the realized vote-share realized by the participating parties. In principle, the number of seats each party wins in a GRC should be the fraction of votes won multiplied by the total number of seats available in that GRC. In practice, however, these numbers are never prefect whole numbers. Thus, it is important to deal with this matter in as fair a manner as possible.

This means that the objective is to use a rule of seat allocation that, in all cases, under-represents as few voters as possible, and over-represents as few voters as possible.

To calculate the level of over/under-representation, take the fraction of allocated seats and divide it by the vote-share of the relevant party. Let that number be γ. If that γ is greater than 1, then the party is over-represented by (γ-1)×100%. If that γ is less than 1, then the party is under-represented by (1-γ)×100%. If γ is exactly 1, it would be sufficient cause to "go buy 4D".

Going back to the example of the 55% - 45% result, if there were only a single seat (or the winning party took all seats), 55% of the constituents would be 81% over-represented and the remaining 45% would be unrepresented (infinitely under-represented/disenfranchised). In the case where there are two seats and one went to each party, the 55% would be 9% under-represented and the 45% would be 11% over-represented. This is a much better result. Now, in the case where there are three seats and 2 went to the party with a 55% vote-share and 1 went to the other party, the 55% would be 21% over-represented and the 45% would be 26% under-represented. Flipping this around, in the case where there are three seats and 1 went to the party with a 55% vote-share and 2 went to the other party, the 55% would be 39% under-represented and the 45% would be 48% over-represented.

Now, I would like to propose a truly optimal rule, so like many academics, I will shift the goal posts slightly. Philosophically, we might say that each constituent is allocated a representative holding a seat, and each representative in a GRC with K seats may be allocated to at most 1/K of all constituents. It is clear that almost always, even in the best case, some constituents will be allocated to a representative whose party he/she did not vote for. Now, we would like the number of such consituents to be as small as possible. With such an objective, it is easy to propose an optimal rule.

Now, suppose the vote share of each party i is given by v(i) and the total number of seats is N. Then the number of seats that party should get (in a world where seats are infinitely dividable) is f(i)=v(i)×N. Since this is not to be, each seat is to be taken by a single representative from some party. Now, party i is initially allocated a number of seats equal to f(i) rounded down. The remaining seats are allocated in order of how close each f(i) is to "the smallest whole number greater than f(i)" (a.k.a.: f(i) rounded up if f(i) is not a whole number, and f(i)+1 if f(i) is a whole number).

Using this rule, it is obvious that as few as possible voters are left unhappy ("allocated to a representative from a party they did not vote for"). This is because we made "unallocated" groups of voters "happy" in order of size. So the left over ("unhappy") groups are, thus, the smallest ones.

Before dealing with another important issue, here is a worked example. The vote share of three parties are 25%-45%-30% in a 6 seat GRC. This means 1.5-2.7-1.8 fractional seats. So the initial allocation is 1-2-1 seats with 2 balance seats. Now, 1.5 is 0.5 less than 2, 2.7 is 0.3 less than 3, and 1.8 is 0.2 less than 2. So, the third and then the second party are allocated an additional seat each, resulting in a 1-3-2 seat allocation. This means that (1.5-1)/6=0.5/6=8.33% of the electorate are left "unhappy". In a majority takes all system, 55% would be left "unhappy".

A Legacy Issue: Dealing with the Race

Now, race is a legacy issue that Singaporeans have to deal with. The ethnic integration policy that the PAP government implemented in 1989 to prevent the formation of racial enclaves led to the concern that minorities would be disenfranchised as they would not have the critical mass to vote minority candidates into parliament in a first-past-the-post voting system. While it is my hope that, eventually, race becomes a non-issue, I felt it necessary to have a reasonable answer to the question of how to deal with it.

Now, disenfranchisement is not a purely philosophical issue, and to resolve it in a Proportional Representation system one would have to argue that representation at a national-level is a sign of enfranchisement, and the lack absence of minority candidates at a local-level does not affect the level of aid that minorities receive. I will not bother to make the argument for the latter as other commentators have already made it for me, and the former is self-evident.

Now, Singapore's resident population is 74% Chinese. It would be reasonable, then to require that political parties to, of all the candidates they send to parliament over all GRCs, send at least one minority candidate for each four Chinese beyond the first four Chinese candidates. Arithmetically speaking, if the number of candidates that a party sends to parliament is greater than four, the ratio of Chinese candidates minus 4 to minority candidates sent to parliament should not be greater than 4. (e.g.: 4C, 3C+3M, 8C+1M are ok; 5C, 9C+1M are not ok.)

The above system is not perfect. It will fail in the event that the political landscape is so fragmented that small parties with small vote shares all put non-minority candidates into parliament. Thankfully, the political landscape in Singapore is far from being like that (so we can cross the bridge when we get there).

A more major problem would occur when the best candidates of political parties are non-minorities. As such, these candidates would effectively be the ones who carry the ground. Now, if this system results in any of the top candidates not being sent to parliament, then in a sense, voters would have been cheated. On the flip side, such a system would spur all parties to cultivate high-quality minority candidates, ensuring effective representation for minorities in the long run.

Conclusion?

I've sketched a practical means for implementing Proportional Representation in Singapore. In doing so, I have implicitly argued that the basis for using such a system would improve representation and reduce the extent of disenfranchisement. That is to say, it would further the democratization of Singapore.

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Afternote: I'm also an advocate for Approval Voting, which can be said to properly measure "the mandate of the people". (Refer to this past post for details.) I would like to think of a way to integrate Approval Voting with Proportional Representation. Unfortunately, the two obvious ways of doing this (interpreting approvals as full votes and interpreting approvals as fractional votes) are less than satisfactory.