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.

Coordination Problems and Approval Voting

I came across the following abstract. It is not too technical, and highlights the coordination problem that Approval Voting solves (i.e.: vote splitting leading to a strictly inferior outcome for most voters).

This paper shows that information imperfections and common values can solve coordination problems in multicandidate elections. We analyze an election in which (i) the majority is divided between two alternatives and (ii) the minority backs a third alternative, which the majority views as strictly inferior. Standard analyses assume voters have a fixed preference ordering over candidates. Coordination problems cannot be overcome in such a case, and it is possible that inferior candidates win. In our setup the majority is also divided as a result of information imperfections. The majority thus faces two problems: aggregating information and coordinating to defeat the minority candidate. We show that when the common value component is strong enough, approval voting produces full information and coordination equivalence: the equilibrium is unique and solves both problems. Thus, the need for information aggregation helps resolve the majority's coordination problem under approval voting. This is not the case under standard electoral systems.

The conclusion the authors arrive at is not surprising (though the math might be novel, noting that the journal it is published in is regarded as top-tier in the economics establishment).

In the article, the benefit the majority perceives for the two preferred candidates is modelled as a combination of a "common value component" (with different values for the majority and the minority) and an "individual component".

What the authors conclude is that when the "common value component" for the majority is "large enough", then the use of approval voting produces a outcome with a perfectly coordinated majority (as if there were perfect information) where the candidate with the largest number of expected (approval) votes is the majority candidate preferred by more (majority) voters.

The intuition behind it is that the "common value component" serves as a signal of the possibility of a bad outcome is the majority does not coordinate itself. When the inferior outcome is a threat, the majority unites; when it is not, the majority falls into partisan voting.

The citation information of the article is as follows: Bouton, L. and Castanheira, M. (2012), One Person, Many Votes: Divided Majority and Information Aggregation. Econometrica, 80: 43–87. (Here is a link to a recent pre-print.)

Measuring the Mandate of the People: Approval Voting

The Elected Presidency is an office where the President is directly elected by the people. In our current elections, there are four "approved" candidates, which makes it tough for a single candidate to garner more than 50% of the electoral vote in a First-Past-the-Post (a.k.a. one-man-one-vote) voting system. With 50% being the default standard for "having the mandate of the people", this poses some difficulties.

The objective of a voting system, at least for this election, is to measure the mandate of the people. While First-Past-the-Post has been widely used in Singapore and elsewhere, it does not make sense in this setting. This is because an individual may support more than one of the candidates to be President. This would certainly be likely in a situation where all candidates have been screened for suitability. As such, first-past-the-post is the wrong tool for measuring the mandate of the people.

Enter Approval Voting. (Which I've written about previously. [1] [2]) Approval Voting is a system where voters indicate all the candidates that they would support for a position. That is to say each candidate is rated with either "Approve" or "Do Not Approve". The candidate with the highest number of approvals wins the election. Based on this description alone, one might conclude that Approval Voting:

(i) is straightforward and comprehensible, (ii) is simple to implement given our present electoral practices, (iii) removes (or at least greatly reduces) personal dilemmas of choosing between two or more favored candidates, and (iv) directly measures mandate of people.

A further minor feature is that Approval Voting may increase the percentage of valid votes. This is because a voter may approve of all or none of the candidates available, reducing the incentive to destroy one's vote. In addition, Approval Voting has good theoretical properties, which the interested reader may look up. The property of "truthfulness", in particular, is described in the Annex below.

Approval Voting is a good voting system and should receive consideration for subsequent elections. In parliamentary elections, it would mean that multiple opposition parties will be able to contest in a constituency without fear of splitting the opposition vote. But foremost should be the fact that Approval Voting directly measures the mandate of the people.

Approval Voting is already in used by bodies such as the Mathematical Association of America and the Institute for Operations Research and the Management Sciences. In the selection of the Secretary-General of the United Nations, rounds of preliminary approval polling are used to build consensus before a formal vote is held in the Security Council.

As such, there is a strong argument for exploring Approval Voting for use in future elections. More generally, it makes sense to form a committee to re-examine our voting system and make a recommendation on whether or not it should be changed, and if so, to what system. Such a committee might contain senior public servants, representatives from major political parties and academics who are familiar with the properties of various voting systems.

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Annex on the "Truthfulness" of Approval Voting:

Under a reasonable model of preferences, it can be mathematically proven that Approval Voting ensures voters need not misrepresent their preferences on the ballot to pursue an election outcome they prefer. We say that "truthful voting" is an optimal response for each voting individual.

Specifically, the model of preferences referred to is one where individuals either support or do not support each candidate. Each candidate in the "Approved" category are equally supported, and all candidates that are in the "Not Approved" category are equally un-supported. This is known in the literature as "dichotomous preferences". This is a realistic model of the "voter thinks candidate is suitable for position" and "voter thinks candidate is not suitable for position" dichotomy.

What I mean by "misrepresenting preferences" is best illustrated by an example from the USA. In the 2000 US Presidential Elections (using First-Past-the-Post), the front-runners were Al Gore (Democratic Party), George Bush (Republican Party) and Ralph Nader (Green Party). The final outcome was that Nader got 2.74% of the popular vote and Bush (47.87% of the popular vote) won by a razor thin margin only through the electoral college versus Gore's 48.38% of the popular vote (yes, Gore had more votes). If one were a Green Party supporter, one would typically favor the Democrat platform far over the Republican platform. Thus though one would prefer Nader to Gore to Bush in that order, since the election results in just one winner, it would be strategically sensible to vote Gore even though one preferred Nader. Such misrepresentations of preferences, which can occur in first-past-the-post elections with more than two candidates, represents a distortion in the electoral poll which may have unpredictable results.

While the assumed model of preferences which generates "truthful voting" is wrong, as all models are (to any given voter, not all Tans are equal), approve/do not approve is a reasonable approximation. At the very worst, when inter-candidate preference effects are strong in the extreme, Approval Voting produces exactly the same result as First-Past-the-Post, with each voter approving only their most preferred candidate.

As a matter of personal preference, I believe it is sensible to encourage "truthful", "non-strategic voting" among voters. This is very much akin to asking someone to talk straight and direct.

Election Aftermath in Punggol East: Plurality vs Approval Voting

The aftermath of the General Elections in Punggol East is sad, especially for SDA's Desmond Lim who garnered only 4.45% of the valid votes in a 3-cornered fight and will lose his $16,000 election deposit.

Our electoral system, with the electoral deposit in place, is broken. The intent of the deposit is to prevent frivolous nominations for the ballot by demanding some level of assurance that the voters think of the candidate in question as a viable representative of their interests in Parliament.

Even in one-on-one straight contests, this intent is subverted. It is possible that both candidates are thought of as viable candidates by, say 40% of the voters, but one candidates has more people who thinks of him/her as a possible representative. There can be voters who think of both candidates are possible representatives. Say the approval ratings stand at 80% - 60%, and in some extreme case the results of a plurality vote turn out to be 90% - 10% of the valid vote. The 10% candidate loses his/her deposit needlessly.

I have previously written about approval voting and feel that it is the right voting system for gauging the mandate of the people. The results of an election are directly translated into a mandate: a candidates percentage of valid approval votes is exactly the number of voters who approve of him/her as a representative. If a voter thinks a candidate is a possible representative, that's a +1 for a candidate's/group's mandate, nevermind that that same voter also approves of another candidate/group.

Politically, this has implications. In a non-polarized Singapore, this will lead to the ruling PAP winning more seats as their candidate will be seen as "viable" by more people, while their base will staunchly disapprove of the opposition.

From an (behavioral) economics standpoint, in a polarized nation, the modeling assumption of internal perceptions being approve/disapprove are greatly weakened/broken by the clear favoritism that hardcore party supporters have. Even if they would approve of the candidates of the opposite camp, the huge favoritism would lead them to lie about their preferences on the ballot slip. This is because the assumption is "no favorites, only approval-disapproval".

Perhaps with a more mature electorate with less polarization, this better form of voting will be feasible.

Truthful Voting through Approval Voting

Noting that enthusiasm is building up for the coming General Elections, it is timely to assess our current voting system. We use a simple plurality system where each voter may choose only one candidate and the candidate with the most votes wins. In situations with more than two candidates, this system entails the possibility of voters being in a situation where they have the incentive to misrepresent their preferences.

Consider a situation where candidates A, B, and C have 40%, 35% and 25% of the electorate in support respectively. B's supporters do not mind C, but do not want A to win. C's supporters do not mind B, but also do not want A to win. In the plurality voting system, C's supporters have the incentive to misrepresent their preferences and vote for B rather than vote truthfully and have A come into power.

It can be proven mathematically that where voters' preferences are represented by a ranked order of candidates, any voting system offers situations where voters have the incentive to misrepresent their preferences. This is an unfortunate and inescapable reality. However, where voters' preferences are represented as "Approve"/"Do not approve" ratings for each candidate, a voting system known as “Approval Voting” gives voters the incentives to vote "truthfully". In Approval Voting, voters cast "Approve"/"Do not approve" votes for each and every candidate, and the candidate with the highest approval level wins.

The truthfulness of the Approval Voting system rests on the idealized "Approve"/"Do not approve" representation of preferences. I argue that elections are not popularity contests but polls of the electorate to see who has a mandate to represent them. As such, a voter might conceivably support multiple candidates or none at all. With Approval Voting, the results of the election unambiguously describe "the mandate of the people". A winner with 90% approval can be said to truly have 90% approval from the electorate as there is no incentive to misrepresent preferences. Conversely, a winner with just 20% approval can be unambiguously seen to have a weak mandate.

In addition, this ameliorates the situation for the opposition with regards to election deposits, since a viable candidate may stand and have approval from a large fraction of the electorate, yet that same large fraction may prefer another candidate.

I suggest that such a system be considered for subsequent elections. This would be a worthy matter to debate after the upcoming elections.