14 March 2008

The mathematics of elections

Suppose a vote shift happened in Singapore at the next election similar to what happened recently in Malaysia, what will the resulting parliament look like in terms of political party representation? The mathematics of it explained. Full essay.


WL said...

An excellent article, Alex. The GRC system should be abolished and every MP must be able to enter Parliament on his or her merits, rather than ride on the coattail of some heavyweights. There are ways that we can still have minority representations without the GRC.

Chris said...

There has been much debate here about first-past-the-post voting vs. proportional representation of some sort. My party, the Liberal Democrats, usually polls about 20-22% of votes but has only about 10% of MPs (62 at the last election). They have been agitating for and end of FPTP for years now, but as the Conservatives and Labour alternate in power due to FPTP there has been no urge to change this, especially since the two devolved governments of Scotland and Wales use single-transferable vote systems, and they've ended up as coalitions between Labour and LibDems or, after this last election, Labour and Plaid Cymru, the Welsh Nationalists.

There has been some discussion of what would happen if we had a hung Parliament after the next election (which must be held by May of 2010). The LibDems will probably do a deal with whichever party offers them an end to FPTP.

Perhaps you might comment in a future post about FPTP vs. some sort of single-transferable or proportional representation system in Singapore.

I enjoyed this article immensely. Thanks for writing it.

Anonymous said...

I doubt they will ever abolish the GRC system because it has worked to their advantage so far. If they can come up with the idea of NCMPs getting into Parliament, I don't understand why they cannot do that for minority MPs, with some modifications of course. As I said, abolishing GRC is not to their advantage and I think they may make it even more ludicrous by increasing the number of people in each GRC in time to come.

Anonymous said...

Dear Alex,

It's my very first time here. May I introduce myself, my name is Hamdan. I happen to go by the moniker burgerman and Barry. I am one of the editors who featured in a site in Malaysia mentioned by your newspapers, where it was mentioned, we had overwhelming responses!

Your article captures the main points clearly. However, a comparative may not be applicable as there are many differences between BN and PAP. BN is a tripartite arrangement between MIC< MCA < UMNO. PAP is not.

My second point relates to demographics and geographics. Much has been said abt the win in Penang, but DAP had it coming this time round. They have been laying down the ground even long when Lim Chong Eu was around some 20 years ago. So Penang can be discounted from the post analysis.

Perak and Selangor and the short fall in Wilayah was certainly a shokalingham.

I am happy to see that you Singaporeans are taking an interest in our affairs and destiny.

There is however one article that captures my mixed feelings concerning this elections. It is here, the author did do a good job in underscoring the dangers


We have been trying to recontact them since they first appeared in our site in Malaysia.

They came mixed with us and shared but no sooner had we all broken bread, one day for no apparent reason, they just left.

Leave that as it may be. Whatever. I am sure they had their reasons.

My best regards and wishes to all Singaporeans.

Anonymous said...

There is one group that you have not mentioned Mr. Au. That is the vast opaque civil service which I belief is to be estimated at more then 1miilion Singaporeans. Therefore we can safely say that when the PAP created this virus called the GRC the civil service would always ensure that the PAP will always win. It will take an evolution for the civil service to vote against their pathetic masters. So I believe Singapore will never have a freak election result and the electoral system will never be refurbished.

Yawning Bread Sampler said...

Chris - it probably says something about the enormous archive that Yawning Bread has become, that I'm pleased to inform you that I have written something about proportional representation - nine years ago!!!

See the article Reengineering our electoral system

I just took a quick read and even I myself am amazed how consistent my views in 1999 were with my views in 2008.

Another article from 3 years ago that also takes a magnifying glass to our perverted democracy is this one: Again, why we need proportional representation

Both are long, heavy pieces.

Yawning Bread Sampler said...

Hamdan, I'm not sure I fully understand what you're trying to say. Perhaps you'd like to email me privately if you care to. At yawningbread at gmail dot com.

BTW, this essay was about the arcane mathematics, not about the composition or merits of BN or DAP. Also, as you might have noticed, I only referred to the Malaysian federal election for comparison, not the state elections as I realise those may have dynamics of their own.

Anonymous said...

The assumption that the 30% of those who did not cast their votes in GE 2008 would vote for BN is terribly wrong.

The reality is, these people are neither BN supporters nor Opposition supporters. Even if there is compulsory voting in M'sia, most likely this group of people will vote for Opposition.

And I would like to highlight to you that, there is a lot of fraud going on in the GE, the % of Opposition is in fact much higher than statistic.

The Opposition, despite all facing all these hurdles, still manages to deny BN's 2/3 majority and takes over 5 states, this makes all M'sians proud and this shows the maturity of M'sians.

Yawning Bread Sampler said...

Anon, 14 March, 22:14 -

"30% of those who did not cast their votes ... most likely this group of people will vote for Opposition."

You didn't provide any reasoning to back this up.

"And I would like to highlight to you that, there is a lot of fraud going on in the GE, the % of Opposition is in fact much higher than statistic."

Then how is it that no one has lodged any official complaints to challenge the poll results?

However, this essay is NOT about Malaysia, since I don't claim any expertise. It's more about Singapore and the math coming out of Singapore's system.

KiWeTO said...

Bleached for a future
"Trust us" said the men in white
(Starched so white to be stainless)
progress for all through meritocracy
(nurtured at one's own scholastic pace)
To each according to one's ability
(as determined at the tea parties in white)
the rewards of one's efforts
(one's magnitude of the reward)

yuen said...

Dear YB: an excellent article, but for what audience? given its parliamentary majority, only the government can change the electoral system, but would it find the changes you advocate acceptable? I guess your discovery

"how consistent my views in 1999 were with my views in 2008"

is to be expected, since the government has made no change in the 10 years so you were/are addressing the same situation

The government is willing to accept a small number of elected and non-elected non-PAP parliamentarians, too weak to hamper its legislative control; I doubt it would accept 1/3 elected opposition members under a proportionate representation

on the other hand, a separate upper house elected under proportionate representation, with limited power, would be more acceptable; this is an idea where those in the government and outside it, who desire to hear more alternative voices, could find common ground

Yawning Bread Sampler said...

Yuen -

Indeed, only parliament can change the electoral system, but I hope we're not giving up before we even begin. We shouldn't fall into a defeatist mode of thinking that if something isn't conceivable within the next 12 or 24 months, then don't bother.

There is such a thing as public opinion, which over time, can apply pressure until the government of the day finds that it has to yield, at least partly.

Discussing a subject or an idea is meant to seed such change in public opinion. Where will it lead? How long before anything concrete comes out of it? I don't know, but until we begin to raise consciousness, we'll never know.

Trust me, I've been doing this for 15 years now. When People Like Us began, the police were still entrapping gay men with sting operations, courts were sentencing them to jail AND CANING, and SPH newspapers were gleefully splashing their faces on their pages like some monsters that must be made an example of.

99 percent of gay people then said we in People Like Us were mad, wasting our breath, to even dream of talking about equal rights for gay people, let along changing anything. The govt will never change its ways; just speaking up would get us all arrested, they said.

While the journey is far from over, I don't think anyone can deny that we've come a long way since then.

Same for electoral reform. Please don't give up before we even begin. Change in this world is wrought by optimists who persevere, not pessimists who quit.

Yawning Bread Sampler said...


I've seen your long second comment, but there is a reason why I am not posting it here. As I said earlier, if you wish to pursue this topic, you should email me.

Anonymous said...

Dear Alex, great point and fabulous statistical charts, I am impressed.

I thought about this difference MY-Sin too in the last weeks but couldn't come close to such a detailed analysis. I have 2 points to add to your article:

I think you - maybe purposely - left out one great weakness and indeed huge danger of our unfair GRC system: if it came to the point of 49% votes for the ruling party, then suddenly the opposition would hold >80% of the seats. But who would sit there? Although this is somehow hard to imagine, it is absolutely possible. One big scandal or some economic tsunami, and 17% shift are very easy to imagine. And then? Then, we are in chaos. I really wishe we had a bunch of capable and tested people there, but there arent.

Secondly, I do disagree with your statement that the 30% forced to vote by compulsory voting would tend to vote conservatively, ie ruling party. I always believed and observed the opposite. Mainly because of the fact that in the past, most GRCs were not even contested, and a lot of people HAD to vote weeks after the ruling party had declared their preempted victory. I strongly sensed people would then vote opposition, just for fun.

I think it will be much safer and do good for Singapore if the GRC system is changed swiftly, before the unthinkable happens and our political landscape would end up in turmoil. I am really frightened by this possibility and I know others are as well....


yuen said...

YB: surely you are aware that the two are not comparable? non-enforcement of anti-gay law is hardly a threaten to the government's legislative control, and given the change in social standards here and elsewhere, saves it trouble, and the acceptance of change is minimal since de-criminalization has not succeeded, just to avoid the political cost of upsetting some segments of the community; having 1/3 opposition MPs would be a far less acceptable political cost

I believe electoral reform need to start with changes whose political benefits to the government appear to outweight political costs, such as the idea of a proportionally elected senate

BTW, I am a foreigner, so I only discuss political activities, not engage in them

Yawning Bread Sampler said...

EsExpat -

"then suddenly the opposition would hold >80% of the seats. But who would sit there?"

In order to beat the ruling party (PAP) down to 49%, the opposition would have to put up candidates for the GRC contests. Who will sit there after winning? They will.

Regarding the 30% - you shouldn't see in your mind the Singapore voter and then discuss what he would do. This 30% of which I spoke were Malaysians who stayed at home. Why did they stay at home? Many reasons I'm sure but chief among them would be (a) not interested in politics and (b) believed the BN propaganda before the poll that they would win, and were complacent about that. They obviously weren't the ones who didn't want the BN to win, otherwise they would have gone out to vote.

That is why I said, if you added back the 30% of the electorate (in order to make the Malaysian data comparable to Singapore's compulsory system) you should count most of these 30% as pro-BN. Therefore BN's true support is not 51 or 52% as per the count of votes actually cast, but something like 60% of the entire electorate.

Anonymous said...

Hey Alex yes right about the 30%, I talked about Singapore here...


"In order to beat the ruling party (PAP) down to 49%, the opposition would have to put up candidates for the GRC contests. Who will sit there after winning? They will."

Correct, the issue I have with this is: suddenly they might be in power, without being tested or used to political work. I know there are capable people there, but suddenly have 50 capable parliamentarians, how will this work out. A bit discomforting isnt it. In Malaysia, opposition is really in charge of one or another state since some time - in Singapore, they are marginalized, are not in the important committees and had no chance to directly influence political decision making. In my view at leas.

So the potential danger I see in Singapore is to go from 0% actual participation to 100% ruling, this is strange right!


yuen said...

actually, the idea of a "freak" result is just one of the government's methods to persuade voters against supporting the opposition; even if such a result actually occurs, it should be possible to persuade some of the newly elected MPs, even a whole party, to join the "national front"

shaox said...

I believe there is one statistical assumption you have made which cannot be done so.

You have assumed that for the 2-sided contests, the distribution of the vote share per constituency tends towards a normal distribution (bell-shaped) curve (This represents the approximation of binomial distribution to normal distribution). This will be true given a large number of data points; a conventionally accepted number will be somewhere in the range of 30.

However, in Singapore's example we only have 9 contested SRCs and 7 contested GRCs, hardly enough points to make a normal distribution approximation. True we have tens of thousands of people in each group of SRCs and GRCs, but as an aggregate there are only 9 and 7 data points to be considered respectively.

To improve on the accuracy of the depiction, I suggest, since we have so few data points, to mark out the points on the graph individually and calculate the mean and standard deviation based on these actual points, the former being a simple average and the latter being the square root of the sum of squares of the differences between each point and the mean. We can then base the analysis on these numbers of mean and standard deviation.

(I'm a fan of Yawning Bread, but I'm also a mathematician; I can't tolerate statistical inaccuracy ;))