Sampling checks in GE 2015

The Elections Department released early indications of polling results for the first time during the 2015 General Elections by publicly announcing the result of sampling checks within 2 hours of the close of polls. Sampling checks have been carried out since 2001 or earlier, but the results were not made known to all candidates or the public until this year. The sampling check is carried out by Counting Assistants drawing a sample of 100 ballots from each counting table after opening the ballot boxes and mixing the ballot papers together. As each counting table corresponds to one polling district and there are about 2,000-3,000 voters per polling station, the 100-ballot sample per polling district corresponds to 3-4% of votes cast and is a large enough sample to make a good estimate of the final polling result

As shown in Table 1, the margin of error varies from ±1.2% points for a large GRC, Pasir Ris-Punggol with 66 polling districts, to ±4.4 % points for Potong Pasir, the smallest Single Member Constituency (SMC) with only 5 polling districts.  For simplicity, no adjustments are made to account for the variation in number of voters in each polling district, and the error margin is calculated for a 50:50 vote split.  The Straits Times has reported that the error margin for sampling counts is ±4% but this is a worst case and only applies to Potong Pasir which is the smallest SMC by far. On average, the uncertainty in the sampling check is within 1.3% points for GRCs and 3.3%  points for SMCs.

Table 1 – Error margins for selected constituencies and SMC and GRC averages
Number of polling districts Sample size Margin of error at 50% vote share
Pasir Ris-Punggol GRC 66 6,600 1.2%
Aljunied GRC 50 5,000 1.4%
East Coast GRC 32 3,200 1.7%
Bukit Panjang SMC 11 1,100 3.0%
Potong Pasir SMC 5 500 4.4%
GRC Average 45 4,500 1.5%
SMC Average 9 900 3.3%
Error margin is calculated as half the width of the two-sided 95% confidence interval (Normal approximation) at 50% vote share. All polling districts within a constituency are assumed to have an equal number of voters.

In a first-past-the-post election, however, what counts is not the actual vote share but crossing the 50% threshold. If we ignore three-cornered fights and make use of the normal approximation again, we can calculate a “victory threshold” or minimum sampling check result for which a candidate can be 95% certain of victory.  This is shown in Table 2 for selected constituencies.  Note that the victory threshold is slightly lower than would be obtained if we simply added the error margin from Table 1 to 50% because the victory threshold is a one-sided rather than a two-sided test. If you’re not statistically-inclined, don’t worry about it – that effect is small in this case. In Aljunied, despite the appearance of a nail-biting finish, the 52:48 sampling check result was above the victory threshold for the Workers’ Party and the PAP in fact had only a 0.2% chance of winning in that constituency once the sampling check result was known [See note 1].  In Punggol East, however, the sampling check result of 51% for PAP was lower than the victory threshold of 52.4% and the PAP could only be 75% certain that they would win there. Put another way, Lee Li Lian still had a 25% chance of winning even after seeing the sampling check results. In all the other constituencies, the winning party’s sampling check result significantly exceeded the victory threshold so the final result was not in doubt once the sampling checks were completed.

Table 2 – Victory threshold for selected constituencies.
No. of polling districts Victory threshold Actual PAP share in sampling check Probability of PAP win given sampling check result
Pasir Ris-Punggol (6-member GRC) 66 51.0% 73% 100%
Aljunied (5-member GRC) 50 51.2% 48% 0.2%
East Coast (4-member GRC) 32 51.5% 61% 100%
Sengkang West (SMC) 13 52.3% 63% 100%
Punggol East (SMC) 12 52.4% 51% 75%
Hougang (SMC) 9 52.7% 42% 0.0%
Potong Pasir (SMC) 5 53.7% 68% 100%
1. Victory threshold is defined as the minimum sample count result for which a candidate can be 95% certain of receiving over 50% of the actual vote (one-sided test).
2. Probability of PAP win is the probability that the actual PAP vote share is > 50%, given the observed sampling check result.

The error between the sampling check and the actual result gets smaller as the sample size increases. Hence GRCs will have smaller error margins than SMCs and 6-member GRCs will have smaller error margins than 3-member GRCs. This is seen in Figure 1 where the difference between the sampling check and the actual result was only 0.1% points in the 6-member Pasir Ris-Punggol GRC while the largest difference of 2.6% points was observed in MacPherson SMC.  The observed differences between sampling check and actual vote counts were all within the expected 95% error margins except for one constituency, but one out of 29 is about right, statistically. We also did not take rounding errors into account, which slightly widen the margin of error.

image001

The sample check is a form of a quick count, which is used in developing democracies where there are concerns with regards to the compilation of electoral results by the central government. In Singapore’s case, there is no obvious need for a quick count as the entire counting process can be observed by candidates’ counting agents and elections results have always been announced within a few hours. Nonetheless, given that the Elections Department has chosen to conduct sampling checks, the decision to publicly reveal sampling check results is a welcome one.

Notes

[1] Some additional uncertainty is caused by the sampling check results only being reported as whole number percentages. The true PAP sampling check result from 5,000 samples could have been as high as 48.5% rather than the reported 48%.  However, this would still have given the PAP only a 1.8% chance of victory once the sampling check results were known.

Data

Sampling check results  and actual vote counts are tabulated in Sample check vs actual v3 (Excel format).

A version of this note was previously published on The Online Citizen, http://www.theonlinecitizen.com/2015/09/how-accurate-is-the-ge-sample-vote-count/.

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What proportion of Singapore citizens are on the electoral rolls ?

DOS does not publish breakdowns of citizen population by age group. The published population pyramids are for “residents” which includes permanent residents. However, the government did publish the actual number of Singapore citizens aged 20-64 in 2011 in the population white paper together with forecasts up to 2060. Chart 6 shows their forecast for the number of citizens aged 20-64 in 2015 as around 2.2 million (I use their scenario with maximum intake of new citizens). The ratio of working-age to elderly citizens is around 5 in Chart 8. This allows us to estimate the total number of Singapore citizens 20 and above in 2015 as 2.64 million.  An ELD press release on 27 July 2015 states that there are 2,460,977 electors on the electoral register. Thus, approximately 2.46/2.64 = 93% of Singaporeans of voting age are on the electoral register. For simplicity, I’m not adjusting the denominator for those above 20 but below 21.

Apart from those who were dropped from the the electoral register for failing to vote in previous elections, various other categories of people are not eligible to vote (Section 6 of the Parliamentary Election Act), but the biggest category are probably prisoners. The total number of prisoners (including drug detainees) in Singapore is around 10,000 so that should not affect the figure that much. I presume that the NPTD population figures do not include overseas Singaporeans, so that would not contribute to the missing 7% either. The predominant explanation for voting-age Singaporeans not included in the electoral register is probably be that they failed to vote in previous elections but did not apply to restore their names to the electoral register by choice, ignorance or inability to pay the $50 fee required. 93% registration is high by international standards, but does seem a bit low considering that Singaporeans are automatically enrolled when they turn 21 and only drop off (mostly) if they fail to vote without reasonable excuse.

The International Institute for Democracy and Electoral Assistance (International IDEA) has published a table showing that only about half of Singapore’s voting-age population actually voted. While the first three columns are consistent with ELD figures, the fifth column, Voting Age Population, appears to have been derived by subtracting the number of residents below 21 from the total population including non-citizens. The high proportion of non-citizens (including PRs) living in Singapore, especially in the working age population, therefore inflates the denominator and the low Voting-Age-Population turnout calculated by IDEA may be literally true but not meaningful because a large proportion of the denominator are non-citizens. The numerator is also only for voters in contested constituencies. The voter participation rate is thus further reduced by the prevalence of walkovers in past elections.

Screen Shot 2015-08-25 at 6.03.30 am

(Documenting here for reference as the question came up in discussion recently)

Kremlinology Singapore-style: Reading the electoral district tea leaves

UPDATE: The EBRC report has been released. See comments at bottom of post.

The Elections Department (ELD) recently published revisions to polling districts. This revision comes six months after the last revision in February, which is an unusually short interval as previous revisions were spaced a year or more apart. Polling districts (PDs), also known as precints, are sub-divisions within constituencies and their main significance is that all voters in a polling district will vote at the same polling place within a polling station. Changes to constituency boundaries are normally made by rearranging polling districts into different constituencies so that ELD will not have to compile new electoral registers before the next election. However, changes to precint boundaries do not necessarily mean that those precints will be moved to a different constituency. As usual, ELD did not highlight the changes that were made, but a quick comparison of the July notificaton with the previous February one shows changes in the following polling districts.

Choa Chu Kang GRC CK10,CK11
East Coast GRC EC01, EC41
Jurong GRC JR10, JR11
Moulmein-Kallang GRC MK03, MK05
Nee Soon GRC NS53
Pasir Ris-Punggol PN69, PN70
Sembawang SB02, SB03, SB18, SB21, SB22
Tanjong Pagar TP12, TP13

(If readers spot any other changes which I missed, please drop me a note at shihtung@ngiam.net) Many of the changes do seem to be errata in the sense of just being minor clarifications or streamlining of precint boundaries. However, there are some which could foreshadow changes in constituency boundaries.

The scenic polling district with nobody living in it

ConeyIsland Pulau Serangoon (Coney Island) has been cut out of polling district EC01 and placed into its own precint, EC41. This is quite strange because I’m quite sure no one actually lives there right now. While part of it is zoned for residential use, it will probably remain a “rustic park” for several more years. Why carve it out into its own precint now ? My guess is that the intention is to move it from East Coast GRC into a new Punggol GRC so that it can be managed together with the rest of Punggol New Town. The electoral register is not publicly accessible so I do not know the actual number of electors living in Punggol estate but there are only 24 polling districts, which may be just enough for a 3-member GRC.

Hougang, Sengkang, Pasir Ris, Where Am I ?

Talking of Pasir Ris-Punggol GRC, that GRC includes one-third of Sengkang new town and stretches all the way to Hougang Ave 8. Two of the PD’s at the border of Sengkang and Hougang estates were also rationalised in the recent revision. PN69 previously included a condominium and nursing home north of Buangkok Drive as well as 9 HDB blocks along Hougang Ave 8. In the latest revision, that PD was redrawn to include only the condo and nursing home between Compassvale Bow and Buangkok Drive. The HDB blocks in Hougang Ave 8/10 were consolidated into one precint, PN70.  This seems unusual to me because the new PN69 polling district comprises one condo with 625 units, and a relatively small (72-bed) nursing home while PN70 consists of 24 HDB blocks. If the intent of tweaking polling districts is to balance out the distribution of voters, this change would seem to go against that. Interestingly enough, however, Buangkok Drive is the boundary between Sengkang and Hougang estates. Whereas before, half of PN69 was in Sengkang and the other half was in Hougang estate, PN69 is now entirely in Sengkang. MARUAH has previously called for electoral boundaries to be aligned with URA planning areas. If the boundaries are to be redrawn, a logical spliit would be to assign PN69 to a new Sengkang GRC while PN70 is merged into a Hougang GRC.

Sengkang-Hougang

Sengkang estate is currently split between three constituencies: Sengkang West SMC, Pasir Ris-Punggol GRC and Punggol East SMC. While the government has traditionally not made major changes to opposition-held constituencies such as Punggol East, and many other HDB estates are also split between different Town Councils, it would make far more sense to simply consolidate Sengkang into a single GRC and to hive off the Hougang portion of Pasir Ris-Punggol into an enlarged Hougang or Aljunied-Hougang GRC.  Combining Sengkang West, Sengkang Central (now in Pasir Ris-Punggol) and Punggol East would give a GRC with 43 polling districts – about right for a 5-member GRC. Of course, boundary delineation is not based solely on objective estate management grounds. Government may instead leave Punggol East alone and combine Punggol and Sengkang West and Central into a Punggol-Sengkang GRC instead. If they do create a Sengkang GRC, however, that would leave 6 Pasir Ris-Punggol precincts (PN64-PN68 and PN70) which are actually in Hougang estate, orphaned. Perhaps these should be merged into Aljunied-Hougang together with another 5 precincts presently in Ang Mo Kio GRC (AM16-AM20) but which are part of Hougang estate, in exchange for Punggol East ?

Constituency boundaries are not aligned with estate boundaries
Constituency boundaries are not aligned with estate boundaries

UPDATE 8:00 PM Haha. This post was posted in the wee hours of the morning of 24 July and the Electoral Boundaries Review Committee (EBRC) report was released at 3:00 pm. Looks like my predictive ability can be described as half-full or half-empty.

Coney Island – Coney Island was indeed transferred out of East Coast GRC but not into a new GRC. Instead it was added to the existing Pasir Ris-Punggol GRC

Sengkang – A new boundary was indeed created along Buangkok Drive by hiving off the Hougang portions of Pasir Ris-Punggol. PN69 was retained within Pasir Ris-Punggol while PN70 went to Ang Mo Kio.

Hougang – As predicted, PN70 was transferred out of Pasir Ris-Punggol but not into Hougang-Aljunied. Instead, it was absorbed into Ang Mo Kio GRC together with the portion of Pasir Ris-Punggol south of Buangkok Drive.

Whitley Road – I didn’t get round to writing this up last night, but I did notice that MK03 and MK05 in Moulmein-Kallang GRC were realigned so that the boundary would be along Whitley Road rather than in the middle of the landed housing estate at Chancery Lane. My inference was that this was in preparation for Whitley Road to become a boundary between two constituencies, and this was borne out when Moulmein-Kallang was dissolved and MK03 went to Holland-Bukit Timah while MK04 was added to Tanjong Pagar GRC.

So overall, my predictions were accurate at micro-level but I did not do so well at higher level. My two correct predictions, Coney Island and Whitley Road, are not very consequential. Where I failed was being too idealistic in the North-East region. The PAP presumably recognised that they would face a tough fight in the Punggol/Sengkang/Hougang North area so instead of creating a new GRC for the HDB’s latest showcase estates in the North-East, they bled off the voters into AMK and Pasir Ris-Punggol, both six-member GRCs, to dilute the voting strength of the younger voters in those estates. I completely did not foresee that Sengkang would be split further, into four constituencies, with part of Sengkang going into AMK GRC. At this rate, Ang Mo Kio is becoming the new Marine Parade. Specifically, the area around Hougang Street 51 and 61 was transferred from Pasir Ris-Punggol GRC to Ang Mo Kio GRC. The HDB Blocks near Street 61 have thus moved from Aljunied to Pasir Ris-Punggol to Ang Mo Kio GRC in the last three elections. In addition, one-third of the voters in Sengkang West SMC have been moved from the constituency into Ang Mo Kio GRC.

MARUAH Electoral Boundary Delimitation Position Paper

In brief,

  • The delimitation process in Singapore is opaque and not subject to public scrutiny. Some boundaries appear to be arbitrary or designed to favour one party. This results in weaker community ties and cynicism towards the political process.
  • Maruah urges the government to raise the level of impartiality, equality, representativeness, non-discrimination and transparency of the boundary delimitation process in Singapore

Slides from the press conference are here:

4GRCs-in-5-elections

MARUAH Electoral Boundary Delimitation Powerpoint Presentation

and the position paper itself is at Maruah’s website. Maps of changes in electoral boundaries from 1991-2011 are in Annex 2 (with thanks to the people at http://www.singapore-elections.com).

Guide for Counting Agents (ELD)

Looks like the Elections Department has released its’ Guide for Counting Agents in the Hougang by-election, and the sampling check for “the purpose of checking against the result of count for that counting place” remains in place. Seems fairly pointless to check “against the result of count” given that there’s no way to change what’s on the ballot papers even if the final results don’t agree with the sampling check.

The real question is whether the AROs will disclose the results of the validity check to Counting Agents at the time that it is carried out, and who receives the “sampling check” information after it is compiled by ELD HQ, but before the announcement of the vote counts at the counting centres.

http://www.eld.gov.sg/pdf/Guide%20for%20Counting%20Agents%20(Final).pdf

Background here:

https://stngiam.wordpress.com/2012/05/01/electoral-procedure-sampling-checks/

Electoral Procedure: Sampling checks in the 2011 Presidential Election

As recounted in my earlier posts, I served as a Counting Agent in both the General Election and Presidential Election last year. One of the pleasant surprises of the 2011 elections was the number of Singaporeans who stepped forward as volunteers to assist the different parties and candidates in campaigning and to serve as Polling Agents and Counting Agents in both elections. Polling agents are appointed by candidates to observe the polling process while Counting Agents observe the counting of ballot papers. Unfortunately, I think the smaller parties were overwhelmed by the response so the administration and training of their volunteers was less than ideal. Still, it is a good sign of the health of Singapore’s political development that so many did step forward to serve.

The Elections Department (ELD) also helped by publishing for the first time two guides for Polling Agents and Counting Agents. Unfortunately, these guides were only released three days before polling day so it was too late for the candidates to use them in their training sessions. Hopefully, the Elections Department will update these guides for future elections and release them earlier so that candidates, agents and voters will have a clearer understanding of the procedures and rules regarding the casting and counting of votes.

By and large, I think both elections went off smoothly and by the time of the Presidential Election, both elections officials and Counting Agents were already familiar with the procedures and in some cases, with each other, because they had met previously during the General Election. The Elected President is intended to be above party politics and I was pleased to find that at least in the counting centre that I was assigned to, there was a high level of co-operation between the Counting Agents representing all four of the candidates. Apart from Tony Tan, the other candidates did not manage to recruit enough Counting Agents to cover all the Counting Places. Nonetheless, Counting Agents for the other three candidates informally spread themselves out among the tables and held watching briefs for each other. In any case, there were few disagreements between the Counting Agents and Assistant Returning Officers (AROs) or among the Counting Agents over adjudication of ballots.

Counting Procedures

The counting procedures for both Parliamentary and Presidential Elections are substantially similar and ELD’s Guide for Counting Agents provides a good overview. One of the interesting features of the process is what ELD calls in its guide a “sampling check”

Sampling checks

5.16 During the counting process, the ARO will conduct a sampling check to obtain a sample of the possible electoral outcome for that counting place, for the purpose of checking against the result of count for that counting place.

What I observed was that after the ballot boxes were opened and the contents mixed together on the counting table, one of the counting assistants would randomly select 100 ballot papers and do a quick tally of the votes on that sample and then report the results to the Assistant Returning Officer in charge of that Counting Place. The results of the sampling check were not formally announced to those present but Counting Agents could observe the recording of the results by the AROs. As I mentioned earlier, there was very good co-operation and sharing of data between the Counting Agents representing all four candidates so I managed to collect the sampling check data for all the counting tables at our Counting Centre (Table 1).

Table 1 – Sampling check results for Presidential Election, 27 August 2011
Nanyang Junior College Counting Centre
Counting Place

Polling District

Polling Station

Tan Cheng Bock

Tan Jee Say

Tony Tan Keng Yam

Tan Kin Lian
1

GK01

MA27

Nanyang JC

33%

25%

36%

6%
2

GK02

MA24

Braddell Heights CC (B)

22%

34%

39%

5%
3

GK03

MA23

Braddell Heights CC (A)

30%

28%

38%

4%
4

GK04

MA22

419 Serangoon Central

35%

21%

34%

10%
5

GK05

MA26

305 Serangoon Ave 2

21%

32%

43%

4%
6

GK06

MA25

240 Serangoon Ave 2

26%

30%

35%

9%
Overall for Counting Centre

27.8%

28.3%

37.5%

6.3%
Sampling is conducted by taking a sample of 100 ballots at each Counting Place after mixing of ballot papers but before commencement of counting. The overall share for each candidate was computed by simply averaging the results for each polling district without adjusting for the different number of voters in each polling district.

Tony Tan came out ahead in all the polling districts in the sampling check, just as he did in the final tally (Table 2) though there was some difference between the final result and the sampling check (Table 3).

Table 2 – Actual results for Presidential Election 27 August 2011
Nanyang Junior College Counting Centre
Counting Place

Polling District

Polling Station

Tan Cheng Bock

Tan Jee Say

Tony Tan Keng Yam

Tan Kin Lian

Total number of valid votes

1

GK01

MA27

Nanyang JC

34.1%

26.6%

34.0%

5.3%

3,237
2

GK02

MA24

Braddell Heights CC (B)

32.5%

28.6%

33.0%

5.9%

3,074
3

GK03

MA23

Braddell Heights CC (A)

31.5%

28.7%

34.8%

5.1%

3,198
4

GK04

MA22

419 Serangoon Central

32.5%

26.0%

35.8%

5.7%

3,539
5

GK05

MA26

305 Serangoon Ave 2

33.5%

25.3%

36.4%

4.9%

2,946
6

GK06

MA25

240 Serangoon Ave 2

32.7%

24.8%

36.6%

5.9%

3,434
Overall for Counting Centre

32.8%

26.6%

35.1%

5.5%

19,428
See https://stngiam.wordpress.com/2011/08/29/flash-results-micropolling-results-of-presidential-elections-2011/ for more polling-district level results.
Table 3 – Difference between actual vote share and sampling check
Nanyang Junior College Counting Centre
Counting Place

Polling District

Polling Station

Tan Cheng Bock

Tan Jee Say

Tony Tan Keng Yam

Tan Kin Lian
1

GK01

MA27

Nanyang JC

1.1% pt

1.6% pt

-2.0% pt

-0.7% pt
2

GK02

MA24

Braddell Heights CC (B)

10.5% pt

-5.4% pt

-6.0% pt

0.9% pt
3

GK03

MA23

Braddell Heights CC (A)

1.5% pt

0.7% pt

-3.2% pt

1.1% pt
4

GK04

MA22

419 Serangoon Central

-2.5% pt

5.0% pt

1.8% pt

-4.3% pt
5

GK05

MA26

305 Serangoon Ave 2

12.5% pt

-6.7% pt

-6.6% pt

0.9% pt
6

GK06

MA25

240 Serangoon Ave 2

6.7% pt

-5.2% pt

1.6% pt

-3.1% pt
Overall for Counting Centre

5.0% pt

-1.7% pt

-2.4% pt

-0.8% pt
e.g, in polling district MA27, Tan Cheng Bock actually received 34.1% of the vote compared to 33% in the sampling check, a difference of 1.1 % points.

The sampling check is not specifically called out in the Presidential Elections Act or Parliamentary Elections Act though it does not appear to be prohibited either. I did not observe the counting assistants carrying out a sampling check during last May’s General Elections. However, I did observe the ARO at a different counting centre personally pick up a stack of ballots and scrutinize them very closely. When I asked him what he was doing at that time, he answered that he was checking the validity of the ballot papers. Possibly, he was referring to Section 50(1)(a) of the Parliamentary Elections Act under which ballot papers must bear an official authentication mark to be considered valid. Given the thoroughness of ELD’s pre-election preparations and the scrutiny of Presiding Officers and Polling Agents, not to mention voters, during polling, I find it very unlikely that any unauthenticated ballot papers could slip through. In any case, the ARO is required under Section 50 to check the validity of every ballot paper when it is counted so a validity check on a subset of the ballots appears to be superfluous.

Regardless, the validity check or sampling check cannot affect election results because they are only conducted after polls have closed. Conceivably, the sampling check could be construed as being a form of exit polling and while Section 78D of the Parliamentary Election Act prohibits the publication of exit poll results on polling day, this prohibition only applies while polling stations are open. Even if a sampling check were conducted during a Parliamentary Election and the results leaked out, there would not be any violation of the Act because polls would already have closed by the the time the sampling check is conducted.

Sampling check as predictor of election result

The ELD Guide for Counting Agents says that the purpose of the sampling check is to “obtain a sample of the possible electoral outcome for that counting place, for the purpose of checking against the result of count for that counting place.” This sentence is quite awkwardly constructed and doesn’t make a lot of sense since the the final vote tally will be the official result regardless of whether it agrees with the sampling check. Presumably, what they really meant to say was that the sampling check is used to predict the outcome of the election early in the counting process.

As can be seen in Tables 1 to 3, the sampling check predicted correctly that Tony Tan would come out on top at Nanyang Junior College, though his actual vote share was 2.4% lower than that in the sampling check. The sampling check result for Tan Cheng Bock in polling district MA24 stands out as it was 11 percentage points lower than his actual vote share. I estimate a slightly more than 1% chance of this occurring by chance, which is a low probability but not exceptionally low. Of course, it’s also quite possible that the Counting Agent at that table just made a mistake because the ARO did not officially announce the sampling checks results over the table.

For this election, analyzing the sampling check results is quite challenging because there were four candidates so the problem is a multiple comparison problem rather than the usual comparison of two proportions. In a normal two-horse race, we would just have to predict whether the votes for one candidate exceed 50% and that would tell us the outcome of the race. In this case, however, we would have had to predict the vote shares of at least two, perhaps three, candidates, but the vote shares of the candidates are not independently distributed, which makes the problem rather difficult. If any more statistically-inclined reader has a good method for estimating probability distributions for this type of problem, please contact me.

Four-way elections will hopefully remain rare in Singapore, so I present a simplified analysis of the sampling check in a standard two-way election instead. There were 782 polling stations in the last election and if 100 ballots are sampled from each one, there would be a total of 78,200 ballots in the sampling check for a nation-wide election such as the presidential election. We assume that each polling district has the same number of voters, and using the normal approximation to the binomial distribution, the 95% confidence interval for the sampling check is roughly ±0.4% points. If we don’t need to estimate the actual vote share and only need to know whether a candidate has won (i.e., received > 50% of the vote), we can be 95% confident that he has won if he receives over 50.3% of the votes in the sampling check (one-tailed test). For the elections officials, what counts perhaps is not who won but rather whether there would be a recount. To avoid a recount, the winning candidate must receive at least 51% of the final vote (2% winning margin over his opponent) so if the sampling check reveals that one candidate has scored at least 51.4% in the sample, the elections officials can be 99% certain that they would not have to stay overnight. In reality, the number of voters varies from about 2,000 to 3,500 per polling district and since voter turnout will be known by the close of polls, we could make some adjustments for polling district size and voter turnout to improve the accuracy of the forecast. Of course, there is no way to estimate the number of spoilt votes, which could affect the results, but I don’t think those would have a large effect in most circumstances.

Because the sample size is large in a presidential election, the forecast made by the sampling check is quite precise. In parliamentary elections, however, there may be as few as five polling districts in a single-member constituency (SMC) such as Potong Pasir so the sample would be smaller and the uncertainty in the sampling check larger. Assuming a sample of 500 out of a total of 15,870 valid votes in Potong Pasir, a candidate would have to receive at least 53.7% in the sampling check to be 95% certain of winning the election (one-tailed test). Hougang is larger and has nine polling districts with 23,000 voters. For that constituency, a candidate would have to poll at least 52.7% in the sampling check to be 95% certain of winning the election. Again, I’m assuming equal polling district sizes in these analyses but adjusting for polling district size and turnout would be more important in small constituencies.

Purpose of the sampling check

A rather obvious question is what ELD does with the sampling check data. As described above, one possible use of the sampling check is to predict whether recounts would be necessary and to prepare the elections officials accordingly. I do not know whether this was done during the presidential election, but I presume not, because I did not observe the elections officials at my counting centre start to make preparations for the recount until very late in the night. Since the sampling check takes place after the close of polls it cannot affect voter turnout and it cannot have any effect on the ballot papers which have already been poured out and mixed together on the counting table. The only possible effect that I can conceive is that if a candidate learns that the results are close in a particular counting centre, he could redeploy his more persuasive Counting Agents there in the hope of swaying the ARO into interpreting unclear ballots in a more favorable manner. This has less of an impact in Presidential Elections where every vote has the same weight regardless of location, but in a General Election, political parties may be able to use sampling check data to reposition Counting Agents from safer seats to more contested constituencies where they might be able to make a difference. Smaller parties in particular could benefit more from this information in that they could make more effective use of their smaller pool of volunteers whereas larger parties already have an excess of Counting Agents so have lesser need to redeploy them even in the event of a close fight. To ensure the appearance of impartiality, however, ELD should formally announce the results of the sampling check rather than leave it to Counting Agents to look over the shoulders of the AROs. While the AROs at my counting centre did not prevent the Counting Agents from jotting down the results of the sampling check, they did not explicitly announce the results in the same way that they announced the final vote count over the table.

On reflection, however, it is not really clear to me what purpose the sampling check serves. ELD does not appear to use the results to prepare its officials for recounts, and it does not officially share the results with candidates or media. Hopefully ELD would be able to explain the purpose and use of the sampling check when it prepares its Guides for Candidates and Counting Agents for the next election — whether General Election or by-election. While I can appreciate it if ELD has concerns that revealing sampling check results could raise temperatures in close elections, I also don’t think it is tenable for them to conduct a sampling check during the course of counting without being more open and transparent as to the procedure and the use of the data generated by the sampling check.

Why does it take so long to get election results ?

In a posting on his journalism.sg blog, Cherian George reminds readers of MediaCorp’s refusal to air any hints of election results prior to the official announcement by the Returning Officer:

Members also commented that while they understood the need for CNA to ensure that the results were verified before they were announced on air, the delay between announcements on other new media platforms such as Facebook and Twitter, and the updates on CNA did not reflect well on the latter as a national news channel.

George attributes MediaCorp’s slowness to their reluctance to attribute news breaks to a competing news organisation (George’s former employer, the Straits Times). While that may be one of the reasons, I don’t think it is the primary one. The main problem is that MediaCorp, like much of the civil service, just has an aversion to making estimates or judgement calls for fear that they might have to make a correction later. So they just wait until a “final” result is out, preferably one endorsed by a higher authority.

But that then raises the question of why it takes so long for the Returning Officer (RO) to announce the results. I’ve been involved in 3 elections – GE 2006, GE 2011 and PE 2011 – and each time, counting at the centre I’m at is done by 10:00-10:30, but the official result doesn’t come out till over an hour later. It is true that in this year’s elections, I didn’t necessarily have the whole picture, and there could be some problem in some counting centre which delayed the announcement. But in 2006, I was stationed at a Principal Counting Centre, and results from all the Counting Centres for a constituency would be in for a really long time before the RO would officially announce the results. Why such a long wait ? My recollection is hazy by now, but I think it was over an hour.

Now, it is true that this is one of those things where you really don’t want to make a mistake, and I’m sure part of the delay was that Elections Department (ELD) HQ was double-checking and triple-checking the results that we were sending in. Out in the Principal Counting Centers, we were also checking the results, both manually and in a spreadsheet I had built for the purpose. Realistically, the probability of a clerical error is very very small, especially if appropriate IT systems are used. In principle, the candidates themselves also serve as independent checks because they would also have their own count, relayed through their counting agents. So what really is the point of waiting for ELD clearance to announce the results ? Seems to go against the whole point of having decentralized counting.

And the problem gets even worse with recounts. This time round, rumors of a recount started swirling before midnight, but the official order to recount didn’t go out till almost 1:30 and the final result only came out at 4:20. The bad news is, I think this will likely be a feature of all future presidential elections. With relatively low (though probably irrelevant) eligibility criteria, multiple candidates will end up splitting the vote leading to a high probability of recounts.

And as 27-hour shifts for election officials become routine, there will inevitably be even stronger calls for electronic rather than manual voting. Call me a Luddite, but I have very very grave reservations over electronic voting. This probably warrants another blog post, but the bottom line is given the simplicity of the electoral choices in Singapore, the benefits of electronic voting do not outweigh the risks. The best way of defusing calls for electronic voting is to make the paper ballot process faster. The intial sorting and counting of the ballots may take some time, but there is no reason for it to take so long to simply add up the tally from different counting centres. At least for parliamentary elections, let the Group Assistant Returning Officers (GAROs) announce the results rather than waiting for the RO himself to do it. [I think that’s how it used to be done in the old days – Can anyone confirm ?]. Yes, it makes the job of the media a bit more difficult because they have to have reporters at more places, but so be it. At the end of the day, voters, candidates and election officials would all rather have the results earlier.