An Analysis of Presidential Elections

1:21 pm PHT

If you understand the title, then it sounds intuitive doesn’t it? If you have a plurality elections (like what we have here in the Philippines), then the more candidates there are, the lower the probability of the winner getting the majority votes. To interpret that in another way and to put it into statistical terms, there is an inverse correlation between the number of candidates and the percentage of votes that the winning candidate gets.

So I read Manolo’s post pointing to an analysis by Sass Rogando-Sasot regarding the past Philippine presidential elections from 1935 to 2004. Apparently, that intuitive statement I mentioned earlier does not work in our elections. The inverse correlation is very weak because Marcos managed to win the 1965 and 1969 elections with a commanding majority (52% and 62% respectively) despite running against 11 other candidates in both elections! If you’re a relatively new voter, that’s unheard of. Estrada, the masa candidate, only managed 40% against 10 others. (You really need to read or at least scan Sass’ post to put my article into context.)

Because of this weak correlation, Sass argues that there must be really something wrong with our political system in the last three presidential elections because we don’t manage to elect a majority president. The problem is that it’s supposedly impossible to run a country if majority of voters don’t really like you for president.

Well, first of all, just because someone voted for Miriam Santiago doesn’t necessarily mean that that person doesn’t want Fidel Ramos to be president. It does not follow. That vote just means that the voter considers Santiago to be the best person for the job. There’s nothing there at all to say whether the voter thinks Ramos is good or bad as president.

Secondly, for the correlation analysis, I would argue that instead of the 1992, 1998, and 2004 elections being statistical anomalies, I think that it’s the 1965 and 1969 elections that are the real anomalies. Looking at the 1965 and 1969 elections, we find out that almost all of the 12 candidates in both elections could be considered as nuisance candidates. In the former, the top 3 candidates got 99.99% of the votes while in the latter, the top 2 candidates got 99.98%. Now there’s your statistical anomaly!

So let’s try the analysis again ignoring these weird candidates. Shown below is the revised table of presidential election results with the number of candidates reduced to the serious ones based on the votes they received. The highlighted number of candidates are the reduced values. (You may disagree with the exact value of reduction but I think the conclusion would still be the same.)

 Table showing the number of effective candidates for Philippine president versus the percentage of votes the winning candidate got.

If we graph the data in a scatter plot and draw the linear regression (orange line), the magical intuitive negative correlation appears! (The pink line is the equal distribution curve—what each candidate would get if the votes were equally distributed.)

 Graph showing the data in the table above with the linear regression and equal distribution curve drawn in.

I don’t have to compute any correlation coefficients (I’m not a stats major) to show that the negative correlation is now stronger. Looking at the graph above, we can now conclude that Erap really was an exceptionally strong candidate and that FVR had too much competition. We also see that Manolo’s grandpa’s victory in 1941 is clearly the best presidential victory of all time (and unprecedented because it was a second-term win).

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Comment times are in Philippine time (+0800).


On 2:03 p.m., 26 May 2007, mlq3 wrote:

it would be interesting to see the first term victories, though, in which case magsaysay’s the record-holder. also, the relative percentages.


On 7:15 p.m., 26 May 2007, seav wrote:

Looking at the first-term victories, I think Erap was the bigger winner than Magsaysay. Erap got 29% more than the equal distribution (11%) while Magsaysay got only 20% more than the equal distribution (50%). Also, Erap’s percentage is far higher on the regression line than Magsaysay’s is.

For the relative percentages, is this the percentage of the winner above the second placer?


On 12:23 a.m., 27 May 2007, mlq3 wrote:

it didn’t occur to me to compare the percentage of the winner above the second placer. would that be interesting to look at, too?

your observation re: magsaysay is very interesting indeed!!


On 1:43 a.m., 28 May 2007, max wrote:

i like the french model where in the top two winning candidates have another run at it which assures the presidency a majority.

the system we have here in the philippines is bound for disaster as had been demonstrated ever since it was established.


On 2:10 a.m., 28 May 2007, seav wrote:

Max, I agree that a run-off system like what the French do would help assure that we elect a majority-backed leader and avoid the compromise candidates that an approval or preferential voting system are prone to.

The problem is, having two election periods will exacerbate the cheating problem. Twice the elections? Twice the cheating.

On the other hand, Indonesia elects its president using the same run-off system as France. Maybe we can learn from them.

But we need to amend the constitution to change our voting system. And you know how divisive the issue of charter change is.


On 5:49 p.m., 29 May 2007, Mike wrote:

From the 1946 election to the 1969 election we basically had a two-party system with the Nacionalista Party and Liberal Party dominating things, so the winning candidate would have a big percentage of votes. I would also prefer the run-off election system. That would have prevented Erap from getting elected in 1998, since (I think) the majority of people were anti-Erap but just didn’t have a single candidate to unite behind.

I know quite a few people who would preferred Roco for president in 2004 but voted for Gloria since they really didn’t want FPJ, and Roco didn’t have a fighting chance. In fact, it may just be the anti-FPJ sentiment rather than the pro-GMA sentiment that pushed Gloria into the lead in those final weeks. That’s not the ideal way democracy should work, but it’s the reality.


On 1:01 a.m., 31 May 2007, benj wrote:

I’m a big fan of the run-off system! I dunno how that will work in the Philippines, though.


On 1:51 a.m., 14 Jun 2007, talksmart wrote:

So what does your graph tell you then? The more candidates in the election the lesser the percentage of votes? How would you interpret the regression equation derived from the relationship? Don’t you think that by eliminating “other” candidates you eliminate outliers?

I would have loved to see more interpretation of your charts.

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