Philippine Post Election Analysis: 2010 Election Theme and The Runoff Theory

My earlier post about election runoffs and the impossibility theorem have led me to ponder more about counterfactuals or how elections would have resulted if we had a majority based way of selecting our leaders.

Taking a glimpse at the survey leading to the elections, we find that Presidential candidate Noynoy Aquino as practically having maintained the same share level in voter preference from November to May, as shown by the chart courtesy of Social Weather Survey
And it would be further interesting to note that there seems little change in the distribution even prior to the declaration of candidacy by the other contenders last November.

This from Pulse Asia,

``Compared to the October 2009 Ulat ng Bayan survey, the support for Sen. Aquino III remains virtually unchanged. On the other hand, there is a significant improvement in voter preference for former President Estrada (8 percentage points, from 11% to 19%) and marginal increases in the support for Sen. Villar (+4 percentage points, from 19% to 23%) and Lakas-Kampi-CMD standard bearer Gilbert ‘Gibo” Teodoro (by 3 percentage points, from 2% to 5%)."

In short, the 2010 Presidential election THEME appears to have revolved around a pro-Aquino versus anti-Aquino camp. Unfortunately, the votes of the latter had been distributed among 8 contending parties. Therefore, the landslide victory by candidate Aquino.

While the elections did show the rankings of first preference of every voter, it doesn't reveal the second or third preferences needed to ascertain a mathematical estimate on the possible alternative outcome.

But the distribution presented in our original post and the discerned dynamics from the voting patterns (pro Aquino versus anti Aquino) seems to echo an outcome from Mr. Arrow's Impossibility Theorem.

Bottom line: under an election runoff or if the elections were reduced just to two participants, Mr. Aquino's victory isn't all that certain.

Philippine Elections: In A Hypothetical Runoff Elections, Will Noynoy Aquino Still Be The Winner?

Perhaps not.

That's if we base this on Kenneth Arrow's Impossibility Theorem.

Just a reminder, in the Philippines we have a plurality and not a majority representative government, therefore, runoff elections are precluded.

Runoff elections by definition is a "two-round system (also known as the second ballot, runoff voting or ballotage) is a voting system used to elect a single winner."

In other words, if we were to pursue a majority representation, then the top two contenders, Aquino and Estrada would have to compete again in a second round of elections to secure the top spot through a majority vote.

Perhaps we can talk about more of this once the final outcome have been declared.

Anyway, what may be popular may not be the actual. Professor Don Boudreaux lucidly explains how under the "Impossibility Theorem" the outcome of the popular elections may dramatically change, under a runoff.

And when applied to Philippine national elections the outcome may be a surprise.

Here is Professor Boudreaux,

Suppose there are nine voters.

Voters 1, 2, 3, and 4 each prefer candidate A to candidate C and candidate C to candidate B. That is, each of these four voters ranks the three candidates as such: A>C>B.

Voters 5, 6, and 7 rank the candidates like this: B>C>A.

Voters 8 and 9 rank the candidates like this: C>B>A.

In the general elecation, A will receive 44.4 percent of the vote (4 of 9 votes cast); B will receive 33.3 percent of the vote (3 of 9 votes cast); and C will receive 22.2 of the vote (2 of the 9 votes cast).

[my comment- this looks somewhat like the distribution share of the still pending final count for Presidential election results- where Aquino has 40.19%, Estrada has 25.46% and Villar has 14.22% (wikipedia.org). To consider the above theory is based on 3 contenders while we have 9 contenders for the recent election!]

Because no candidate won a majority of the vote in the general election, a runoff election is held between the top two vote-getters from the general election: candidates A and B.

In the runoff election, candidate B will win 55.6 percent of the vote (5 of 9 votes cast). B will then be sworn into office, presumably as the voters’ preferred candidate.

But look more closely. Suppose that the candidate who received the fewest votes in the general election – candidate C – were to run against candidate B in a runoff election. Which of these two candidates would win? Answer: C. In such an election, C would win 66.7 percent of the vote (6 of 9 votes cast), thus trouncing candidate B! (Also note that if a runoff election were to pit C against A (the candidate who received the most votes in the general election), C would also defeat A: C would get 55.6 percent of the vote (5 of 9 votes cast) to A’s 44.4 percent (4 of 9 votes cast).

So is it correct to say that candidate B is the voters’ most-preferred candidate? Clearly not.

Nevertheless, Professor Don Boudreaux concludes, ``The point of this exercise is to make clear that describing the winner of any fair and honest election as being the ‘choice of the voters’ is fraught with potential inaccuracies."

Indeed.