A Condorcet Outcome for Dr Tony Tan?

Owen Tan

If Marie Jean Antoine Nicolas de Caritat – more famously known as the Marquis de Condorcet – were still alive to witness the Presidential Election, he might have found it extremely interesting. A French aristocrat, Condorcet contributed heavily in the mathematical arena, but was also one of the pioneers in contemporary political science.

According to Condorcet in a landmark paper written in 1785, an election can only be considered “fair” if it meets the Condorcet criterion: the winner must be able to defeat the rest of the candidates in the election if he was running against them, one-on-one. He then suggested that there were some electoral methods that were much better at selecting this Condorcet winner than others.

The Condorcet method for selecting the winners in an election was preceded by the Borda count, developed by and named after Jean-Charles de Borda – yet another Frenchman – whose method had been the French Academy of Sciences for fifteen years before Condorcet released his paper. Condorcet, however, strongly argued against the Borda count, believing that it was not a fair method of election. To demonstrate why Condorcet was so concerned about making use of his Condorcet criterion in determining an electoral winner, let us take a look at the recent electoral results:

Vote Count (%) for 2011 Presidential Election

The current Presidential election system is a legacy of our former British colonial masters: a one-round, plurality system that ensures that whoever gets the biggest slice of the pie will be the winner. If candidacy were approved to 50 people, then on average, any candidate that gets 2% or more of the vote will be victorious (which would of course be ridiculous – as ridiculous as giving 50 candidates the certificate of eligibility).

We now know that Dr Tony Tan is the elected President for Singapore. This means that he should fulfill the Condorcet criterion to be declared a Condorcet winner – he needs to beat all three remaining candidates in a one-on-one contest. The plurality system is not a sufficiently good enough system to get a Condorcet winner, however. We only know the 35.2% of the electorate had their first choices on Tony Tan; but we do not know, subsequently, who are the second and third choices.

Obviously, second and third choices do not make a difference in a plurality election, but in a Borda count there is a possibility that the results can change. We can see how this might have resulted in a difference, assuming that the following voting distribution was true (I round up the voting results for simpler calculations):

The Borda count takes overall preferences into account – meaning, a score is assigned depending on which candidate you most prefer. In this case, even if a candidate were to not be voted as the top-most preferred candidate (e.g. Tan Cheng Bock in my illustration), the 900,000 who put him as the second choice make a difference and gives him a 200,000 point advantage. This electoral method, however, is more prone to tactical voting than the plurality method. Consider a case where the majority of the population do not want a particular candidate to win. (My selection of candidate – Tony Tan – is for illustrative purposes only.)

Knowing that Tony Tan will win the election if there is a sufficient number of voters who place him as the second choice, these voters decide instead to vote for Tan Jee Say and Tan Kin Lian, knowing that this will not affect the outcome of their eventual choice of winner.

This method also does not necessarily generate a Condorcet winner: Tony Tan may defeat the rest of the candidates in a straight fight, yet is unable to win in this election because he is outranked by a candidate that wins the majority of the second-place and third-place votes – Tan Cheng Bock.

Hence we know that Condorcet, if he was alive, would probably have thought the electoral system might need a slight modification. But there is a slight problem with Condorcet’s voting methods: they are way too complicated to be calculated manually, especially for an electoral base of 2 million voters. (One can take a look at the Schulze method, which is the most commonly used official Condorcet method today, for a sneak preview.)

The simplest method I have seen that mostly satisfies the Condorcet method is called approval voting, where essentially one can vote for multiple candidates. This is a method that seems to be well-regarded in the academic arena, although few organisations have adopted such a method in elections.

With approval voting, tactical voting will be unlikely, since if a voter prefers two candidates, he can simply cross two boxes rather than decide to put one candidate over the other. This voting system appeals most to swing voters, because it effectively provides them an opportunity to put their support behind two or more candidates that they find can both do the job.

Note that in an extreme case, approval voting will degenerate once more into a one-round plurality system: for instance, if the majority of the population is strongly inclined towards Tan Kin Lian, then most voters will only cross the box belonging to Tan Kin Lian on the ballot.

If Marquis de Condorcet were to be forced to choose between the three possible methods, it is likely that he would have decided on approval voting simply because of its ability to allow the Condorcet winner to emerge victorious. Of course, this is not to suggest that the approval voting system must be adopted: it is more to open up a topic of discussion on whether there can be a voting method in the near future that can generate an even better result.

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Photo courtesy of the Istana. The hypothetical results stated with the different types of electoral systems are merely for examples and should not be construed as guaranteed truth.