Delightful numbers

The simple mathematics of the Delhi elections

By Ashok Sanjay Guha
  • Published 19.02.15
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The spectacular victory of the Aam Aadmi Party has sparked a virtual fire-storm of analysis and explanation. But while conjectures and hypotheses about its causes proliferate, no one has yet tried to explain its precise quantitative dimensions.

One approach to such an explanation can be based on a variation of what economists call the "median voter theorem". Suppose voters choose according to a single key criterion (such as how Leftist or Rightist are the alternatives?): they vote for the party whose position on this (say) Left-Right spectrum is closest to theirs. Suppose further that a two-party system exists in which the two parties are primarily interested in the electoral route to power. Each party will seek to position itself on the spectrum where it is likely to attract the largest possible vote. However, this depends not only on its own position but also on its rival's; therefore, the position it adopts depends on its beliefs regarding its rival's behaviour. Since both parties know that their rival is, like them, passionately interested in victory, each assumes that its actions will evoke the best response from its rival (in terms of the latter's chances of winning). In such circumstances it follows that each party would position itself at the median of the spectrum, where the number of voters on its left is equal to the number on its right. For, if A had positioned itself to the left of the median, its opponent B could win by assuming a position slightly to the right of A: B would then capture almost all voters to the right of A (who constitute more than half the electorate). Likewise, A believes that it will lose if it positions itself to the right of the median.

The median voter theorem predicts that both parties assume identical positions and therefore receive identical vote shares. Who wins is a matter of chance, but it is also a matter of indifference (except, of course, to the parties themselves): since the policy promises of both parties have converged, the policy implemented by the winner will be identical with that which would have been implemented by the loser, provided they carry out their promises (as they should if they are to retain their credibility). The classic example of such an election was Kennedy vs Nixon, 1960 - which is supposed to have been decided by Chicago's Mayor Daley who rigged the Cook County vote in favour of Kennedy. Not too different was Bush vs Gore, 2000, which was decided by the number of votes declared invalid by the state of Florida, then governed by Bush's brother.

The median voter theorem works best for contests between fresh entrants to the electoral arena. The burden of incumbency reduces the freedom of the incumbent in credibly projecting the kind of image he would like to present to the electorate.

There are, however, two interesting variations of the median voter result. When a segment of the electorate is swayed not by a party's position on the spectrum but by other considerations, one has to apply the median voter analysis only to the remainder of the electorate and then add in the effect of the excluded segment. In Obama vs McCain, 2008, 90 per cent of the blacks (who comprise 13 per cent of the population) voted for Obama. Split the remaining 87 per cent evenly between the candidates and add in the the black vote, the predicted count works out to approximately 55 per cent for Obama against 45 per cent for McCain - not too far from the actual figures of 54 per cent to 46 per cent.

A second variation emerges when one party is less interested in winning than in projecting its ideology. During Goldwater vs Johnson, 1964, the Republican party had been captured by the conservative Right, who were obsessed with the idea of differentiating their product from the Democrats'. They succeeded - so that Goldwater projected an image somewhere around the middle of the right-wing. Johnson retained his medial position - so that he received the votes not only of the 50 per cent to his left, but of half the voters on his right between his position and Goldwater's. The upshot - an estimated 62.5 per cent for Johnson, against 37.5 per cent for Goldwater. The actual count - 62 per cent against 38 per cent.

Delhi, 2015, saw both these variations. Neither major party was weighed down by incumbency: the Bharatiya Janata Party had been out of power in Delhi for decades, and memories of the AAP's 49 days had been erased by the long eventful year that intervened. Normally, the median voter theorem doesn't work well in Indian elections because of the multiplicity of parties. Long before the Delhi elections, however, it was transparent that this was a two-horse race; the others were only also-rans. Those who voted for the latter were diehard supporters who voted not in any hope of victory but to demonstrate their loyalty. In this election, their number added up to 13 per cent.

The remaining 87 per cent was divided between the two majors. Had the two been equally interested in winning, they would each have projected a medial image and ended up tied with vote shares of 43.5 per cent each. The AAP was certainly passionately focused on winning, especially after its parliamentary debacle. It projected a mellow civilized image with no more dharnas or nocturnal vigilante raids on African women, well-orchestrated attacks on the BJP's offices or "jokes" on "dark and ugly" Kerala nurses. Kejriwal himself did not repeat his earlier obeisances at the shrine of Maulana Tauqeer Reza Khan, the cleric whose claim to fame was his offer of Rs 5 lakhs for Taslima Nasreen's head on a platter. When Shazia Ilmi, who, in her AAP incarnation, privately preached communalism to a clutch of Muslim leaders, was safely exported to the BJP, the AAP could well claim a respectable medial image.

The BJP, in contrast, seemed far more interested in projecting Hindutva than in winning an election. Its maharajes and sadhvis, now elevated to the status of MPs and in full voice, its Adityanaths, its affiliates like Togadia daily provided televised comedy to the nation with their counsels to women on dress and the number of children they should have and what should happen to them if they met a boy on Valentine's Day, their theories on the ancestry of those who do not revere Ram and their comparative analysis of Mahatma Gandhi and Nathuram Godse. And while this so-called "fringe" entertained us with their antics, more responsible ministers ran berserk, demanding that Hindu scriptures should be adopted as 'National Books' and recited every morning in school. By not silencing these voices, the BJP and Narendra Modi created an image of themselves as belonging to the tribe of Hindutva fanatics. On the Hindutva spectrum, they positioned themselves with the 25 per cent most ardent believers while Kejriwal corrected earlier suspicions that he was anti-Hindu without creating the least suspicion that he was anti-Muslim. The electoral consequences were a replay of the Goldwater-Johnson drama, but now scaled down to 87 per cent. The predicted vote shares are 54 per cent (87 per cent of 62.5 per cent) and 32.5 per cent (87 per cent of 37.5 per cent). This is exactly what happened.

The BJP committed electoral suicide because it was less interested in winning the elections than in bolstering its Hindutva image. All that the AAP had to do was to keep its nose clean and watch in delighted surprise.

The author is professor emeritus, JNU