# The algebra of the Bihar assembly

Live Mint
By Professor

The Bihar assembly elections are over. Commentaries on rationalizing failed predictions have started pouring in. For most, the election results were a surprise—a humiliating defeat of the Bharatiya Janata Party (BJP) and its allies, and a stellar performance of the Mahagathbandhan. Here, we dig a little deeper and understand the coalition elements that made it happen. Deductively, no one can determine why the voters voted the way they did. But if we focus on numbers alone, many interesting explanations emerge.

These numbers emerge from the algebra of votes and seat share. The former denotes how many votes a party received, while the latter how many seats. In most parliamentary democracies such as India, vote share doesn’t matter. If a party wins in two constituencies with a 1% margin, and loses in the third by 90%, it would still win the elections even though, based on collective preference, it wasn’t preferred.

When a chief minister or prime minister is chosen not by voters but by elected representatives, the popularity with which these candidates are elected does not trickle down (rather squeeze up). Each elected candidate acts as a single unit, irrespective of the weight of people’s will that they carry with them in victory. Hence, a candidate winning with a margin of 90% carries the same weight as one with a 1% margin. In other words, how much a candidate is liked or disliked becomes irrelevant. Representative democracy converts an analog preference of people into binary “winning or losing” tables.

Since both weak and strong winners exert an equal mandate in forming the government, the real mandate that finally gets translated into the formation of the government lies somewhere midway. This means that voters’ will in a high-margin victory is diluted, while in a small margin it is strengthened. In other words, in electing the ruler, there is always some leakage of people’s will.

This leakage is explained through the difference between seat share and vote share. Mathematically, an index—called Disproportionality Index (DI), attributed to Michael Gallagher (1991)—shows the extent to which the assembly is representative. DI takes a value of zero when seat share and vote share are the same. This means the assembly is 100% representative. On the other extreme is dictatorship, when vote share is zero but seat share is maximum. Therefore, the higher the value of DI, the farther we are from being a genuine democracy.

In our article published in the Economic and Political Weekly (September 2015 issue), we departed from standard narratives offering predictions, and attempted to predict the nature of elections. The election results of the present Bihar legislative assembly are very similar to our predictions.

We measured the values of DI in 14 elections for the Bihar assembly since 1951 and excavated the results. The average value of DI has been 17.66. Interestingly, the DI value has been consistently increasing from 9.81 (in 2000) through 17.48 (in 2005), and reaching an all-time historic high at 35.4 in 2010 (compare this with the Lok Sabha elections, where the highest value of DI has barely touched 23).

If high value of DI is symptomatic of disparity between seat share and vote share, the 2010 Bihar assembly elections (with a DI of 35.4) indicated hugely displeasured voters. Indeed, chief minister Nitish Kumar’s winning margin in 2010 was 3%. A crude generalization shows that 47% of the voters didn’t want his party, the Janata Dal (United), or JD(U), to come to power. This suggests that for the past five years, he had been ruling an electorate that was mostly unhappy with his victory.

This led us to expect two things in 2015. Firstly, Kumar—unless fulfilling his duties as chief minister exceedingly well, which he didn’t—should not be surprised by a poor performance by his party in 2015. Secondly, it was unlikely that the nature of the mandate would deteriorate further compared to 2010. Both predictions were right.

If we look at the JD(U), it has lost 15% of its seats (adjusting for number of seats contested). The JD(U) performed rather poorly. From our perspective, either Kumar had already realized it and was smart in partnering with the Rashtriya Janata Dal (RJD) (he couldn’t have sided with the BJP after his split before the Lok Sabha election in 2014), or he had no idea. But now is the time he needs to reflect critically on his party’s position in Bihar.

Further, the DI for the 2015 elections has fallen to 24.13, from 2010’s 35.4. This shows that the quality of the verdict is better (however, not for individual parties: the BJP’s vote share is the highest among all the parties). In other words, results indicate fewer unhappy voters compared with previous elections. The 2015 elections have witnessed a better reflection of people’s preferences when compared with the 2010 elections. Perhaps the caste-based grand coalition can explain this.

What are the lessons? More importantly, for whom? For any party that comes to power with a high level of disproportionality, its performance becomes very crucial—after all, it is ruling a population largely dissatisfied with the verdict. It takes a high level of performance to retain the seats. Kumar could not deliver it.

Interestingly, this is also the story for the BJP. In 2010, it secured 37.4% of the seat share, but a mere 16.5% of the vote share. This signifies high disproportionality. We predicted that the difference between seat share and vote share will come down. It definitely did. This year, the BJP has a 21.8% seat share with a 24.4% vote share. This means that more people voted for the BJP, but it won fewer seats. Arguably, the BJP’s situation is a true reflection of people’s preferences. Truer than the mandate Kumar has received. Now that’s something to think about.