# The algebra of Uttar Pradesh election results

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Uttar Pradesh stands for a floating signifier of whatever urban, educated India doesn’t. Covering 7.3% of the area of India and 16.16% of India’s population, it is crammed with 200 million people suffering from huge poverty and inequality. No wonder the elections here become hugely important.

The Bharatiya Janata Party (BJP) with its allies secured 325 seats in Uttar Pradesh (312 by the BJP alone)—more than 80% of all the seats. This is unprecedented. In the 2012 assembly elections, they had secured a mere 47 seats (contested 398 seats). This is unprecedented. We try to explain what happened here. Not why, but what. Detailed data will take time to trickle in, but some interesting numbers are emerging.

The BJP alone has secured 77.4% of seats in Uttar Pradesh with 39.7% of the total votes. The seat share in 2012 was 11.7%, and the vote share, 15%. This means that while seat share has increased almost seven times, the vote share has increased a mere 2.6 times. What does this mean?

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Aggregating people’s preferences is not easy. In a representational democratic process like India’s, we do not care about how much a candidate is preferred. Elections convert an analogue preference of people into binary win-loss tables. In other words, candidate winning with a margin of 90% in a million-plus constituency will carry the same weight as someone who wins with a 1% margin in a constituency having a relatively smaller number of inhabitants. What matters is the seats, not the number of votes. But in reality, the number of votes reveals preferences. A strong vote share denotes a very strong mandate. A weak value indicates that margins must be thin—in other words, the mandate is not very clear.

Let’s examine the situation of the Samajwadi Party (SP) and the Bahujan Samaj Party (BSP). The SP secured 11.7% seats with 21.8% of votes. The BSP won in 4.7% seats, with 22.2% of votes. In 2012, the SP gained victory by winning in 55.6% seats with 29.1% votes. The BSP got 19.8% seats with 25.9% of votes. What it tells us is that in 2017, the SP and BSP didn’t lose that much in votes but they did substantially in seats. Put simply, they were just very, very unlucky. The Congress on, the other hand, has lost on all counts—from around 6.9% of seats and 11.6% of votes in 2012 to 1.7% of seats and 6.2% of votes in 2017.

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How do we estimate and make sense of these vote- and seat-share dynamics? A few simple, mathematical variables can sum up the idea.

If one looks at the dispersion between seat shares and vote shares, the 2017 assembly elections in Uttar Pradesh were unprecedented indeed. This dispersion is an interesting entry point into the minds of the voters. We can use a variable, ‘effective number of parties’ on the measure of seats (ENP) and votes (ENPv), developed by M. Laakso and R. Taagepera (1979), to understand how competitive the polls were. Mathematically, it’s the inverse of the sum of squares of seat/vote share. An ENP value of 2.6 indicates that hypothetically, elections had 2.6 equal-sized parties. That means, the minimum value of ENP will be 1, when one party takes up all the seats. The maximum value would be the actual number of parties if they all take an equal number of seats.

For the 2017 Uttar Pradesh assembly elections, the ENP and ENPv are the lowest in the last 40 years—the ENP was 1.49 and the ENPv was 3.42. In general, the ENPv is always higher than the ENP because not all votes will translate into a winning mandate. But the interesting thing in these elections is the dramatically low values of the two variables, indicating very little competition.

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The idea of how clearly the aggregate preferences have been able to translate into the election of the ruler can be estimated using the disproportionality index (DI), attributed to M. Gallagher (1991). It shows the extent to which Parliament or the assembly is representative. DI, mathematically, is the square of the difference between seat and vote share. It assumes a value of zero when seat and vote shares are the same, signifying no leakage of political preferences of the voters. At the other extreme is dictatorship, when the value of DI will be 100 (all seats but no votes). A more representative democracy has a low value of DI.

Again, we estimated the values of DI for all Uttar Pradesh assembly elections since 1967. This year’s value of DI has been the highest in history—32.75! This leads us to think about how truthfully their preferences have been translated. A 39% vote share for the BJP is impressive indeed and clearly many people voted for it for the first time. A high DI alongside tells us, however, that the BJP cannot take this victory for granted. If voters are dissatisfied, they may swing in 2022. They are taking a leap of faith, not out of loyalty but perhaps out of hope.

*Yugank Goyal and Arun K Kaushik teach Economics at the O.P. Jindal Global University.*

*Comments are welcome at theirview@livemint.com.*