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Vote share politics: Lessons from the Bihar verdict

By Yugank Goyal and Arun Kumar Kaushik
Last updated on: December 08, 2015 11:46 IST
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More than predicting the nature of elections, a closer scrutiny of seat and vote share difference yields an important tool to assess the value of our democratic process, say economists Yugank Goyal and Arun Kumar Kaushik

In September, we published an article on the Bihar elections, in the Economic and Political Weekly. In that article we departed from mainstream narratives of speculating who may win the elections, and who would lose. Rather, we relied on numbers, and numbers alone.

For us, the numbers revealed that the previous election results were the only source of making any predictions. This meant, we did not predict who will win the elections, not which party will lose. We could only surmise as to what type of elections and mandate we will see this year.

That is why, while election results were shocking to many, they weren't to us. We made two predictions. Firstly, the quality of verdict will improve, and secondly, the Janata Dal-United may not repeat the success of the 2010 assembly elections. On both were spot-on.

In this article, we explain our methodology and the terms we relied on making these predictions. For some, this could be very basic. Yet, it is a good tool to analyse the quality of electoral outcomes. More importantly, we will show why some numbers must not be ignored.

For instance, consider three constituencies A, B and C with 100 people each, where political parties X and Y are competing in an election. X gets 90, 49 and 49 votes in A, B and C respectively, while Y gets the remaining 10, 51 and 51. X wins in A, and Y wins in B and C. Y comes to power. Simple enough! But note that X got 188 (90+49+49) votes in three constituencies while Y got 112 (10+51+51) votes.

Clearly, at aggregate level, more people wanted X to win the elections. But Y becomes the ruler. This is precisely the much talked demerit of the 'first past the post' system that the Indian electoral system uses. It is possible to have a highly disproportional representation.

Y had a higher seat share, while X had a higher vote share.

If a democratic process ought to reflect the will of the people, indeed, votes are more important than seats. But in representative forms of government like India, we do not vote for our leaders at the positions of prime minister or chief minister. We vote for constituency's leaders, and their number determines who assumes the positions of PM or CM. This means that total votes don't count, and all that matters is constituency level votes.

One can say that when indirect representation occurs (like in India), people's collective preferences are leaked. Representative democracy converts an analog preference of people into binary 'winning or losing' tables.

In other words, how much a candidate is liked or disliked becomes irrelevant. Only winning and losing matters. In singularly emphasising what winners want, this mechanism disastrously ignores what people want.

The moment voters choose their candidate in a constituency, they implicitly and unknowingly assume the leakage of their mandate when a government will be chosen.

Perhaps total votes must matter, and not just total seats. This is because it is the aggregate voting pattern that reflects how representative Parliament or the Lok Sabha is, not individual constituencies.

When a leader is chosen not by voters, but by those representatives elected directly, 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 quantum of people's will s/he carries with him in victory.

The nature of constituency victories become meaningless. Constituency level winners -- regardless of how much did they win by -- exert equal mandate in forming the government. This clearly means that while people's preferences in a high-margin victory is diluted, that in a small-margin-victory is strengthened.

We must recognise that to understand voting preferences and election dynamics, measuring how much of people's preferences have leaked is important.

If the aggregate preference of people does not get translated in power, it leads to unsatisfied voters. In other words, in a democracy like India, a loser's followers can be numerically more than a winner's.

Hence, in the 2014 Lok Sabha elections, the party with the third highest number of votes did not get a single seat in Parliament (the Bahujan Samaj Party). Differently put, the third largest bunch of voters are not represented at all.

They will begin to matter in the next elections. In other words therefore, people happy with the verdict is one part of the story. There is a lot happening in the unhappy quarters.

This unhappiness is measured by taking the difference between vote share and seat share. Seat share is the ratio of seats won to the total number of seats contested. Vote share is the ratio of number of votes received to the votes polled.

Analytically, these are terms akin to the strike rate in cricket. Political scientist Michael Gallagher developed an index (external link) in 1991, by squaring, subtracting and taking square roots of the terms (a neat way of removing the negatives).

This index, called the Disproportionality Index tells us how representative an assembly/Parliament is. DI takes a value of zero when seat share and vote share are the same.

This means the assembly is 100 per cent representative, and the people's will has been translated without any leakage. On the other extreme is dictatorship, when the vote share is zero, but the seat share is maximum, giving the DI value as 100.

In general therefore, the higher the value of DI, the farther we are from being a truly representative electoral outcome.

Alternatively, one can think of a higher value of DI leading us to an assembly which does not adequately reflect the will of the people. In other words, a high-value DI means an unhappy electorate.

In our Economic and Political Weekly article, we measured the values of DI for 13 elections in Bihar since 1951. he results were striking. The average value of DI has been 17.66. More interestingly, the DI value has been consistently increasing in the last three elections from 9.81 (in 2000) through 17.48 (in 2005) and reaching an all-time historic high at 35.4 in 2010.

In an article published in the Economic and Political Weekly in 2012, Arun Kaushik (with Rupayan Pal) showed that in the Lok Sabha, the highest value of DI has barely touched 20.

What are the lessons learnt from the current election results in terms of representativeness of the Bihar assembly?

In our editorial published in Live Mint newspaper, we examined the algebra of the Bihar assembly. The value of DI came down significantly in the current assembly when compared to the previous assembly, even though it is still quite high, at 24.13.

As compared to the last assembly, this assembly is more representative. In fact, for the Bharatiya Janata Party the seat share and the vote share has been quite close -- 21.8 per cent and 24.4 per cent.

The high value of DI represents the disproportional win for the Mahagathbandhan (JD-U+Rashtriya Janata Dal-Congress). As the grand coalition received 73.25 per cent seats with just 41.9 per cent vote share whereas the National Democratic Alliance (the BJP and its allies) received 23.8 per cent with 34 per cent vote share.

In other words, the NDA is under-represented and the Mahagathbandhan is over-represented in the current Bihar assembly.

More than predicting the nature of elections, a closer scrutiny of seat and vote share difference yields an important tool to assess the value of our democratic process.

The 2012 Economic and Political Weekly paper argued for the need for electoral reforms in view of this disproportional representation. In a fragmented electorate where caste and religion become central, an inquiry into difference in seat and vote share could furnish valuable insights into the electoral reform processes.

Yugank Goyal and Arun Kumar Kaushik teach economics at the O P Jindal Global University, Sonipat.

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