What’s the worth of each vote? Priceless

Atanu Biswas
Professor, Indian Statistical Institute, Kolkata

What a tremendous effect a single vote might have in democracy! Atal Bihari Vajpayee could possibly be the best person to vouch for it. In 1999, Vajpayee’s 13-month-old government failed to survive a no-confidence motion in Parliament for just one vote. However, that was not a people’s vote directly, and the number of voters was small. But, there are incidences of a victory by one vote in the Assembly elections, too — Santhemarahalli (SC) in Karnataka in 2004, and Nathdwara (Rajasthan) in 2008 — although the chance of occurrence of such an event is understandably small. In the Lok Sabha elections, a nine-vote victory margin occurred twice — Anakapalli in Andhra Pradesh in 1989, and the Rajmahal constituency in Bihar in 1998.

In the US, an entire state is treated as a constituency, and just 537 more votes in Florida could have been enough for Al Gore to win the state and also the entire 2000 presidential election over George Bush. And this is only 0.009 per cent of the votes!

Certainly, we might struggle to understand the worth of our single vote in a big country having 90 crore voters. Can my vote really change the course of election? Andrew Gelman, a Professor of Statistics at Columbia University, has obtained the probability of a single vote changing the outcome of the US presidential elections. In fact, this probability is effectively zero if the voter is in a ‘safe state’ like California, and the odds are one in one crore or better for a voter in a swing state like Florida, Nevada or New Hampshire, which might become one in 10 lakh in the closest state. And, although this probability looks too small, it is 18 times better than the chances of winning the US Lottery!

However, this probability is small due to the ‘winner-takes-all’ rule of the electoral college in the US, where the winner in a state takes all of the state’s electoral votes. This probability would become even smaller in a proportional representation system (as in Israel) where the entire country is treated as a constituency. 

However, in an electoral system like ours, with smaller units like the Lok Sabha constituencies, this probability shouldn’t be that small. I didn’t find any study for obtaining the probability of a single vote defining the outcome of the election in India, and as a statistician, I tried to find that. In our set-up, assuming about 16.5 lakh voters in a parliamentary constituency, and a 66 per cent voter turnout, the probability that my vote would change the outcome of the election of that constituency (that is, there will be a tie among the top two vote-getters excluding my vote) is roughly one in 1,300 if there are only two candidates. However, with more candidates, this probability will be reduced. For example, in a three-candidate set-up, the chance that my vote would determine the outcome of my constituency is one in 4,200, or less.

The chance of obtaining 271 seats among the remaining 542 by any party/coalition is one in 30. And, thus, the probability that my vote would decide the entire election of the country is the product of these two, which is roughly one in 39,000 for a two-candidate setup in my constituency; or one in 1,26,000 for a three-candidate setup  — a much higher chance than in the US, even if the size of the Indian electorate is about four times that of the US, thanks to our electoral system.

Let’s see how much money is spent on the elections. In India’s first General Election in 1952, the Election Commission spent only Rs 10 crore, which was just 60 paise per elector. During the Lok Sabha elections in 2014, the expenditure was Rs 3,870 crore, which was Rs 46 per elector — a three-fold jump over 2009 when it was about Rs 15 per elector. India’s budget allocated Rs 262 crore to the Election Commission this fiscal. The expenditure by political parties and by the government on security measures are on top of that. A candidate for a Lok Sabha constituency is entitled to spend Rs 50-70 lakh; that’s the official limit.

According to US-based expert Milan Vaishnav of the Carnegie Endowment, the 2019 Lok Sabha elections would possibly be one of the most expensive ever held in any democratic country. Vaishnav claimed that 464 parties and over 8,000 candidates spent $500 crore (Rs 35,000 crore) on election-related expenditures in 2014, a sharp rise from the expenditure of $200 crore in 2009. Based on a projection of the New Delhi-based Centre for Media Studies (CMS), Bloomberg estimated that the total election expenditure of the ongoing Lok Sabha elections could rise to $700 crore (Rs 50,000 crore). It might even reach to Rs 60,000 crore, who knows. That’s a huge amount of money, indeed.

I've no idea whether these estimates are correct or not. However, if they are close to reality, about Rs 600 is spent for every single voter in this country, on an average, even if one’s potential to decide the ultimate outcome is one in 39,000 or less. Is that the price tag for our votes?

The barber who does my haircut hails from Chhapra, Bihar. He is off to his native village to cast his vote. One of my neighbours from Odisha went to visit his hometown to cast his precious vote. One of our students from eastern Uttar Pradesh is going to his village to vote. My colleague is going to cut short his Sandakphu trekking to cast his vote in his hometown in Midnapore in South Bengal. All these people, from different segments of the society, with varying socio-economic-cultural-and-political status, have one thing in common. They don’t care whether the price of their vote is Rs 60 or Rs 600. And this, in turn, makes our democracy priceless!