United Voters of India: The Logic of Collective Action (Part 7)

A Single Vote

Logically speaking, voting in an election is an exercise in futility. A single vote makes no difference to the eventual outcome of a contest for a Lok Sabha seat. Here’s why. If a contest is decided by, say, five voters then each of the five votes matter enormously because if two voters vote one way and the two others vote the other way, then the fifth person’s vote decides the outcome. However in a contest that has nearly 2 million voters (a typical Lok Sabha constituency), no person’s vote will ever be the decisive vote.

Here is an explanation from Robert Wiblin (in the US context, but applicable to any election):

We can start small. Imagine that you’re on a small committee making a decision. The odds that you’ll change the outcome of a vote like that — assuming 2 options and 4 other voters, each 50% likely to vote for either option — is about 19%. We could confirm that empirically if we liked.

We can then work upwards to the size of national elections: with 8 voters it’s 14%, with 16 voters it’s about 10%, with 32 voters about 7%, and so on. In fact, the likelihood you’ll change the outcome ends up being roughly proportional to one over the square root of the number of voters.

Statisticians who specialise in politics add real polling data to the mix, and compare it to actual election results to figure out how accurately polling predicts how people will vote. This gives them a ‘probability distribution’ for the likelihood that each elector will choose to vote for each candidate.

With all of this information in hand, we can go ahead and model tens of billions of elections to estimate how often the entire result will be changed by a single vote.

The famous statistician Andrew Gelman of Columbia University has done just this for US presidential elections, which are broken down into states, and has published several papers outlining the results.

He found that if you’re in a ‘safe state’ like California, the odds of your vote changing the outcome of a presidential election really is effectively zero (the model spits out 1 in 100 trillion, but it’s very hard to assign meaningful probabilities to something so unlikely). Something similar would be true for voters in ‘very safe seats’ in the UK or Australia.

So, a single person’s vote makes no difference in the outcome of the election. But what if a collective of voters came together and publicly said prior to an election, “We will all vote and vote as one”? If their number exceeds the typical winning margin, they can be the swing vote that determines the outcome of the election. Politicians and their parties have to listen to them if they are to retain (or gain) power. As the phrase goes, “Boond boond se banta sagar.”

Tomorrow: Part 8

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Rajesh Jain

An Entrepreneur based in Mumbai, India.