A recent academic paper on probability theory shows how beliefs are influenced by interpretations of data rather than the data itself, says T C A Srinivasa-Raghavan.
Ever since Indira Gandhi turned it into a closely-held family company -- and even more so since Sonia Gandhi turned it into a brain-dead dinosaur -- one of the hallmarks of the Congress party is that it often ends up doing the right thing for the wrong reasons.
Whether it was the National Rural Employment Guarantee Act or the Right to Information Act or the food security Bill or the land Bill, the story is the same. So, it is entirely consistent that it should be demanding a ban on opinion polls. It has written to the Election Commission requesting it to do so. Its demand has been supported publicly by some important political parties. Others seem to be quietly in favour.
Editorial writers, to whose tribe I once belonged, have also rejected the idea, as has their common bête noire, Narendra Modi. The edit writers, following Soli Sorabjee, have cited Article 19 of the Constitution, which guarantees freedom of speech as their reason. Modi has simply said the Congress is scared of him.
The EC has written to all the political parties seeking their views. No consensus has emerged.
But it should be remembered that the EC has already banned exit polls because it fears they influence undecided voters. It now has to decide whether opinion polls do the same.
How should it arrive at a decision? Merely on freedom of speech grounds or some other forms of analysis as well? A highly technical paper written by three experts on probability theory could help the EC make up its mind.
I have tried below to give a simplified summary. I have also sent it to two Congressmen who will be able to decipher the math in it.
The reason for writing about this paper is that such critical decisions cannot be taken on the basis of opinion alone; there must be rigorous analysis from all academic disciplines, most notably logic and experimental data.
The paper (external link), by Roland G Fryer, Jr, Philipp Harms, and Matthew O Jackson, is called ‘Updating Beliefs with Ambiguous Evidence: Implications for Polarization’. It is based on the theories of an 18th century Presbyterian priest by the name of Thomas Bayes who showed how beliefs could influence probable outcomes. Thus, in the Bayesian system, beliefs play a crucial role.
Fryer, Harms and Jackson’s paper on the polarisation of beliefs is an extension of Bayes’s theorem. That is why it is important in the context of the current controversy over opinion polls.
Their proposition -- which they have proved with the help of a lot of experimental work by psychologists and some advanced math -- is that people look at signals about what’s going on in the real world. Some of these signals are not clear and can be interpreted differently by different people.
What happens then is that people, instead of looking at the whole picture, interpret parts of it sequentially as the signals appear. It is only then that they form a full belief. But because this is based on a series of interpretations, it can lead to beliefs that do not wholly square with facts. That is, beliefs are formed not on the basis of the signals but on the interpretation of those signals that vary from person to person.
The authors say their ‘model provides a formal foundation for why agents who observe exactly the same stream of information can end up becoming increasingly polarised’ in their beliefs. In other words, the same information can lead to different opinions that result in ‘society-level disruptions, intolerance, and discrimination’.
The experimental evidence they have provided in support of this theory is impressive. So, before you reject this highly simplified article on a partial interpretation of the signals it is sending you, I would urge you to read the full paper.
…And in some detail
To understand the importance of this paper, it is important to understand Bayes’s theorem in probability theory. It says that probability can also measure a degree of belief. The theorem then connects this degree of belief before and after the evidence has been collected.
If you happen to believe at the start that a dodgy coin will come up heads twice the number of times it comes up tails, then as the coin is tossed, the degree of your belief may increase and grow stronger with each toss of the coin.
Now apply this to opinion polls. If each successive poll says that party A is ahead of party B and the margin of the lead increases fractionally with each subsequent poll, the voter is not only basing her belief on an interpretation of the data as provided by the pollsters, she is also getting gradually convinced that party A is set to win.
For a large proportion of undecided voters, this could prove crucial when they are finally deciding how to vote. That is, if an outcome seems preordained, even after a large number of polls have had some cancelling effect on each other, only some very stubborn people will ignore the evidence as presented.
To quote the authors, ‘People interpret information as it is received and store the interpreted signal in memory rather than the full information, and this simple modification of Bayesian updating can lead to increasing and extreme polarisation.’
According to them, this problem arises because some of the signals are ambiguous and people store a sequence of information not as the original information but as interpretations in their memory.
Nowhere does this apply more than to Sachin Tendulkar. Many people I know see him as a “failure” now because they have been interpreting partial data instead of the whole of it -- and that too interpretations based on his latest scores, instead of the scores themselves.
If they were polled, they would rate him a mediocre batsman!