Exposing the Irrational Voter, Mathematically!

The Indian elections are right around the corner and the mood is currently in full swing. Check the papers and you’ll barely find any real estate left for anything else (but you can always check back with The Pangean for more). The juries are out and so are the manifestos. The line between celebrities and candidates gets blurrier by the day and election campaigns are quickly turning into promotional tours.

One has to feel sorry for the manifestos, which the majority of voters will probably have only a glance of at most. Studies at the frontiers of decision theory have shown that when people do not pay attention to candidate policy choices, uninformed voters end up making decisions based on personalities. This seems to explain most of the name-calling and on-stage singing that candidates have resorted to.

In the midst of all this, three main talking points have emerged: youth unemployment, farmer’s perils and the safety of women. It is no doubt that these topics will be sticking out as the major drivers of the 2019 Indian election.

Here’s a look at some data that will give us some insight into the State of the Nation. The Centre for Monitoring Indian Economy (CMIE) estimated that 11 million jobs were lost in 2018 – pushing the unemployment rate to 7.38%. A leaked NSSO report pegged the unemployment rate at 6.1%, the highest in over four decades. Things do not look so good for our youth at work.

But what about the farmers, the bedrock of our society? Well, this is where things go further downhill. According to Wholesale Price Index (WPI) data for the month of December released by the Ministry of Commerce and Industry, the WPI sub-component for primary food articles has been negative for six consecutive months beginning July 2018. This is a direct indication of the sliding prices that farmers have been facing for their produce, which has led to innumerable suicides.

Women’s safety is also experiencing issues that India cannot seem to get away from that have been lingering for far too long and are only getting worse. According to a recent poll of 548 experts by the Thomson Reuters Foundation,

“India ranked 1st among the world’s most dangerous countries for women.”

No progress here, ladies and gentlemen.

The situation is dire and the immediate need for change is crystal clear. It is also understood that this summer the onus is on the people to effect change.

But can we trust the voters? How rational are they when it comes to making decisions? How rational are you?

This is where our rant comes to an end and the dissection begins.

Let us play a little game.

Elections are only about promises and promises do not hold up most of the time, so we reduce them to a matter of probability. Now, let’s see how you and your choices fare in our mock election.

Let there be two political parties, A and B, standing in the elections. Party A promises to reduce unemployment by 20%, with a 100% chance of fulfilling his promise. Whereas, Party B promises to reduce unemployment by 35%, with a 15 out of 16 chance of fulfilling his promise. To put it neatly,

Case 1

A: 20% unemployment drop, with certainty (100% Guarantee).

B: 35% unemployment reduction, with 15/16 chance.

Go on. Take your pick. Is it party A or party B? Who would you bank on for the country’s sake?

Ok, here’s a second case to choose from.  Party A promises a 20% reduction in unemployment, only now with a 16% chance of fulfilling his promise. Whereas, Party B promises 35% fall, with a 15% chance. Restating it,

Case 2

A: 20% unemployment drop, with a 16% chance.

B: 35% unemployment reduction, with a 15% chance.

So, whom did you pick? If you happened to pick Party A in Case 1, then you are like the majority, who prefer certainty over chance. For those who chose Party B in the first case, you were ready to take the risk for the greater reward. But there is nothing wrong with either choice, the real game starts with Case 2.

Now, what about Case 2?

Well, here’s the bombshell. Case 2 is equal to Case 1 with a one-sixth chance. That is, Case 2 is the same situation as Case 1, only with a 16% probability. The change between the party’s probability of fulfilling promises in both cases was proportional and thus, renders both cases to be the absolute same.

So if the problem never changed, did your choice of candidates change? From B to A, or A to B?

If you did not, then congratulations, you have rational preferences. If you did, then there are more than a few things at work here.

Let us try another problem of this sort. Whether or not the government promised to deposit Rs. 15 Lakh in everyone’s accounts, it is always possible another party will make a similar promise in the run-up to the elections. Farmers are definitely in need of severe financial help, so take Party A and Party B who make the respective income-support promises:

Case 1

A: Rs 11,000 a year, with an 11% chance

B: Rs 15,000 a year, with a 10% chance

Case 2

A: Rs 11,000 a year, guaranteed (100% chance).

B: Rs 15,000 a year, with a 10% chance, and Rs 11,000 a year, with an 89% chance

Who gets the vote, in each case, this time around? Did you choose the same party both times, or different parties? Choosing different parties is a sign of incoherent decision-making. This is because Case 1 is once again of a similar form as Case 2. There has been no significant change in the factors that should influence your decision-making. Yet there will be more than a few instances of people making unidentical choices for Cases 1 and 2.

Time to do a bit of explaining. Consider these cases as lotteries. Both Party A and Party B have an 89% chance of not fulfilling any promise in Case 1. But wait? Didn’t Party B promise a 10% chance? So it gives us (100% -10%=) 90% chance of empty-handed farmers.

Here, there is the existence of a lottery within a lottery; a compound lottery, so to speak.

The lottery within is actually a 10 out of 11 chance of receiving Rs 15000 and 1 out of 11 chance of getting Rs 0. So when it is nested inside the outer lottery of Party B, we get

B: 11% x [( 10/11 x Rs 15000)+(1/11 x Rs 0)]   + 89% x Rs 0

Which is essentially,

B: Rs 15,000 a year, with a 10% chance and Rs 0, with a 90% chance

I know, things are getting discombobulated in your head, but stay with me. Eventually, what we are left with is a much detailed way to re-write and represent Cases 1 and 2 as nested probabilities.

Case 1

A: 11% x Rs 11,000 +   89% x Rs 0

B: 11% x [( 10/11 x Rs 15000)+(1/11 x Rs 0)]   +  89% x Rs 0

Case 2

A: 11% x Rs 11,000 +   89% x Rs 11,000

B: 11% x [( 10/11 x Rs 15000)+(1/11 x Rs 0)]   + 89% x Rs 11,000

The parts marked in Red are the actual determinants and the only factors when it comes to decision-making between the two parties. The segments marked in Blue are offered by both parties and thus, should not be a determining factor in rational choosing.

So if you ended up choosing A in Case 1 and B in Case 2 (or vice versa), you have just chosen two different answers for the same problem. Do you see it now? That is where rational preferences are violated and we can now find our irrational voter.

After all this, we come to the origins of the problem. The lack of coherence empirically observed above is called the Allais Paradox, and has been the talk of game theorists and psychologists for years. First published in 1953, in the Econometrica journal by French economist Maurice Allais, the Allais Paradox was observed among subjects who, when presented with choices such as the ones above, made snap decisions that were proven to be incoherent upon further study.

Although not everyone got it wrong, a significant number of people made the error which prompted him to wonder whether there was more than just rationality behind human choices. So the Allais Paradox started off as more of a standout against conventional rationality theory, than as the rationality test that it has evolved to today.

Maurice Allais did end up winning the 1988 Nobel Prize in Economics but it was not until 20 years after it was first published, that the Allais Paradox was brought back to the mainstream by Daniel Kahneman. In a way, the Allais Paradox was what got Nobel laureate Daniel Kahneman (2002 Nobel laureate) into economics. He along with Amos Tversky, were two young psychologists back in the 1970s who came across this paradox and were so intrigued by the study of human approach towards uncertainty that they opened up new dimensions in the world of economics and decision-making under uncertainty.

Maurice Allais had made one of the foremost and yet perplexing dives into human rationality and for that, today, the world is in a better position to understand human behaviour and decision-making. And while we are on the topic of making decisions, we get back to the decision of the year.

This election may be driven by 3 central issues: unemployment, farmers and women’s protection. But at the end of the day, it is the people who drive elections. Yet what we often overlook is what drives the people and their choices.

Are we as smart as we think we are? Does being irrational only mean being ‘unreasonable’ or ‘baseless’ as the Dictionary says? Or is there more to this than meets the eye or brain?

On that note, we ask you to think twice before calling someone else irrational. Oh, and yes, don’t forget to think twice before voting. Happy elections!

*31st May, 2019 marks the 108th Birth Anniversary of French physicist and economist Maurice Allais, best known for his contributions to the neoclassical synthesis and the Allais Paradox.


Shohan Mukherjee

All the powers in the universe are already ours. It is we who have put our hands before our eyes and cry that it is dark. -Sw.

The Pangean does not condemn or condone any of the views of its contributors. It only gives them the space to think and write without hindrance.