## Storytelling Science

## Mad Scientist's Election

Amitabha Mukerjee

Like most people, I bet you haven't heard of my new political party, MSP (Mad Science Party). Yet we are winning in this elections.This is because we are not at all competitive. "Long Live Atal-ji, Long live Sonia," is our slogan. "Live and let live."

Here is my winning pitch. There are 543 seats in Parliament. In 271 districts, we have tied up with BJP and Allies. In another 271, we are tied up with Congress and its allies. All we asked is that in the one measly seat remaining, they leave us alone, so we win without hassles. So, here is what we will have:

"Bah!" you are saying – "What good is one moth-eaten seat, against those big sofas?"

Cong and co (C) – 271

BJP and co (B) – 271

MSP (M) – 1Hold your horses. To form the government, the winning group must have 272 seats. Here are all the ways this can happen:

C+B, C+M, B+M, C+B+MIn this list, the last coalition is not as important, because if any of the three partners drop out, it still survives, so no one is critical. Of the others, C is critical in 2 out of 3 possibilities, as is B. This indicates the power of these big parties – since they have so many votes in the assembly, they will form the government in any two out of three scenarios.But look at my party, M – it also appears in 2 out of 3 possibilities! Although we have only

oneseat, our power is actually the same as C or B, for we can be in as many majority coalitions as they!You are saying – "Hah, all this is bogus and you are just a mad scientist!" But this is reality, and it happens all the time – just a few years back Deve Gowda became PM with 17 seats. This is exactly what this arithmetic says. In an assembly with a (271,271,1) breakup, the party with the one seat is as powerful as that with 271.

The Mad Science Party is going to show the world how mathematics actually influences lives. Democracy strives for equality between its members, and "one man, one vote" is its rallying cry. However, sometimes "one vote" can be "equal" to 271!

## Power Struggles in your Family

Let us now turn to your own family – Father, Mother, Daughter, Son, say. With some indulgence from the ladies, let us make Father(F) the most powerful figure, so his opinion counts for 8 votes. Despite being India, this is an enlightened HT-reading family, so Mother(M) is nearly equal and has 7 votes. Each child has a flimsy 1 vote each. Now assume the family has the rule that important decisions need 9 votes (e.g. what car to drive, what flavour of ice cream to buy).So. How many ways can someone be in the deciding group? The players (F,M,D,S) have (8,7,1,1) votes. 9 votes are needed to pass a decision.

Here are all the ways to form a winning coalition: FM, FD, FS, FMS, FMD, FDS, FMDS, MDS. F is critical in the first 6 – i.e. if F opted out it would no longer be a majority. Similarly, M is critical in FM and MDS. Surprisingly, the children are also critical in two situations each. So, when the children and the mother disagree, the children are actually as likely to get their way as the mother, i.e. they are just as powerful as mother!

## Measuring Power: The Banzhaf Power Index

This notion is captured in the Banzhaf Power Index, which is one of several measures of power that emerge in a fascinating area called Game Theory. Let us say that player "i" is critical in Bi number of situations. Now Bi situations are a subset of the total number of situations B. The larger Bi is in relation to B, the higher the power of the i-th player. This can be captured by its fraction of the critical situations, i.e. Bi divided by B.So for the family here, we see that the number of times (F,M,D,S) is critical is (6,2,2,2) respectively – so Father is critical in 6 ÷ 12 situations and has a Power Index of 50%. Mother, at 2 ÷ 12 or 17%, unfortunately has the same BPI as the children.

Before you mothers all get mad at me, let me tell you that in my own case, I, the father, have a meager 1 vote – our family votes go (1,8,4,4), and the same 9 votes are needed for a decision. So can you tell me if I would have been better off in a (7,8,1,1) situation?

And yes... the children are as powerful as a parent! The advertisers, you see, knew this all along! Just as the third parties know their power in a "trishanku" lok sabha...

Finally, here's a top secret you can use. It is clear as day that after the elections, the Mad Science Party will be very powerful indeed. We will form the cabinet, with both the BJP and the Congress offering to support it, possibly from "the outside". With this kind of power, you can be assured that all our supporters will become ministers in our hyper-bloated-cabinet. So come join the MSP today and who knows – you might just become the Minister of Tall Tales. . .