# Mata Amrita Index needs a new dimension

Some of the hugs look too flimsy for a 10-year reunion
Pinky

As anyone here who has tried to construct an index will know, any index, however well constructed, will end up being way too simplistic, and abstract away way too much information. This is especially true of indices that are constructed as weighted averages of different quantities, but even indices with more “fundamental” formulae are not immune to this effect.

Some eight years ago, I constructed an index called the “Mata Amrita Index“, which my good friend Sangeet describes as the “best ever probabilistic measure” he’s come across. It’s exactly that – a probabilistic measure.

Quoting from the blog post where I introduced the concept:

The Mata Amrita Index for a person is defined as the likelihood of him or her hugging the next random person he/she meets.

Actually over time I’ve come to prefer what I’d called the “bilateral MAI”, which is the probability that a given pair of people will hug each other the next time they meet. The metric has proved more useful than I had initially imagined, and has in a way helped me track how some friendships are going. So far so good.

But it has a major shortcoming – it utterly fails to capture quality. There are some people, for example, who I don’t hug every time I meet them, but on the random occasions when we do hug, it turns out to be incredibly affectionate and warm. And there are some other people, with whom my bilateral MAI tends to 1, but where the hug is more of a ritual than a genuine expression of affection. We hug every time, but the impact of the hug on how I feel is negligible.

In fact, I’d written about this a couple years back, that when the MAI becomes too high, the quality and the impact of the hug inevitably suffers. Apart from the ritualness of the hug robbing it of the warmth, a high MAI also results in lack of information flow – you know you hug as a rule, so the hug conveys no information.

So, now I want to extend the MAI (all good index builders do this – try to extend it when they realise its inadequacies) to incorporate quality as well. And like any index extension, the problem is to be able to achieve this without making the index too unwieldy. Right now, the index is a probabilistic measure, but not that hard to understand. It’s also easy to adjust your bilateral MAI with someone every time you meet.

How do you think I can suitably modify the MAI to bring in the quality aspect? One measure I can think of is “what proportion of the time when you meet do you hug, and it makes you feel real good?”. As you can see it’s already complicated, but this brings in the quality component. The ritual hug with the high MAI counterparty makes no impact on you, so your modified MAI with that person will be low.

The problem with this Modified MAI (MMAI) is that it is automatically capped by the MAI, given the “AND” condition in its definition. So a person you hug infrequently, but feel incredibly good after each such hug, will have a low MMAI with you – it’s more to do with the low frequency of hugging than the quality.

If you can think of a more elegant measure, do let me know! Whoever said building an index is a simple process!