Tag: propagation

Gossip Propagation Models

More than ten years ago, back when I was at IIT Madras, I considered myself to be a clearinghouse of gossip. Every evening after dinner I would walk across to Sri Gurunath Patisserie, and plonk myself at one of the tables there with a Rs. 5 Nescafe instant coffee. And there I would meet people. Sometimes we would discuss ideas (while these discussions were rare, they were most fulfilling). Other times we would discuss events. Most of the time, and in conversations that would be entertaining if not fulfilling, we discussed people.

Constant participation in such discussions made sure that any gossip generated anywhere on campus would reach me, and to fill time in subsequent similar conversations I would propagate them. I soon got to know about random details of random people on campus who I hardly cared about. Such information was important purely because someone else might find it interesting. Apart from the joy of learning such gossip, however, I didn’t get remunerated for my services as clearinghouse.

I was thinking about this topic earlier today while reading this studmax post that the wife has written about gossip distribution models. In it she writes:

This confirmed my earlier hypothesis that gossip follows a power law distribution – very few people hold all the enormous hoards of information while the large majority of people have almost negligible information. Gossip primarily follows a hub and spoke model (eg. when someone shares inappropriate pictures of others on a whatsapp group) and in some rare cases especially in private circles (best friends, etc.), it’s point to point.

 

For starters, if you plot the amount of gossip that is propagated by different people (if a particular quantum of gossip is propagated to two different people, we will count it twice), it is very well possible that it follows a power law distribution. This well follows from the now well-known result that degree distribution in real-world social networks follows a power law distribution. On top of this if you assume that some people are much more likely to propagate quantums of gossip they know to other people, and that such propensity for propagation is usually correlated with the person’s “degree” (number of connections), the above result is not hard to show.

The next question is on the way gossip actually propagates. The wife looks at the possibilities through two discrete models – hub-and-spoke and peer-to-peer. In the hub-and-spoke models, gossip is likely to spread along the spokes. Let us assume that the high-degree people are the hubs (intuitive), and according to this model, these people collect gossip from spokes (low degree people) and transmit it to others. In this model, gossip seldom propagates directly between two low-degree people.

At the other end is the peer-to-peer model where the likelihood of gossip spreading along an edge (connection between two people) is independent of the nature of the nodes at the end of the edge. In this kind of a model, gossip is equally likely to flow across any edge. However, if you overlay the (scale free/ power law) network structure over this model, then it will start appearing to be like a hub and spoke model!

In reality, neither of these models is strictly true since we also need to consider each person’s propensity to propagate gossip. There are some people who are extremely “sadhu” and politically correct, who think it is morally wrong to propagate unsubstantiated stories. They are sinks as far as any gossip is concerned. The amount of gossip that reaches them is also lower because their friends know that they’re not interested in either knowing or propagating it. On the other hand you have people (like I used to be) who have a higher propensity of propagating gossip. This also results in their receiving more gossip, and they end up propagating more.

So does gossip propagation follow the hub-and-spoke model or peer-to-peer model? The answer is “somewhere in between”, and a function of the correlation between the likelihood of a node propagating gossip and the degree of the node. If the two are uncorrelated (not unreasonable), then the flow will be closer to peer-to-peer (though degree distribution being a power law makes it appear as if it is hub-and-spoke). If there is very high positive correlation between likelihood of propagation and node degree, the model is very close to hub-and-spoke, since the likelihood of gossip flowing between low degree nodes in such a case is very very low, and thus most of the gossip flow happens through one of the hubs. And if the correlation between likelihood of propagation and node degree is low (negative), then it is likely to lead to a flow that is definitely peer-to-peer.

I plan to set up some simulations to actually study the above possibilities and further model how gossip flows!

Festivals and memes

We don’t normally celebrate festivals. We don’t particularly enjoy them. The only festival we celebrate to some degree is Dasara, when we set up dolls and invite people home to view the dolls. Of course, the last couple of years it’s been similar arrangements and there hasn’t been much innovation in what we do, but we enjoy it as a process and hence take forward the festival. Last year, we even got some fireworks during Deepavali and burst them. Again – it was a fun element. We aren’t too enthused by rituals and since most other festivals are little more than rituals we don’t celebrate them.

The wife, however, sometimes have existential doubts. “There must be a reason that our ancestors celebrated these festivals”, she pops up from time to time, “so it may not be correct on our part to simply stop celebrating. We should take forward the tradition”. This is question that comes up each time we don’t celebrate a festival (which you might guess is fairly often). Before today I hadn’t been able to give a convincing reply either way – whether it makes sense to follow our instinct or if it’s a cultural duty to take forward the tradition.

Towards the end of his classic book The Selfish Gene, Richard Dawkins introduces the concept of the meme.  In fact it was Dawkins who “invented” the concept of the meme. It is meant to be a cultural analogy to the gene, and it’s a “cultural’ concept that propagates like biological concepts are taken forward through the generations via genes. Given the multitude of so-called memes that keep popping up every other day, I’m sure all of you know what meme means. I’m just providing the context here since my argument depends on the original Dawkinsian definition of the meme.

Let us say that there is a genetic attribute I inherited from my father, let’s say it’s my height (my father was 5 feet 10 inches, and I’m an inch taller than that). Now, it is not necessary that this particular gene is passed on to my progeny. It is not even necessary that the corresponding gene from my wife gets passed on – there might be a mutation there and despite the wife and I being fairly tall (by Indian standards) we cannot rule out producing a short child. The point I’m trying to make is that while genes propagate, not every trait needs to pass on from you to your offspring. Only a few traits (chosen more or less at random when your and your gene-propagating partner’s genes undergo meiosis) get passed on. Yet, through the network of you and your siblings and cousins and extended family, the family’s genetic code gets passed on.

Now, festivals and other cultural practices can be described as memes. We in the Indian society have a set of memes, which are called “Ganesh Chaturthi”, “Deepavali”, etc. That these memes have survived through the generations shows their strength – who knows about festivals that had been invented but didn’t survive. Now, the fact that we have inherited this meme doesn’t necessarily mean that we need to propagate it. Unlike genetics, the choice here is not random combination – it is our personal choice (we can’t decide what genes our offspring inherits from either of us or through a mutation).

So, just like every genetic trait doesn’t need to be propagated from a parent to an offspring, not every cultural trait needs to be passed on. If I were to pass on every cultural trait I inherit irrespective of whether it is desirable, even when circumstances change, undesirable cultural traits continue to exist. This is not efficient. As a society, we have bandwidth only for a certain number of cultural traits, and if traits are passed on without much thought, the bad ones won’t die. And will crowd out the good ones.

So if you were to look at it in terms of responsibility to society, you need to propagate only those cultural traits that you deem to be relevant and important. “So what if everyone stops celebrating Ganesh Chaturthi?” you may ask. If that would happen that would simply mean a vote of no confidence for the festival and an indication that the festival needs to be phased out. If everyone were to propagate only those cultural traits they find useful, traits that a significant proportion of society finds significant will continue to survive and thrive. For Ganesh Chaturthi to exist 30 years hence, it isn’t necessary for ALL families that have inherited it to celebrate it now. As long as a critical mass of families celebrate it, the festival will survive. If not, it probably doesn’t need to exist.

(the choice of Ganesh Chaturthi for illustration is purely driven by the fact that the festival is today).

The Theory of Consistent Fuckability and Ladders for Men

Ok so the popular Ladder Theory states that men have only one ladder. It states that all men want to sleep with all women, and they simply rank every woman on the scale of how badly they want to sleep with her or whatever. Women, on the other hand, have two ladders – the “good” ladder, and the “friends” ladder, which allows them to get close to men without harbouring any romantic/sexual thoughts. Since men are incapable of exhibiting such behaviour, you get the concept of Gay Best Friend.

However, this absence of dual ladders for men exists only if you look at the short term. If you are a man and you are looking for a long-term relationship with genetic propagation as a part of your plans, I argue that the female twin ladders can be suitably modified in order to separate out “friends” from potential “bladees”. In order to aid this, I present the Theory of Consistent Fuckability.

From the ladder theory, we know that every man wants to sleep with every woman. For a fruitful, long-term, gene-propagating relationship, however, this is just a necessary but not sufficient condition. As I had argued in another post, given that divorce is usually messy, the biggest cost in getting married to someone is the opportunity cost of getting into long-term relationships with the rest of the population. And if you are involved in gene-propagation, it is ideal if neither of the propagators cheats on the partner – from the point of view of the child’s upbringging and all such jazz.

So if you are a man and you want to marry someone, you must be reasonably sure that you want to sleep with her on a consistent basis. You should be willing to do her every day. If not, there is a good chance that you might want to cheat on her at a later date, which is not ideal from your genes’ point of view.

A small digresssion here. You might ask what might happen to “ugly” women (basically women considered unattractive by a large section of men). However, the argument is that the market helps you find your niche. For example, if you want to cheat on a woman, there must be other women who are superior (on your scale) to this woman who want you to do them. Assuming that I am extremely unattractive and the fact that not too many “attractive” women will want to do me, I should be able to set my “consistent fuckability standard” appropriately.

Returning to the point, when you are evaluating a woman for MARRIAGE (note it doens’t apply to shorter term non-gene-propagating relationships), you will need to decide if you will want to have sex with her on a consistent basis. And based on the answer to this question, you can define the universe of all women into two – those that you want to do consistently and those that don’t. And they form your two ladders.

Now, reasonably independent (maybe there’s a positive low correlation on one of the ladders) of this consistent fuckability factor, you can evaluate the women on other factors such as emotional compatibility, strengths, weaknesses, culture fit and all that jazz. And rank them on those. And then use this distinction on the consistency factor and you will have your two ladders. So you have the “friends” ladder – which is differnet from the friends’ ladders of women in the sense that you want to sleep with them but not on a consistent basis. And there is the “good” ladder of those who you want to do consistently.

To summarize, consistent fuckability is a necessary but not sufficient condition for a fruitful, multiplicative, gene-propagating long-term relationship; and because of this, under certain circumstances, men also develop a pair of ladders.

Currently listening to: When I’m Sixty Four, The Beatles