random numbers – Pertinent Observations

Yesterday, the wife wrote a nice blog post on the power imbalance that mutual-like based matchmaking services like Tinder create – since they notify the mutual like immediately after the second counterparty has liked, it is evident to both who liked whom first. And that creates an inherent power imbalance in the relationship, even before it has begun.

She goes on to say that it’s better if these services waited a random amount of time after the second like in order to notify the mutual like. That way, it would be unclear who liked whom first, and that can lead to a more balanced relationship. Here I intend to put on my quant hat and quantify how this random wait period should be determined.

First of all, it must be quite clear why this wait period needs to be random – if it is deterministic, users can be able to back-calculate (after they’ve gotten a few data points themselves) and determine who liked first. Randomness eliminates any such possibility of back-calculation.

Now that this is established, what should the random wait period be? Should it be a minute? Or an hour? Or a day? And what kind of distribution should the random number be drawn from?

The thing with apps such as Tinder is that they match people at different time scales. The intent is for instant match – so that two people who are checking out each other at a bar or a wedding hall can know that mutual like exists, and do something about it while they’re still in close proximity.

In a market such as India, however, where Tinder has still not built up much liquidity, some matches are “offline” – I check you out and “like” you today. You come across my profile tomorrow and like me back. Notice that this time scale is an order of magnitude higher than the bar/wedding timescale. So the random number generator needs to take care of this.

If the random wait period is a lot number, it might work well in the bar/wedding case, but not in the offline like case – if i’ve liked you yesterday and get notified today, I know I’ve liked you first. A high random wait period, on the other hand, can kill the bar/wedding market – there is no use that there was a mutual match at the wedding you attended yesterday, for there’s nothing you can do about it now.

So the solution is rather simple – the random wait period should of the same order of magnitude of the time difference between the two likes. If the two likes have happened minutes apart, the wait should also be minutes apart. If hours, then hours, and so on. The best way to achieve this is to use the time difference between the two likes as a parameter in the random number generation.

And what kind of a distribution should be used? I argue that the distribution should be something closer to an exponential distribution than something closer to a normal distribution. This is because the latter has a long “left tail” as well, and that can be used by users to double guess the minimum possible time before the notification that the last like happened, and know the power balance. Exponential distribution, on the other hand, doesn’t have much of a left tail, and can fuck better with the minds of anyone who tries to double guess.

Moreover, the exponential distribution can be described with one parameter. And we want the wait period to be a function of the time difference between the two mutual likes. It should be easy to build this in without further assumptions!

This is an idea that’s been in my head for a while. About whether it is possible to nudge people who normally travel in cars to use public transport by simply flooding the roads with buses. The motivation for this comes from the hassles associated with marking and enforcing bus lanes, a form of public transport that is generally considered superior to subway trains in terms of cost of implementation and effectiveness.

So the idea is that as the number of buses on the road increases, the average speed of cars comes down. And after a point, the number of buses on the road means there’s enough supply that one can travel comfortably in them. And there will come a point when people will give up their cars in favour of buses since they can now spend the time more usefully rather than waste it by concentrating on the road.

Of course, this point is still far away for a city like Bangalore, though the BMTC has been making efforts, with initiatives such as the Bus Day. Still, now I’ve begun to have my doubts about it. About whether just increasing bus connectivity and frequency and quality will be enough to take cars off the road. I’ve begun to think if the comfort of not having to drive but travel at the same speed is enough to compensate for the cost of walking to and from bus stops and waiting for buses. The other cost of traveling by bus is that once you get into a bus you travel by a fixed route rather than adapting to daily traffic flows.

The important thing here is the distribution of waiting time for catching a bus. If a passenger is convinced that he is very likely to get a bus within a certain span of time with a very high probability (using vague words to avoid putting random numbers) he is likely to wait for a bus. However, if there are no such bounds, then the passenger might choose to travel by an alternate means of transport.

Still it needs to be seen. From what I know, all cities that currently boast of great public transport actually built a lot of the basic public transport infrastructure before the boom of cars in the place. I can’t recall off the top of my head any city that has actually nudged passengers from personal cars to public transport after cars had become default mode of transport (if you know of such cases, please let me know). In that sense, this nudging towards public transport is still a hard problem to solve. Nevertheless, I still think it might still be a good idea to try crowd out private transport by public transport.

Tag: random numbers

Better matchmaking through random numbers

Crowding out with public transport