The subtle art of overcounting

 A few months ago I posted an article in this blog about Income tax and who actually pays them. If you can't find them in the mountain of articles in my blog, here is the link. I found what I was hoping for with that article. Some people actually read it and disagreed with me. In almost the same time, I was noticing some posts on LinkedIn, with people complaining about paying 48% taxes in India. Being the saint that I am, I immediately went ahead and wrote a comment saying how they are wrong and I am right. This article is an elaborate version of that, so that I can control myself when I eventually see the same post during March next year.

 

The post in question claims that Indians ( well-off indians ) pay 30% of their income as Income tax, and then are forced to pay 18% ( on average ) as GST on everything they buy, which brings their total tax contribution to a whopping 48%. That is day-light robbery right ?

Side rant about our actual income

Like it was argued in the income tax article, there is another way to look at our income. Let us consider an item in Amazon ( say a hard drive ), which is priced at 3000 rupees during a sale. But it is not just 3000. It is a humongous 80% discount on its original price of 12000. Before throwing money at Amazon, we take a look at Flipkart to see if the same thing is cheaper. To our shock it is cheaper there. At 2800, it is 200 cheaper than Amazon. But to our dismay, we notice that it just has a 50% discount on the original price of 5600. Will you go with the 80% discount or the 50% discount ? If you say you will take the 80% discount, Congratulations ! You could be famous in LinkedIn one day, if you tried. If you chose to go with the 50% discount, please read ahead.

 

Just like how, the same hard drive doesn't become just because it was initially priced at 12000 instead of 5800, the CTC we "get" doesn't mean anything. It is the money that we actually get to spend, that matters. This is the same argument from the previous article.

 

Rant over.

Now moving on to the next point. Lets delve into the more problematic part of the post. It says we pay a 30% income tax and a 18% GST on things we buy. This is a common line of reasoning I notice everywhere. But the problem hides in our assumptions. This assumes that all the tax burden is on you, and nobody else who is transacting with you has any tax burden. Kinda narcissistic, no ? It makes a lot of sense why this kind of reasoning is popular with LinkedIn influencers.

The Fatal Assumption

Why is that assumption "fatal" to the argument ? Let us remove the assumption, and open our worldview slightly a bit away from ourselves. As mentioned in the previous article, the Income tax you pay, is part of the company's expenditure. The 18% GST levied on your last visit to KFC, is money that KFC has to pay to the govt too. So the same thing can be framed in such a way that you are not paying any of these taxes. But obviously the truth is somewhere in the middle like all things in the world.

 

Another similar reason why it is wrong is the fact that we are over-counting.

 

Over-counting ( Double-counting in specific )

Over-counting is the phenomenon where we count the same things multiple times while making a total. This is very common in Combinatorics. Rather than doing a bad job of explaining this, I will link an article about this here.

A very simple example is a typical IPL season with 8 teams. Each team plays 14 matches in the league stage. But still the total number of matches in the league stage is only 56 ( = (8*14)/2 ) rather than 112 ( = 8*14 ). This is because every match is counted exactly twice, when we add the total number of matches each team has played.

 

Strategic over-counting is very useful in some cases. It can be used to mislead also in many cases.

 

While counting the amount of money we pay as taxes in the above way, if we are not being narcissists, we will end up counting every bit of taxes we pay exactly twice. The income tax is paid both by the company and us. The GST is paid both by us and the service provider. Lets say we work in KFC, we earn 1000 Rs. and pay 300 as income taxes. The next day we go to another KFC and buy for 200, and pay 36 as GST. The total tax expense from our side is 336 and the tax expense from KFC is also 336. But was the total amount that was paid, 672 ? 

 

The not so wrong way of counting

Above is how not to count. But then how do we count ?

 

One way is to fix a particular direction, say outflows(or inflows), and count only the taxes incurred in them, as our own tax expenditure. In every transaction there is only one person, for whom it is an outflow(or inflow), thus avoiding double counting.

Another way is to go the mathematics way of halving the total tax expenditure incurred. Since all the taxes are incurred by exactly 2 entities, it does make sense to take equal responsibility in them.

So you are either paying only one of those taxes , or you are paying exactly half of it. We can pick whatever we want, as far as i can see.

The ( somewhat counter-intuitive ) double edged sword of Comforting Lies

 Every one of us must have been a recipient of a comforting lie at some point in time. A comforting lie, is a lie which is supposed to make the recipient of the lie feel more comfortable than when the truth is made known to them. "Everything will be alright", "You are beautiful", "You are very intelligent", "This article in your blog is very good" are some of these phrases which are usually used as comforting lies. We all know why we lie to comfort our friends.

But as a recipient of a lot of those, I am starting to feel maybe there is another side to this habit. If comforting lies are meant to make the recipient feel good, and if the recipient knows the person saying the lie, doesn't want to hurt them, I am seeing a game theory style problem here. What if the person receiving the lie, finds out that it is a lie ? How does it affect the comfort-level or feelings of the recipient ?

Lets not tell another comforting lie by thinking that comforting lies are selfless and are meant to make someone happier. Comforting lies are almost always selfish. Either it is the selfish need to not face an uncomfortable situation of having a sadder friend, or it is the selfish motive to not get involved in the situation at all. But again.. Selfish isn't wrong always. Our society is built on the assumption that people will try to be selfish. So whats the problem ?

When I realize the true nature of a comforting lie, two things happen. My internal distributions ( probability distributions of my own opinions about myself ) get readjusted drastically to adjust for the reveal. Then guilt kicks in due to the fact that I had put someone in a position, where they had to lie to comfort me. I imagine it is not that different for other people also. I have been rightly caught many a time fishing for complements. I start to wonder if I put someone in that difficult situation so that they had to take the bait, to end the suffering. 

In addition to all this, somehow the distributions end up in a worse state, than it would been, if the truth was revealed in the first place. I will one day try to make a proper probabilistic analysis to see if it makes any mathematical sense. But it might be because of the fact that someone had to lie, the mind wonders if the situation is much worse than thought. Resentment usually follows this, and the distributions inside my mind for judging the liar's opinion of something changes to adjust for the lie. 

So, it is a loss for both the people involved here. The recipient ends up feeling worse. The liar loses credibility, and also (un)succesfully managed to make the recipient worse than if he had chosen to say the truth, in addition to the fact that any future honest opinions will be most likely be treated as a comforting lie. The next time the same liar tries another comforting lie, it becomes easier to catch and more hurtful. It is one of those counter-intuitive exponentially worsening situations, we as humans, are constantly stumped by.

But what am i peddling here ? Do I really want everyone to be brutally honest, all the time ? Probably not. Do I want people to be better liars ? Maybe. Did I post this because I wanted a somewhat honest review of the articles I post here ? Yes!.  I want people to consider the negative impact a comfortable lie can have on the person, if the person realizes it is a lie, and judging by the lies I am constantly fed, often by the same people, most of us don't understand it. If the ultimate aim is to make our friend feel better on average, sometimes the optimal way is to just say the hurtful truth.