Kejriwal, Katiyabaaz and Price of Anarchy

“Yes, I am an anarchist”

  • Arvind Kejriwal , Chief Minister of Delhi on 20th Jan 2014.

 

Yesterday Arvind Kejriwal won landslide victory; people have raised him to iconic status. Opposition leaders are getting vicarious pleasure from Kerjriwal’s victory. Kejriwal will now have tough time in remaining humble. He has made lot of promises like cutting electricity bill by half, free Wi Fi, make Delhi a safe place for women, all illegal residential colonies will be made legal and so on.

power theft

A Mumbaikar like me cannot understand voting preferences of Delhities. But simple maths will tell you that to fulfil promises he needs money equal to 5 times the current budget. Question is how will he raise money? Either increase taxes or lower expenditure. Given his Santa Claus like image he can do neither. Plus he may have to go on strike on regular intervals to maintain his anarchist image.

kejriwal

One person who can help him in this Katiyabazz, local electricity thief, this person can give illegal electricity connections; this will lower electricity bills of lot of Delhities.  In fact it was his Katiyabazz like stunts that won Kejriwal earlier election. In this process electricity distribution companies will suffer, but then that is a small price to pay for populism.

katiyabaaz

Moving from politics to economics, the Price of Anarchy is a concept in game theory that measures how the efficiency of a system degrades due to selfish behaviour of its agents.

Let take an example of a town where 10 cars have to travel from point A to point B. They can take two routes, one is highway which takes 10 minutes and second is narrow road. Narrow road takes less time but there are certain conditions. If only one car travels, it will take one minute, if two cars travel at same time it will take 2 minutes and so on, if 10 cars enter narrow road, there will be chaos and it will take each car 10 minutes to cover the distance.

Given option everyone will opt for narrow road. City authorities decide to make a rule that 5 cars must take highway and rest will go via narrow road. Total commute time = 50 + 25= 75 minutes, so average travel time is 7.5 minutes. But during elections, to gain votes the city authorities decide to repeal the rule and now everyone is free to choose his own route. Result is all 10 cars start using narrow road, so average travel time is now 10 minutes. So average extra time is 2.5 minutes.

The Price of Anarchy here ratio of extra time over global optimum, i.e. 2.5 mins/7.5 mins, which is 33%.

Price of Anarchy has wide applications it can be applied to electrics power and communication networks.anarchist

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