How (Not) To Design a Lottery

Early this year, the Romanian Government, through the Finance Ministry, decided to organize a lottery of receipts. The aim was to encourage Romanians to ask for the receipt at (small) shops, restaurants etc. The goal was to tackle tax evading done by small businesses.

Naturally, the rules of the lottery couldn’t focus only on small shops and restaurants (equal opportunity), therefore all receipts were accepted in the lottery.

About two weeks ago there was the first draw of the lottery… and here’s where things started to go bad.

As in any lottery there are two components: (1) the prize and (2) the probability of winning.

The prize of the lottery is 1.000.000 lei (local currency) which is approximately 220.000 Euros. That’s not bad, all in all.

The probability of winning is rather difficult to understand, but, in this case is rather simple. The lottery is organized each month and the random algorithm determines: (1) a day and (2) an amount. For example, the winning receipts are all receipts from February N^th that are of X lei (the decimals don’t count). X can be between 1 and 999 lei.

Applying a simplistic computation, the probability of winning the lottery is 30 (number of days in a month) * 1000 (approximation of the number of possible amounts on a receipt). This means that the chance of winning the lottery is 1 in 30.000.

This might look like a small chance, but in reality it isn’t (at least when it comes to lotteries). In a country of about 18.000.000 people it is very likely that there will be lots of winners… at there were… between 8 and 9 thousands people who registered with the tax authority to claim their prize in the two weeks after the first draw.

Just as a note, in this first draw receipts from 50 days were able to win, thus the chance of winning the lottery was 1 in 50.000.

Assuming that there will be a total of approx. 10.000 winners, this means that each of them will receive a prize of 100 Lei on which the state will take 16% tax, leaving each winner with 84 Lei (less than 20 Euros).

Personally, I don’t have any kind of (positive) expectations from governmental officials. However, I would have expected from people with an Economics degree (they work in the Ministry of Finance) to know how to compute probabilities and to know the Expected Utility Model. Moreover, the (former) Minister of Finance who promoted this lottery has a PhD. from Harvard University.

Here’s how a lottery should be organized:

You need a very large prize that comes with an extremely low (e.g. 1 in 20.000.000) probability of winning. The very large prize with a very low chance of winning creates appeal – it has a magnetic effect that draws people into the lottery in the illusory hope of having a life-changing sky-fallen amount of money.

You need a large number of small prizes with small (e.g. 1 in 10.000) probability of winning. These small, but rather likely wins create availability – hey, my cousin’s neighbour wan 200 Lei last month at the lottery. They also keep alive the hope of winning the large, but highly unlikely prize.

 Details matter much more than many of us think…