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…

To Be Clear on Ambiguity

One recent trend in writing on applied behavioural science focuses on exceptions on the findings of behavioural science. Simply put, when what we know on Behavioural Science doesn’t work at all or as expected.

Here are some nice illustrations of this trend.

BE careful - A littleknowledge can be a dangerous thing By Crawford Hollingworth

Beyond WEIRD: Investigating Cultural Biases inBehavioural Science – webinar by Brainjuicer.

(Please Open them in new tabs and continue reading ;) )

                                                         

In a nutshell, the idea is that sometimes the effects discovered by behavioural science are very small or non-existent.

This, however, is not a surprise if one knows the fundamentals of behavioural science, namely the role of ambiguity (fuzziness).

Most of the times, people rely on contextual cues only if there isn’t clarity regarding the issue at hand. For example, anchoring works because people don’t know the exact value that has to be estimated. If I ask you what the number of cat breeds is, I bet none of you know the exact answer and this is only natural. In this case presenting anchors such as 30 or 3000 will influence your estimation simply because there is incredible fuzziness regarding how many breeds of man-exploiting cute furry creatures (cats) are out there.

Remaining in the area of anchoring: if we ask an illiterate five-year-old child from East Africa in what year did WWII end, then providing anchors will strongly influence the child’s answer (that is unless he simply says “I don’t know”). However, if we ask WWII veterans the same question, then providing anchors will have zero effect. Moreover, the veterans will be offended by the lack of knowledge of the people asking the question.

Similarly to anchoring, other contextual influences work ONLY (mostly) when there is ambiguity. For example, using mental accounting and default opt-ins for re-routing some of the tax return money into savings (mentioned in the article BE careful - A little knowledge can be a dangerous thing By Crawford Hollingworth) did not work because for the ones most in need (low income – less than 50.000 USD/year/household) there wasn’t any fuzziness on what to do with the money. Low income people are very well skilled in managing tight budgets and any sum of money is allocated (budgeted) well in advance.

I believe that if households with a larger income would get some money back and not expect it, the default opt in on savings would work quite well simply because there is some ambiguity on what to do with the (sky fallen) money.

On the social influences avenue, the most powerful social influence works because there is ambiguity. Social Proof (which is distinct from Social Pressure – what Solomon Asch investigated) works because we infer that others know something we don’t know. If we choose to buy the most popular internet subscription plan, we do so simply because we don’t know which plan best fits our needs.

On the other side of things, I know what shoe size I have (43) and I will never buy shoes of a different size (e.g. 42) regardless of how many other people buy 42 size shoes.

Here’s a wonderful illustration of how the context strongly influences judgment. It works because there is ambiguity… lots of it.  

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