May 23, 2006

Expectation

"Take nothing on its looks; take everything on evidence. There's no better rule."

- Charles Dickens, Great Expectations.


Expectation is what you reasonably think will happen in the future. Mathematically, it deals with all probable future events and their underlying probability. Let's take a look at two examples.

Example 1 (Reading this passage)

Suppose the universe was created randomly, not with the particular intention of creating the planet Earth and human beings. What is the probability of you and I reading this blog?

If this was asked before the existence of the universe, the probability is practically zero. There are millions of other planets, but as of today, we are still not able to find another planet that is suitable to accommodate sophisticated creatures like us. The odds of having a planet like Earth was already extremely small. Then there was the Ice Age that wiped out 95% of lives, but our ancestors luckily survived and miraculously evolved into homo sapiens, our current form. Then there were the brilliant inventions of electricity, capacitors, computers, the Internet, and so on.

Therefore, the combination of all the seemingly impossible events enables us to read this. No one would have expected that these would happen. Now they have occurred. What a miracle!

Of course, expectations will change. Suppose (after the creation of the Earth, human beings, yourself, the Internet, etc.) that you visit this site every day and have read every previous passage. That you will be reading this passage too is certainly a rational expectation. This leads us to the second example.

Example 2 (Survival of miners)

Earlier this year there was an explosion that trapped 13 miners. It was a serious accident and it was expected that most of the 13 miners were killed. Then the news reported that 12 of them survived (without identifying them who they are), raising everyone's hope. However, later it was found that there was a miscommunication between the mine officials and the press. It should be 12 deaths instead of 12 survivors. The miners' families were furious and have asked for a compensation.

I am discussing this event from an academic perspective, putting the ethical issues aside. The false news did not change the fact. It only changed people's expectations. Assuming the 13 miners have an equal chance, the families were hoping that each miner had a 12/13 chance of survival, based on the false news. When the death toll was corrected later, the probability dropped to 1/13.

However, it should be noted that the expectation of survival was close to 1/13 prior to the false news, since the accident was a serious one. If the families did not raise their expectations based on the news, they would not have suffered as much. One could blame more the change in expectations than the explosion itself.


I personally think expectation is the second worst thing (memory is the first). Not only does the change in expectations make you suffer (as in Example 2), the difference between reality and expectations also surprises you (can be good or bad). In fact, many economists believe that market expectations are already incorporated into macroeconomic variables and stock prices. Only surprises can cause big and sudden movements.

If our expectations are set too high, many surprises will come as disappointments. Increased expectations bring happiness, but not as much as positive surprises do. Therefore, one should not raise his expectations unless there is solid evidence. Live by the Dickens's rule. Do not take everything as granted and increase too much the subjective probability of favorable future events. Doesn't everything strike you as a miracle?