Is an understanding of probability a super power ?

Yo! Whazzup bitches ?

So it happened that just the other day, I had an argument with a friend of mine about how to make decisions. I was thinking about it for some time but it was finally the time to get some feedback on my proposed methodology. Here is how I arrived at the model :

Lets imagine the case of two insurance policies,

Policy 1 :

Premium Cost per each month Life Insurance Cover for that month
$100 $10000
$200 $20000

Policy 2 :

Premium Cost per each month Life Insurance Cover for that month
$10 $60000
$20 $80000

Which one would you choose ? Clearly ‘Policy 2’ since it provides a larger cover for a smaller premium cost ( if you are confused there is some additional explaination in the comments section of this post ).

In real life however, things are a little less clear. In the above case we are assuming that the we are definitely going to pay the premium cost and the chances of dying remain the same whether you buy ‘Policy 1’  or ‘Policy 2’. Hence they are left out of the equation that decides your decision. In real life, each cost/benefit will have an associated probability that defines how likely it is for you to encounter that cost/benefit. Multiplying that probability, with the value of each cost/benefit gives you the ‘Expected Cost’/’Expected Benefit’ for that particular cost/benefit. I argue that it is better to choose that choice which offers the maximum Net Expected Benefit.

Lets consider an example :

Choice 1

Probability Cost
P1 C1
P2 C2
Probability Benefit
P3 B1
P4 B2

Choice 2

Probability Cost
P5 C3
P6 C4
Probability Benefit
P7 B3
P8 B4

How will you know which choice to make ?

Total Expected Cost of Choice 1 = ( P1 * C1 ) + ( P2 * C2 )

Total Expected Benefit of Choice 1 = ( P3 * B1 ) + ( P4 * B2 )

Similarly, Total Expected Cost of Choice 2 = ( P5 * C3 ) + ( P6 * C4 )

Total Expected Benefit of Choice 2 = ( P7 * B3 ) + ( P8 * B4 )

Therefore Net Expected Benefit of Choice 1 = (( P3 * B1 ) + ( P4 * B2 )) – (( P1 * C1 ) + ( P2 * C2 ))

Net Expected Benefit of Choice 2 = (( P7 * B3 ) + ( P8 * B4 )) – (( P5 * C3 ) + ( P6 * C4 ))

Therefore the choice that we must make is whatever maximizes the above Net Expected Benefit, i.e the choice we must make is that choice with

Max( { (( P3 * B1 ) + ( P4 * B2 )) – (( P1 * C1 ) + ( P2 * C2 )) }, { (( P7 * B3 ) + ( P8 * B4 )) – (( P5 * C3 ) + ( P6 * C4 )) } )

This looks about right but how do I convince myself that this is true ? You know what they say “Trust, but verify”. So I wrote a small Java program to simulate these conditions. Seems like the probabilistic decision making is better than randomly picking a choice (naive).

Also this seems to be how disagreement happens between two people, either they disagree on the values of these costs, benefits or probabilities or they seem to fail to see some of the costs/benefits that other person sees. It can also happen if they are fundamentally different types of people and want different stuff which means that they will have entirely different Cost/Benefit tables in place of the ones above.

See, all we need is science to make decisions. No lucky numbers, no magical sticks and no divine intervention.

(In Mike Tyson’s Voice) ‘SCIENCE MOTHAFUCKA!!!’ ( unless of course I made a mistake in some derivations or the simulation above, in which case ‘PSEUDO-SCIENCE MOTHAFUCKA!!’ ).

Advertisements

6 thoughts on “Is an understanding of probability a super power ?

  1. Couple of things I don’t understand, the two rows per column, are they different premiums for the same policy ? If this is the case wouldn’t you buy twice the $10 policy and get $12000 ?

    Why do you need to consider the probability of paying the premium, because payouts are generally tied to payments on time which would bring the probability very close to 1? For most salaried position, insurance is collected from the paycheck. So, I was under the impression that the only variable is the life expectancy.

    1. “Couple of things I don’t understand, the two rows per column, are they different premiums for the same policy ? If this is the case wouldn’t you buy twice the $10 policy and get $12000 ? ”

      Ah, in my mind when I formulated those policies, I had some additional rules to make the computation seem simpler.

      These policies can only be bought once to cover the same person. For each policy ( contract ) the first month premium is specified in the first row of Premium Cost column and second month premium is specified in the second row of Premium Cost column. In case the person looses his life in the first month, the insurer has to pay the benefit listed in first row in Insurance Cover column. If the person looses his life in second month, the insurer has to pay the benefit listed in second row of Insurance Cover column and so on.

      “Why do you need to consider the probability of paying the premium, because payouts are generally tied to payments on time which would bring the probability very close to 1? For most salaried position, insurance is collected from the paycheck.”

      You are correct. I have said that they are left out of the equation ( and the tables ). Clearly to enjoy the benefit of an Insurance Policy you have to pay the premium. If you are unwilling to pay the premium, this entire problem of ‘Which Insurance Policy is better’ goes out of the window, since you do not want to be insured. Defaults are not uncommon, but they will only factor into the decision making of the people who offer these insurance contracts.

      “I was under the impression that the only variable is the life expectancy.”

      Yes, this is a factor. Again I was assuming that the policy holder does not experience a change in life expectancy while he is making this decision. For example, if someone has already made a decision on which policy to buy, and just before buying if he was diagnosed with terminal cancer, his decision may change.

      1. It would really help if you make the policy description clearer. What I think would really help is to come up with a life expectancy calculator. Factor in major lifestyle variables to come up with life expectancy, and probability of death for the immediate year which would pipe its results to calculate best insurance policy for you. Collect the policy requirements from vendors, and you have an online service 😀

  2. did you write this thing for computer engineers??? because i understood the first part and 2nd part calculation also… but what is your real idea behind it?? is it to make a good decision?? or good decision in economic fields??

  3. @Arun
    You are right, the idea is to make it easier to make good decision in your everyday life. I also wanted to provide a way to disagree with someone politely. When you made the decision to leave for Germany, you made a list of pros and cons, didn’t you ? Well, add a new column for probability and use some numbers for cost and benefit and ( hopefully ) your decision may be a little better. This is also a decision that may be a little bit more easy to defend, later on.
    Only understanding the simulation program may require any Computer Science knowledge. Everything else said in this post may be useful to anyone.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s