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Optimal Choice

Whether you're an actuary, investment manager, HR-manager of respected consumer, in real life you often have to take a decision in a situation where you have to pick out "the best" opportunity out of "n" possibilities. Mostly in a situation where you (ex ante) are only limited aware about what you can expect in terms of quality or quantity.

Some examples:

• Making the right investment
  You want to make an investment today. Every day your stockbroker offers you about 20 investment opportunities. Your budget allows you to make only one investment today and it should be the best one. How can you be sure to pick the right one?
  You have only limited time (say about 10 minutes) for each investment to decide; after that, you'll have to wait for the next offer.
   
• Selecting the best candidate for the job
  You’re the HR-manager of a certain company. Your external HRM-advisor promised you to present 10 potential candidates for a certain vacancy. After each candidate you have to decide wetter you accept him/her or wetter you go one for a possible better candidate. You want the best candidate. What can you do?
   
• Applying for the best job
  You solicited for a new job. Six companies have invited you for a visit. After each visit you are obliged to say wetter you take the job or not. You want the best job. What is wise to do?
   
• Buying a new car
  You want to buy a new car. Although the price of that car is fixed, every dealer gives a quick-decision discount.
  You decide to visit 7 dealers. After each visit you have to decide wetter you "buy" or "let go" (the dealer will not accept that you come back later after you came to the conclusion that he was after all the best deal).
  You want the highest discount you can get; How can you manage?
   

Optimal Strategy?

In each of these cases you can ask yourself: what is the optimal strategy? Take the first opportunity or wait until the last? Skipping some opportunities or take the median opportunity?

In decision theory literature these kind of problems are known as "Best Choice Problems" (BCP's). More specific the above decision problems are often described as "The Sultan's Dowry Problem" or "The Secretary Problem".

This type of deceision problem is characterised by the following assumptions:

• You want "the best" choice out of "n" possibilities
• You handle each opportunity after another. After each opportunity you have to decide whether you take the offer or go further (you can’t come back on your decision later).
• You only have limited knowledge about the group of "n" possibilities (in terms of quality or quantity)

---

Solution

The best strategy in these kind of cases is to wait (don’t choose) until the first "m" possibilities of the total number of opportunities "n" have passed. After these "m" possibilities you accept the first offer that is "better" than the one you've had until the moment of decision. The word "better" stands for "better candidate", "better financial offer", etc.

If you’re interested in the mathematical theory behind this kind of problems, click on one of the links below:

• The Secretary Problem
• Mathworld Sultans Dowry Problem
• UCLA (pdf)

---

Best Choice Calculator

Objective The 'Best Choice Calculator' calculates the optimal number of possibilities [m] that you have to let pass, before taking the best one thereafter, to achieve the maximum probability [p] that you indeed will realise the best choice from a given total number of possibilities [n]. Try it out! Explanation calculation output The first column returns "m" The second column returns "p" The input-variable "n" is the total number of possibilities

Total number of possibilities [n] =

[m]       [p] Conclusion

---

Rule of thumb

As you perhaps noticed in using The Best Choice Calculator, there is a close relation between the number of possibilities [n] and the number of opportunities you had to skip [m].

When we have to take decisions in "real life", we do not (yet) have a build-in computer-chip in our head to calculate for each [n] the corresponding value [m]. In this case all you have to do is to memorise the next rule of thumb:

Rule of Thumb

Number of possibilities Number of possibilities to skip  =  3

Or, in plain mathematics:

n m  =  3

Of course the rule of thumb is an approximation.
In the next table you see how [n] and [m] are exactly related for values of n from n=1 to n=

Although it’s nice to have a "rule of thumb", don’t forget to decide on your gutfeeling as well.

Mixing intuition, experience and rules of thumb, guarantees the ultimate best choice.

Original blog by Jos Berkemeijer / July 2002/ Updated : April 2013

Free to copy  

Best Choice Calculator

Whether you're an actuary, investment manager, HR-manager of respected consumer, in real life you often have to take a decision in a situation where you have to pick out "the best" opportunity out of "n" possibilities. Mostly in a situation where you (ex ante) are only limited aware about what you can expect in terms of quality or quantity.

Some examples:

• Making the right investment
  You want to make an investment today. Every day your stockbroker offers you about 20 investment opportunities. Your budget allows you to make only one investment today and it should be the best one. How can you be sure to pick the right one?
  You have only limited time (say about 10 minutes) for each investment to decide; after that, you'll have to wait for the next offer.
   
• Selecting the best candidate for the job
  You’re the HR-manager of a certain company. Your external HRM-advisor promised you to present 10 potential candidates for a certain vacancy. After each candidate you have to decide wetter you accept him/her or wetter you go one for a possible better candidate. You want the best candidate. What can you do?
   
• Applying for the best job
  You solicited for a new job. Six companies have invited you for a visit. After each visit you are obliged to say wetter you take the job or not. You want the best job. What is wise to do?
   
• Buying a new car
  You want to buy a new car. Although the price of that car is fixed, every dealer gives a quick-decision discount.
  You decide to visit 7 dealers. After each visit you have to decide wetter you "buy" or "let go" (the dealer will not accept that you come back later after you came to the conclusion that he was after all the best deal).
  You want the highest discount you can get; How can you manage?
   

Optimal Strategy?

In each of these cases you can ask yourself: what is the optimal strategy? Take the first opportunity or wait until the last? Skipping some opportunities or take the median opportunity?

In decision theory literature these kind of problems are known as "Best Choice Problems" (BCP's). More specific the above decision problems are often described as "The Sultan's Dowry Problem" or "The Secretary Problem".

This type of deceision problem is characterised by the following assumptions:

• You want "the best" choice out of "n" possibilities
• You handle each opportunity after another. After each opportunity you have to decide whether you take the offer or go further (you can’t come back on your decision later).
• You only have limited knowledge about the group of "n" possibilities (in terms of quality or quantity)

---

Solution

The best strategy in these kind of cases is to wait (don’t choose) until the first "m" possibilities of the total number of opportunities "n" have passed. After these "m" possibilities you accept the first offer that is "better" than the one you've had until the moment of decision. The word "better" stands for "better candidate", "better financial offer", etc.

If you’re interested in the mathematical theory behind this kind of problems, click on one of the links below:

• The Secretary Problem
• Mathworld Sultans Dowry Problem
• UCLA (pdf)

---

Best Choice Calculator

Objective The 'Best Choice Calculator' calculates the optimal number of possibilities [m] that you have to let pass, before taking the best one thereafter, to achieve the maximum probability [p] that you indeed will realise the best choice from a given total number of possibilities [n]. Try it out! Explanation calculation output The first column returns "m" The second column returns "p" The input-variable "n" is the total number of possibilities

Total number of possibilities [n] =

[m]       [p] Conclusion

---

Rule of thumb

As you perhaps noticed in using The Best Choice Calculator, there is a close relation between the number of possibilities [n] and the number of opportunities you had to skip [m].

When we have to take decisions in "real life", we do not (yet) have a build-in computer-chip in our head to calculate for each [n] the corresponding value [m]. In this case all you have to do is to memorise the next rule of thumb:

Rule of Thumb

Number of possibilities Number of possibilities to skip  =  3

Or, in plain mathematics:

n m  =  3

Of course the rule of thumb is an approximation.
In the next table you see how [n] and [m] are exactly related for values of n from n=1 to n=

Although it’s nice to have a "rule of thumb", don’t forget to decide on your gutfeeling as well.

Mixing intuition, experience and rules of thumb, guarantees the ultimate best choice.

Original blog by Jos Berkemeijer / July 2002/ Updated : April 2013

Free to copy  

test

If you want something to chew on, something that challenges your actuarial brain and associative power, try to solve the next Actuagram.

It's mix of an actuarial crossword puzzle and a cryptogram.

How to play the puzzle:

1. Click on the word you would like to solve.
2. Fill in your suggestion, click on OK
3. Only if you do not know the answer, click on the 'solve button'

Can you manage, without using the 'solve button' ?

Congratulations! Have fun!

[ If your browser doesn't allow you to play here, click on this link]

Actuagram

by Joshua Maggid
EclipseCrossword © 2000-2007

This interactive crossword puzzle requires JavaScript and a reasonably recent web browser, such as Internet Explorer 5.5
or later, Netscape 7, Mozilla, Firefox, or Safari. If you have disabled web page scripting, please re-enable it and refresh
the page. If this web page is saved to your computer, you may need to click the yellow Information Bar at the top of
the page to allow the puzzle to load.

Windows MediaPlayer & Picture

Simple script to replace a self defined picture of a playing file by the active player.
It can be used on blogs to prevent the appearing of the well known ugly black part of the Windows media Player.

Apply the next script in your blog and replace the image-url, video-url, width and height as you like (click to enlarge).




Example (click on player/image):



Good luck!

Example widgets: Welcome

The 'Welcome widget' is a general widget you may use in the sidebar of any Blogger blog.

Here is an example:

Welcome on MCT.

This blog is a Blogspot Multi Column Template (MCT) demonstration.

The basic template contains 4 columns and is based on 'new Blogger' widgets. You can easily add (or skip) columns by changing the code.

If you want to know how, read the Introduction or click right here to start.

You may also want to copy this 'welcome message'.
Click here to learn how.
_____________________

Constructive remarks about this blog are welcome at jos.blogspot@gmail.com.

Instructions to create the widget in your own blog:

• Download, 'select all', and copy the 'MCT E WELCOME TXT' standard code.
  
• Go to the Layout, "Edit HTML" page of your Blogspot blog.
• Click on "Add a Page Element" button in the zone of your choice.
• Select a "HTML/JavaScript"widget. Press on ADD TO BLOG.
  
• Paste the copied code in the Content.
  
• Modify the code as you like (e.g. the 'width' of the widget).
  
• Set the Title as you like. Press SAVE.

That's it. Success!

Create PREPOSTTEXT

You may want to add a special sign before the title of every post (like the integral sign on the MCT posts).

This is how to do this:

• Add Javascript GetelementbyClass to your JAVASRIPT widget.
• Download, 'select all' and copy MCT EXAMPLES PREPOSTTEXT.
• Click on "Add a Page Element" button in the 'Hidden Widgets' zone.
• Select a "HTML/JavaScript"widget. Press on ADD TO BLOG.
  
• Paste the copied code in the Content.
  
• Modify the code as you like.
  
• Set the Title to "PREPOSTEXT" (or any name). Press SAVE.

You're ready!