1 / 10

Let’s talk about a statistical choice. You get to choose game A or game B . Then you get to play that game exactl

Let’s talk about a statistical choice. You get to choose game A or game B . Then you get to play that game exactly once. In game A , you get an 80% chance at winning $40,000. That is, we’ll use a random device so that with probability 0.80 you win $40,000

minnie
Download Presentation

Let’s talk about a statistical choice. You get to choose game A or game B . Then you get to play that game exactl

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Let’s talk about a statistical choice. You get to choose game A or game B. Then you get to play that game exactly once. In game A, you get an 80% chance at winning $40,000. That is, we’ll use a random device so that with probability 0.80 you win $40,000 with probability 0.20 you win nothing In game B, you get $30,000. For sure. Make a note as to whether you’d choose game A or game B.

  2. Now let’s consider another choice, game C or game D to be played exactly once. In game C, you get a 20% chance at winning $40,000. That is, we’ll use a random device so that with probability 0.20 you win $40,000 with probability 0.80 you win nothing In game D, you get a 25% chance at winning $30,000. That is, we’ll use a random device so that with probability 0.25 you win $30,000 with probability 0.75 you win nothing Make a note as to your choice, game C or game D.

  3. So …… how many of you chose game A? Show of hands please. Let’s have a show of hands for game B. Why was game B such a clear favorite? It seems like a bad business decision. Game A should be worth 0.80  $40,000 = $32,000, and this beats game B.

  4. The choice between game C and game D is, for many people, a marginal choice. You might say that game C is worth 0.20  $40,000 = $8,000 while game D is worth 0.25  $30,000 = $7,500. This would give a slight preference for game C.

  5. So most of you chose game B (over A) and then many of you chose game C (over D). Seems reasonable . . .

  6. Game C can be viewed as a 25% chance to play game A. Recall that game C is a 20% chance at $40,000. With probability 0.75, get $0. With probability 0.25, get to play game A: Subsequent 0.80 chance at $40,000 Subsequent 0.20 chance at $ 0 Combining the possibilities, chance of 0.25  0.80 = 0.20 to win $40,000 remaining chance, 0.80, to win $0

  7. Game D can be regarded as a 25% chance to play game B. Recall that game D is a 25% chance to win $30,000. With probability 0.75, get $0. With probability 0.25, get to play game B: Guaranteed $30,000 Combining the possibilities, this is a straight 25% chance at getting $30,000.

  8. If game B is preferred over game A, then you should prefer a 25% chance to play game B (which is game D) over a 25% chance to play game A (which is game C) This example is from “Prospect Theory: An Analysis of Decision Under Risk,” by Daniel Kahneman and Amos Tversky, Econometrica, 1979.

  9. So what’s going on here? Why are so many people inconsistent on this? The math and probability are clear. The psychology is murky.

  10. The A versus B choice was at high probabilities, 0.80 or 1.00. The C versus D choice was much less determined, with probabilities 0.20 and 0.25. • There are many messages here. Among them • * You cannot count on people to be rational. • * Context influences decisions. • * When different people make different choices, money moves.

More Related