At what point does accepting a lower "expected value" make sense?

D

Dan Murray

Guest
Weekend question....

Mathepac or some such poster may have to help me with the terminology but I'd be interested in hearing folks' views on the following.

Say one had the option of (a) €10 or (b) a 50% chance of €21, I think I'd go for option (b) - as its "expected value" (or whatever it's called!) is the greater of the two options. For avoidance of doubt, (b) is a coin toss, whereby you end up with 0 or €21.

My risk tolerance would allow me to continue to take option (b) for progressively higher stakes also - but.............there would come a point where, for me, the attractiveness of option (a) would become compelling.

So, rather than bias the discussion by sharing my own "inflection point" or "inflection range", I'd prefer to leave it to others to comment first.

Ideally, if you could briefly explain your thinking and whether you believe your answer is rational or not!
 
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Your proposition is poorly stated. You will not suffer any actual loss on whichever option you choose. So it all boils down to how desperate you are for money.

You must actually gamble, i.e. have the possibility of loss. So, if you have a 50% chance of winning 15 euro, and a 50% chance of losing 10 euro, do you take the gamble? The expected outcome is (15*0.5)-(10*0.5), i.e. 2.5 euro, so do you take the gamble?
 
PMU said:
Your proposition is poorly stated. You will not suffer any actual loss on whichever option you choose.
.....You must actually gamble, i.e. have the possibility of loss.
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Hi PMU,

If option (a) guarantees you €10 - why do you feel you are not gambling when going for option (b)?
 
The question is a variation of the 'American Game Show' problem. You may remember the character played by Kevin Spacey in the film '21' deals with this in a lecture to his students at the start of the film (before they go to rip off Las Vegas). As Dan Murray has posted it, he had no risk, i.e. he is not gambling as he is not putting any money up. An expected return is the price up to which you would pay to play a game. Dan Murray says "there would be a point where the attractiveness of option (a) would be compelling." That point is the expected return. If you pay more, you will always lose. So, how much would you pay to play this game?
He's not paying, so it's not gambling: it's more like a game show. He has three options (a) to pick definite win of EUR 10; or (b) a chance of winning EUR 21 or (c) a chance on losing, having in the last two options rejected a definite win. In effect, he has three envelopes before him. One has a mark that confirms it has 10 euro in it; the other two have no marks but one has 21 euro and the other does not. If you are not paying to play, which do you choose? That is to say, if you have a definite win of 10 euro, is it to your advantage to select one of the other envelopes?
 
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Dan Murray said:
Ideally, if you could briefly explain your thinking and whether you believe your answer is rational or not!
Click to expand...
If you're interested in how we make such decisions and how they relate to expected utility then you may be interested in reading https://www.amazon.co.uk/Undoing-Project-Friendship-Changed-World/dp/0241254736/ (The Undoing Project).
 
Thanks Michaelm,

Already ready it - two very clever buachaillí....
 
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