Comments on: Why Gambling Isn’t Irrational

By: Odatafan

Odatafan — Mon, 13 Jun 2011 12:54:31 +0000

I think that the assumption of diminishing marginal utility -- "the assumption that each additional dollar matters less to you than the last" is rejected in economic arguments which show that short-term gambling can be rational. Milton Friedman wrote that gambling can be rational... but he supposed that marginal utility can be increasing.

"If money could only be spent or saved this assumption would obviously be wrong." I wrote out the economic argument for increasing utility assuming that money can only be consumed or invested.

By: TruePath

TruePath — Wed, 19 Dec 2007 21:11:24 +0000

No, what I'm really saying (and should have said this way) is that utility does not increase at a uniform rate with respect to total wealth. The extreme example here would be if utility was a highly non-continuous step function. For instance many if you have between $500 and $1000 dollars you have 1 unit of utility between $1000 and $2000 you have 2 units and so forth. In this sort of case even though from a big picture view utility is essentially logarithmic in terms of money (i.e. it's a step function approximating that curve) but if you have $750 dollars it's certainly worthwhile to spend $200 for a 1 in 10 chance of winning $300. Even while your expectation in terms of money is negative your expectation in terms of utility is positive since you don't lose any utility by dropping your wealth from $750 to $550.

Of course in the real world the utility function we have is going to be continuous but the same effect can occur if the utility function has sharp 'jumps' (e.g. at psychologically salient amounts of money...people view $1 million differently than they view $990,000).

However, on second consideration I have to take a slightly more sophisticated explanation. In particular I claim that people are deeply irrational about money (which everyone who thinks the lotto is irrational must believe) and that our utility in terms of spending or saving money has much more to do with the pain of getting a bad deal or the feeling of getting a good one than it does with actual ability to exchange money for goods and services. For instance this is why people will spend time searching for a slightly cheaper item even when in other parts of their lives they would trade off time for money at a much higher rate.

By: jonny blamey

jonny blamey — Wed, 19 Dec 2007 20:35:51 +0000

Are you suggesting that the diminishing marginal utility of money could be given a justification in terms of the probability of gaining a dollar using the doubling technique? It could work. It’s certainly easier to raise ten dollars if you are already a millionaire, as any drunk will tell you. If labour is linked to value, then a millionaire who earns more in his sleep than a jobbing plumber earns in a month will not value his money as much, and consequently tip more at restuarants.
As for the irrationality of gambling, gambling at unfavourable odds is never a way of making money in the long term and any one who thinks it is is irrational necessarily, since that is all unfavourable odds means. But who says it is irrational to gamble at favourable odds?