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The story (picked up from Daniel Davies at http://d-squareddigest.blogspot.com http://d-squareddigest.blogspot.com) goes that the way one argued with Milton Fri
by dbfclark 16y ago
The story (picked up from Daniel Davies at http://d-squareddigest.blogspot.com http://d-squareddigest.blogspot.com) goes that the way one argued with Milton Friedman was to listen until he got to the part of his argument where he said "let's assume x" and then say "no, let's not!" That is, the part of the argument doing all the work tended to be hiding in some premise that economists consider innocuous but is in no way representative of the world.
So here, premise (2): "probability of a transaction resulting in value v is uniform." No! Not true! In reality, people price a disproportionate number of transactions to make easy change with the coins we have, be easily divisible, be .01 less than a larger number of dollars, and so on. The discovery that cash transactions had a uniform distribution of change would actually be quite weird.
But worse is the smuggling in of an unconsidered definition of the good in the form of the efficiency metric -- fewest coins per transaction. Even granting the uniform distribution, making change out of your pocket is still solving the subset-sum problem in your head, which is of course NP-complete. The existing setup of coins, including the first three powers of 5, makes this problem very easy while almost all the proposed "better" solutions actually make this aspect of the problem harder rather than easier. Who cares if I have to handle a few extra tenths of a coin per transaction if it means I don't have to spend two minutes puzzling out how to make change?
I suppose the lesson, as usual, is that business logic is lived experience, not theory.
- xyzzyz 16y ago>making change out of your pocket is still solving the subset-sum problem in your head, which is of course NP-complete. Generally speaking, that's true. Most currencies however are designed, so that the greedy algorithm always works and produces optimal solution. The coin systems given in the linked article do not have this property, so they are actually inferior to real systems. edit: come to think of it, they in fact do, but it requires ridiculous amounts of pennies, so my argument still holds.
- Locke1689 16y agoFWIW I got that from the original poster: the general case problem is NP complete but most of our special cases are not.
- frgbhnmnjh 16y agoNot quite in the USA you buy three items that end in 99c, but two of them have state sales tax, one of those has local sales tax and the other has a liquor tax. SO you can work out the change IF you know the random extra amount that will be added at the checkout
- dbfclark 16y agoThis actually makes the non-uniformity worse, not better -- things priced at an even number of dollars don't factor into the calculation before tax (and there are lots of those), but after, change amounts get disproportionately weighted to the amounts of change produced by even numbers of dollars. Argh.
- chopsueyar 16y agoI've actually started using $2 bills for this reason.
- ahi 16y agoHe's also using the average as the only metric. Some systems may have better distributions.
- j_baker 16y agoReminds me of a joke I heard recently. A chemist, a physicist and an economist were stranded on a desert island when they discover a crate of canned food. The chemist says that they should leave the cans in the salt water for a while and then try opening them. The physicist says they should try banging them open with rocks. The economist says "Let's assume we have a can opener."
- godorito 16y agoI am totally stealing this joke for the next faculty meeting. But, we have to make some assumptions in life. Until we get that cranial recording unit running.
- Gormo 16y agoAlso, his most efficient system of coins in one in which every denomination is a prime number, so no denomination but the penny factors evenly into any other. In our current system, the only one that doesn't work is breaking a quarter into dimes. (And I presume you mean "first three multiples of 5".)