What the U.S. needs is an 18-cent coin
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What the U.S. needs is an 18-cent coin
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Re: What the U.S. needs is an 18-cent coin
#2The assumption that every possible value from 0 to 99 is equally likely doesn't seem like the best idea. In a country where the cost of items usually ends in .99, .97, or the like, and the sales tax is added after the fact (and usually from 0-10%), is it still the best choice? The post (and cited paper) don't seem to mention this.
That said, I don't know where you'd acquire these sorts of statistics.
Re: What the U.S. needs is an 18-cent coin
#3The assumption that every possible value from 0 to 99 is equally likely doesn't seem like the best idea. In a country where the cost of items usually ends in .99, .97, or the like, and the sales tax is added after the fact (and usually from 0-10%), is it still the best choice? The post (and cited paper) don't seem to mention this. That said, I don't know where you'd acquire these sorts of statistics.
I also wondered about the random assumption. The thing that made me question the assumption the most is Benford's law.
Re: What the U.S. needs is an 18-cent coin
#4The assumption that every possible value from 0 to 99 is equally likely doesn't seem like the best idea. In a country where the cost of items usually ends in .99, .97, or the like, and the sales tax is added after the fact (and usually from 0-10%), is it still the best choice? The post (and cited paper) don't seem to mention this. That said, I don't know where you'd acquire these sorts of statistics.
I also wondered about the random assumption. The thing that made me question the assumption the most is Benford's law.
I don't think Benford's law applies here: it's about the first digit of numbers (that are distribute in a certain way), but in most cases the first digit of a price will be denominating dollars, not cents.
Re: What the U.S. needs is an 18-cent coin
#5Earlier quoted context omitted.
I also wondered about the random assumption. The thing that made me question the assumption the most is Benford's law.
I don't think Benford's law applies here: it's about the first digit of numbers (that are distribute in a certain way), but in most cases the first digit of a price will be denominating dollars, not cents.
The leading digit of change is tens of cents...
Re: What the U.S. needs is an 18-cent coin
#6The assumption that every possible value from 0 to 99 is equally likely doesn't seem like the best idea. In a country where the cost of items usually ends in .99, .97, or the like, and the sales tax is added after the fact (and usually from 0-10%), is it still the best choice? The post (and cited paper) don't seem to mention this. That said, I don't know where you'd acquire these sorts of statistics.
But taxes vary throughout the areas. And adding more items together. and splitting the dinner bill among friends. and all sort of other things that can make the final total anything from 0 to 99. I don't think it is silly to make the assumption they are equally likely. But I also don't know where you'd acquire these sorts of statistics.
Re: What the U.S. needs is an 18-cent coin
#7The assumption that every possible value from 0 to 99 is equally likely doesn't seem like the best idea. In a country where the cost of items usually ends in .99, .97, or the like, and the sales tax is added after the fact (and usually from 0-10%), is it still the best choice? The post (and cited paper) don't seem to mention this. That said, I don't know where you'd acquire these sorts of statistics.
Completely agree: prices are not set arbitrarily or via direct calculation in many cases, but are driven by marketing ($1.99) or optimization (the local pizza shop that works everything out to even $ or 50c).
Re: What the U.S. needs is an 18-cent coin
#8An interesting wrinkle to this is that an 18 cent coin would make it much harder to make change with the fewest coins for certain values.
How do we make change in everyday life? The simple algorithm everyone knows, even if they don't know what an algorithm is, is to start with the largest coin and move down, taking as many of each as you can. Thus to make change for 72 cents we: take 2 quarters, leaving us with 22 cents take 2 dimes, leaving us with 2 cents take no nickels take 2 pennies, leaving us with 0 cents and we're done
This algorithm as it turns out is only optimal so long as each denomination is at least twice as much as the previous one. So what happens if we have an 18 cent coin? Let's make change for 37 cents. With the simple algorithm we end up with {1 quarter, 1 dime, 2 pennies}. That's four coins. However you can do it with three coins: {2 18 cent pieces, 1 penny}.
The algorithm for the case with arbitrary denominations isn't np-complete (it's a fun algorithms question to figure out), but it's way too difficult to be doing in your head all the time.
Re: What the U.S. needs is an 18-cent coin
#9Whenever taxation changes it will shift the "average transaction value" by a few cents and invalidate the added usefulness of already minted coins
Re: What the U.S. needs is an 18-cent coin
#10Earlier quoted context omitted.
I don't think Benford's law applies here: it's about the first digit of numbers (that are distribute in a certain way), but in most cases the first digit of a price will be denominating dollars, not cents.
The leading digit of change is tens of cents...
The change may be more than a dollar, so tens of cents is not necessarily the leading digit.