In a literal information-theoretic sense, a percentage has log2(100)≈6.6 bits of information while a per-tenth has log2(10)≈3.3 bits. This might have been what was meant?
I agree that the half of the information that is preserved is the much more valuable half, however.
I agree that the half of the information that is preserved is the much more valuable half, however.
Yes, in most cases if somebody has important information that an event has XY% probability of occurring, I’d usually pay a lot more to know what X is than what Y is.
(there are exceptions if most of the VoI is knowing whether you think the event is, eg, >1%, but the main point still stands).
Yes, in most cases if somebody has important information that an event has XY% probability of occurring, I’d usually pay a lot more to know what X is than what Y is.
As you should, but Greg is still correct in saying that Y should be provided.
Regarding the bits of information, I think he’s wrong because I’d assume information should be independent of the numeric base you use. So I think Y provides 10% of the information of X. (If you were using base 4 numbers, you’d throw away 25%, etc.)
But again, there’s no point in throwing away that 10%.
In the technical information-theoretic sense, ‘information’ counts how many bits are required to convey a message. And bits describe proportional changes in the number of possibilities, not absolute changes. The first bit of information reduces 100 possibilities to 50, the second reduces 50 possibilities to 25, etc. So the bit that takes you from 100 possibilities to 50 is the same amount of information as the bit that takes you from 2 possibilities to 1.
And similarly, the 3.3 bits that take you from 100 possibilities to 10 are the same amount of information as the 3.3 bits that take you from 10 possibilities to 1. In each case you’re reducing the number of possibilities by a factor of 10.
To take your example: If you were using two digits in base four to represent per-sixteenths, then each digit contains the 50% of the information (two bits each, reducing the space of possibilities by a factor of four). To take the example of per-thousandths: Each of the three digits contains a third of the information (3.3 bits each, reducing the space of possibilities by a factor of 10).
But upvoted for clearly expressing your disagreement. :)
And bits describe proportional changes in the number of possibilities, not absolute changes...
And similarly, the 3.3 bits that take you from 100 possibilities to 10 are the same amount of information as the 3.3 bits that take you from 10 possibilities to 1. In each case you’re reducing the number of possibilities by a factor of 10.
Ahhh. Thanks for clearing that up for me. Looking at the entropy formula, that makes sense and I get the same answer as you for each digit (3.3). If I understand, I incorrectly conflated “information” with “value of information”.
In a literal information-theoretic sense, a percentage has log2(100)≈6.6 bits of information while a per-tenth has log2(10)≈3.3 bits. This might have been what was meant?
I agree that the half of the information that is preserved is the much more valuable half, however.
Yes, in most cases if somebody has important information that an event has XY% probability of occurring, I’d usually pay a lot more to know what X is than what Y is.
(there are exceptions if most of the VoI is knowing whether you think the event is, eg, >1%, but the main point still stands).
As you should, but Greg is still correct in saying that Y should be provided.
Regarding the bits of information, I think he’s wrong because I’d assume information should be independent of the numeric base you use. So I think Y provides 10% of the information of X. (If you were using base 4 numbers, you’d throw away 25%, etc.)
But again, there’s no point in throwing away that 10%.
In the technical information-theoretic sense, ‘information’ counts how many bits are required to convey a message. And bits describe proportional changes in the number of possibilities, not absolute changes. The first bit of information reduces 100 possibilities to 50, the second reduces 50 possibilities to 25, etc. So the bit that takes you from 100 possibilities to 50 is the same amount of information as the bit that takes you from 2 possibilities to 1.
And similarly, the 3.3 bits that take you from 100 possibilities to 10 are the same amount of information as the 3.3 bits that take you from 10 possibilities to 1. In each case you’re reducing the number of possibilities by a factor of 10.
To take your example: If you were using two digits in base four to represent per-sixteenths, then each digit contains the 50% of the information (two bits each, reducing the space of possibilities by a factor of four). To take the example of per-thousandths: Each of the three digits contains a third of the information (3.3 bits each, reducing the space of possibilities by a factor of 10).
But upvoted for clearly expressing your disagreement. :)
Ahhh. Thanks for clearing that up for me. Looking at the entropy formula, that makes sense and I get the same answer as you for each digit (3.3). If I understand, I incorrectly conflated “information” with “value of information”.