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Old 11-30-2017, 08:37 PM   #26
NotWise
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Quote:
Originally Posted by LoquiSordidaAdMe View Post
But I have to agree with SD above. What I really want to know is if the story got a 4.5 score because half the readers loved it (5*) and half thought it was pretty good (4*), or if it got a 4.5 because almost everybody loved it (5*), but a few thought it was shit (1*).
Odd voting patterns are possible. I haven't posted in LW but I would expect some quirks.

The first story I counted votes on was mis-posted to Romance (my mistake, not the site's). The Romance readers hated it, and the general population seemed to like it. It got about an equal number of 1* votes and 5* votes and not much in between. Then it fell off the front page of the New list while it was still up in the Romance hub and the 1* votes won.

Laurel let me pull that story out of Romance and put it somewhere else. It saved the Romance readers from spraining their mouse finger by clicking on 1* so many times.
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Old 11-30-2017, 08:44 PM   #27
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Originally Posted by NotWise View Post
Laurel let me pull that story out of Romance and put it somewhere else. It saved the Romance readers from spraining their mouse finger by clicking on 1* so many times.
It's really kind of disturbing how passionate some readers are about the purity of their favorite categories. But that's a discussion for another thread.
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Old 12-01-2017, 03:47 AM   #28
Bramblethorn
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Quote:
Originally Posted by NotWise View Post
The uncertainty in a single value rounded to 1/100th is +/- 0.005. When you perform an operation using two such rounded numbers (as you do when you calculate the change in the number of stars voted) then the uncertainties are convolved and the possible range in the result is doubled to +/- 0.01. The error distribution also changes from a rectangular probability function to a triangular probability function.
Not quite.

If we were talking about a situation where the only information you had was the change in the rounded score, then yes, the uncertainty in that change would be +/- 0.01, for the reasons you state. If you see the rounded scores change from 4.63 to 4.60, and that's all the information you have, then the exact change in the score might be anything between (4.634999... - 4.595 = 0.0400...) to (4.625 to 4.6049999... = 0.0200...) i.e. 0.03 +/- 0.01. Just like you say.

And, yeah, IF story scores were uniformly-distributed random variables, then the distribution of a single rounding error would indeed have a rectangular distribution, and the distribution of the sum of two rounding errors would indeed have a triangular distribution.

But that's not the only information we have. We know the number of votes before and after, and that puts constraints on which pre-rounded values are even possible. And story scores aren't uniformly distributed; they're restricted to a discrete set of values, because they have to be integer multiples of (1/votes).

For example, suppose my story has 80 votes. The exact score has to be an integer multiple of 1/80, somewhere between 80/80 (= 1) and 400/80 (= 5).

369/80 = 4.6125, which would round to 4.61. Too small.
370/80 = 4.6250, which rounds to 4.63. Just right.
371/80 = 4.6375, which rounds to 4.64. Too large.

So if my rounded score is 4.63, from 80 votes, I can tell exactly how many stars it had: 370. Any other possibility will end up being too high or too low to round to 4.63. I even know exactly what the rounding error was: 0.005.

Suppose I then get one more vote, and my score changes to 4.60. This time, I know my score's going to be an integer multiple of 1/81.

372/81 = 4.59259... which rounds to 4.59. Too small.
374/81 = 4.61728... which rounds to 4.62. Too large.
373/81 = 4.60493... which rounds to 4.60. Just right.

So I know my story now has a total of 373 stars, and since I know it had 370 before that last vote, I know that the last vote was exactly 3 stars.

Up to 100 votes, you can always do this to get the exact number of stars at any time you have the rounded score and the number of votes. Between 100 and 200, sometimes, depending on the number.

Quote:
I can give you a graph of the probability of getting a correct result.

I've run numerical experiments that show it to be true. The results of back-calculating the scores are only exact to 50 votes,
Sorry, but there's an error somewhere in your experiments - whether the issue I mentioned above, or something else.

If I'm incorrect, it should be easy to prove it. You just need to give one example of a case with 100 votes or less, where it's impossible to calculate the exact number of stars from the rounded score. (And, obviously, where that score is in fact possible with the given number of votes - e.g. if a story has exactly ten votes, it's impossible to have an average of 4.18.)

But I guarantee that no such case exists.

Quote:
There's also a problem that when you get a vote that doesn't change the score then the only result you can back-calculate correctly is the rounded-off version of the score, which may or may not be the right result.
Sorry, I don't understand this. If my story has 4.85 off 99 votes, and then gets another vote but stays at 4.85, I can tell you with certainty that the last vote was a 5. There is no other combination of numbers that can produce this result.
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Old 12-01-2017, 02:13 PM   #29
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We're actually talking about different things.

I am saying that the back calculation of votes has a significant probability of error with more than 50 votes. This



Shows the probability that your back calculated vote will be correct. The jagged blue shows the probability resulting from numerical experiments in the very simplified case where you have received 1 vote. The smooth dark red line shows the theoretical probability. In either case, the errors start at 50 votes.

What you have said is that you can use forward calculations to determine the exact number of votes. I won't dispute that, but I might suggest that doing so isn't very practical--especially if you don't start by doing the back-calculation first.

This is a screenshot of voting results on one of my stories on the morning it posted.



The columns from left to right are the # of votes, score, estimated # of *s, the change in *s, the change in votes, then the estimated # of votes from one to five. If the number of votes cast (5th column) is one, then the change in the *s (4th column) is the estimated vote.

The screenshot shows obvious errors at 64 votes and 72 votes. The errors are only obvious because you can't get 6 *s from one vote. Any of the other estimated votes could also be in error. And yes, I can do a forward calculation to ascertain that the correct vote was probably a 5 in each case. Sweeps hadn't started yet, otherwise the 6 * result could come from a combination of votes and sweeps.

Each of us decides when the level of effort goes beyond the point of diminishing returns. Given the ambiguity that comes from getting multiple votes between observations and of combining incoming votes with sweeps, I'm rarely willing to do a series of forward calculation to check the results. It doesn't add much to what I already know.
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File Type: png Screenshot from 2017-12-01 10-56-30.png (11.8 KB, 0 views)
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Last edited by NotWise : 12-01-2017 at 02:17 PM.
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Old 12-01-2017, 06:45 PM   #30
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Quote:
Originally Posted by NotWise View Post
We're actually talking about different things.

I am saying that the back calculation of votes has a significant probability of error with more than 50 votes.
Can you clarify what you mean by "back calculation" vs. "forward calculation"? I'm not familiar with that terminology.

Quote:
What you have said is that you can use forward calculations to determine the exact number of votes. I won't dispute that, but I might suggest that doing so isn't very practical--especially if you don't start by doing the back-calculation first.
I think you're rather overstating the difficulty. It just takes a couple of simple spreadsheet formulas and once it's set up, it can be used over and over. The slowest part is the data entry, which you'd have to do for any method. I'm willing to go to the trouble of typing an extra formula, once, for a method that gives perfect certainty up to 100 votes and doesn't estimate 6s.

Quote:
This is a screenshot of voting results on one of my stories on the morning it posted.



The columns from left to right are the # of votes, score, estimated # of *s, the change in *s, the change in votes, then the estimated # of votes from one to five. If the number of votes cast (5th column) is one, then the change in the *s (4th column) is the estimated vote.

The screenshot shows obvious errors at 64 votes and 72 votes. The errors are only obvious because you can't get 6 *s from one vote. Any of the other estimated votes could also be in error.
Nice scores!

For comparison, here's what I get when I do it my way, using the same inputs as your example. It took literally two minutes to set up this spreadsheet, and it gives exact numbers with no uncertainty and no 6s. From that table, I can figure out that you got exactly 24 five-star votes and 4 four-star votes during that period, with no 1s, 2s, or 3s... which is the answer to the OP's question. All that for far less effort than either of us have spent discussing the issue here.

For vote counts over 100, "unrounded score" and "change in stars" would be ranges based on min and max # of stars, but in this example there's no space between them so I've just left one column.
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Old 12-01-2017, 06:55 PM   #31
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Think of the actual writing you folks could be doing.
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Old 12-01-2017, 08:12 PM   #32
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Quote:
Originally Posted by Bramblethorn View Post
Can you clarify what you mean by "back calculation" vs. "forward calculation"? I'm not familiar with that terminology.
"back" calculate mean deriving the unknown # of *'s voted through a formula like:

T=round(N1*S1-N0*S0)

N1 and N0 are the current and previous number of votes
S1 and S0 are the current and previous ratings.
T is then the change in the total number of stars voted, which translates to the value of the vote if there's only one vote.

"forward" calculate means to derive the number of stars by finding out what is necessary to achieve the reported score, given the change in votes and the number of stars in the previous vote.
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Old 12-01-2017, 08:31 PM   #33
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Originally Posted by sr71plt View Post
Think of the actual writing you folks could be doing.
It's a good thought, but Saturday morning isn't great for writing for me; for some reason I find stories flow better at night.

Arguing mathematics, that I can do 24/7 ;-)
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Old 12-02-2017, 12:39 AM   #34
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Originally Posted by sr71plt View Post
Think of the actual writing you folks could be doing.
LOL. I say this to myself sometimes, especially when I've been complaining to myself about not getting a story done and instead am brainstorming a reply to something someone said on these threads.
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Old 12-02-2017, 06:41 AM   #35
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Think of the actual writing you folks could be doing.
I tell myself that too, yet here I am, reading all the new posts in my writing time.....
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