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02/19/2011 04:45:19 PM · #1 |
A continuation of the discussions that started here:
Voting Stats - Average and Central Tendency
Simulation – A low vote and its effect
Introduction:
I came across an old voting thread containing an interesting debate about the affect of a single Troll vote on an average score. The OP proposed that his dramatic example showed the "true effect" of a low vote. In this section we'll take a second look.
The premise:
If you have 150 votes that average to 6.5 and a Troll votes a 4, it will take five 7 votes to return your average to 6.5
A second look:
I take no exception with the mathematics; the OP is correct. However, I do have to take exception with problem statement. It’s a bit of a semantic fallacy. It reminds me of the riddle where three men rent a hotel room. Each pays $10 for a total of $30 spent on the room. The next day the hotel owner tells the three men that they over paid for the room as it only costs $25. The three men tell the owner to give them each a dollar back and he can keep two dollars. If you do the math, each man paid $9 a piece for the room for a total of $27. The owner kept $2 which brings the total to $29. The question is where did the other dollar go? There is no other dollar really; $25 for the room + $2 for the owner + 3 dollars for the men = $30.
My first concern with the premise is that a vote of 4 is 2.5 points below the mean of 6.5 and a vote 7 is only 0.5 points above. Obviously it takes more votes of 7 to equalize the effect of a single 4. It’s like saying if I have 50 cents in change in my pocket and I lose a nickel it will take 5 pennies to bring me back to where I started. True, but not really that dramatic.
The drama is increased by common sense telling us that it’s harder to achieve a 7 vote than it is to achieve a 4 vote so how can we possibly compensate for the Troll's attack by getting five more 7 votes. However the OP's argument takes the 4 and 7 votes out of context. He isn't considering the distribution of votes that brought us to the 6.5 average to begin with. If 150 votes average 6.5 it's likely that we already received more 7 votes than 4 votes and the probability of getting more 7 votes as voting continues is probably higher than getting another 4. The closer that a value is to the central peak of the distribution the higher the probability of occurrence. Let's look at this graphically:
Because we vote in whole numbers only, the distribution above shows how an average of 6.5, with the least possible variation, could be achieved in 150 votes. Seventy five voters would have to choose 6 and seventy five voters would have to choose 7. Any other distribution with an average of 6.5 will have more variation. If the next vote was a 4 it would clearly stand out in this distribution as a special cause.
However, the reality is that the distribution of votes that brought us to the 6.5 average probably looks more like this second one. It has the same average but it has variation that is more typical of a DPC vote distribution (~1.3 standard deviation). It’s hard to call a 4 vote Troll activity in this distribution or most others for that matter. Seven 4 votes were already registered in the first 150 votes. If an additional 4 vote is questioned as Troll activity like the OP suggests then any additional 9 should be questioned too. If you were betting on what the next vote in the series would be, knowing this distribution, would you put your money on 4 or 7?
Repeating the simulation that produced this distribution 150 times shows that with the 150 votes per distribution, 6.5 average and 1.3 standard deviation parameters a vote of 7 occurs 6.4 times for every 4 vote according to the OP's calculation it only takes five to compensate. This doesn’t even consider the greater than 7 votes in the distribution that have already more than compensated for all of the less than 6 votes.
A few points to consider:
This problem is not nearly as dramatic when you say that for every 4 vote from a Troll it takes one 9 to recover but these votes are equidistant from the mean of 6.5 and have about the same probability of occurring.
Do you realize the reverse of the OP's premise is also true? If you have 150 votes averaging 6.5 and a Pollyanna voted a 9 it would take five votes of 6 to bring your average back to 6.5. Nobody ever complains about that.
The OP says; “to all the naysayers: of course you will get 4 votes. You will even get 1 votes occasionally. Do they affect your net score? You bet they do, so don't try to rationalize that a few low votes will not affect your final placement!” The corollary is; “of course you will get high votes. You will even get 10 votes occasionally. Do they affect your net score? You bet they do, so don't try to rationalize that a few high votes will not affect your final placement!”.
Your average score while voting is in progress is just a snapshot in time. For every additional vote you receive one of three things is going to happen your average will go up, down or stay the same. Just because the first 150 voters average 6.5 doesn’t mean that they all voted 6 or 7. If the 151st voter selects a 4 (or lower) it doesn’t make them a Troll.
Link to Voting Stats site
Message edited by author 2011-02-19 16:54:08. |
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02/19/2011 05:01:52 PM · #2 |
There are a couple of problems:
1. Hardly anyone thinks of a 4 as a troll vote. 1s or 2s are the troll votes.
2. The reason people are upset that it takes so long to recover, is because they don't feel the 1 is justified.
So that's why the complaints. |
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02/19/2011 05:05:51 PM · #3 |
Originally posted by vawendy:
1. Hardly anyone thinks of a 4 as a troll vote. 1s or 2s are the troll votes. |
That's Del's whole point. Read his very last paragraph. |
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02/19/2011 05:18:09 PM · #4 |
Originally posted by bvy:
Originally posted by vawendy:
1. Hardly anyone thinks of a 4 as a troll vote. 1s or 2s are the troll votes. |
That's Del's whole point. Read his very last paragraph. |
But a vote of 1 would be a deviation of 5.5 below the average. I'd agree if there was an equal chance of getting a deviation of 5.5 above the average but there's no option to score an image a 12.
bazz. |
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02/19/2011 05:26:31 PM · #5 |
Originally posted by sir_bazz:
But a vote of 1 would be a deviation of 5.5 below the average. I'd agree if there was an equal chance of getting a deviation of 5.5 above the average but there's no option to score an image a 12.
bazz. |
Del's logic still holds. I've written about this before, in fact. When we look at voting distributions for very high scoring (or low scoring) images, the distribution gets pushed up against the side of the scale. In this case, you'd think that all the votes that would lie above 10 (or below 1) get truncated, but that's not the case. They "pile up." In other words, there will be lots more tens (or ones) than you'd expect, and so the effect of one very low vote is more easily offset because there are even more moderately high votes.
We don't see as many troll-vote-bitching threads as we used to, but when we did, a common complaint went something like "look at this vote distribution! Tell me why there's a big "spike" of ones! Shouldn't there statistically be less than the number of twos??" All it was was just the piling up of votes at the end of the scale, and it was perfectly normal. No one however, to my memory, ever complained about piling-up of tens ;-)
Edit for typo
Message edited by author 2011-02-19 17:28:23. |
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02/19/2011 05:29:29 PM · #6 |
Nor a minus 2.
Whenever I start out with an 8 or a 9, nearly all subsequent votes are "troll" votes.
Now everybody assume the lotus position and meditate on Del's last paragraph while  bvy and I hit you with sticks. |
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02/19/2011 05:30:29 PM · #7 |
Originally posted by sir_bazz:
Originally posted by bvy:
Originally posted by vawendy:
1. Hardly anyone thinks of a 4 as a troll vote. 1s or 2s are the troll votes. |
That's Del's whole point. Read his very last paragraph. |
But a vote of 1 would be a deviation of 5.5 below the average. I'd agree if there was an equal chance of getting a deviation of 5.5 above the average but there's no option to score an image a 12.
bazz. |
Deviation or not... a 1 vote is an expression of what someone thinks this image is worth. The collective may not agree with this view, but that in itself does not make it invalid.
Ray |
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02/19/2011 05:34:43 PM · #8 |
Originally posted by kirbic:
When we look at voting distributions for very high scoring (or low scoring) images, the distribution gets pushed up against the side of the scale. In this case, you'd think that all the votes that would lie above 10 (or below 1) get truncated, but that's not the case. They "pile up." In other words, there will be lots more tens (or ones) than you'd expect, and so the effect of one very low vote is more easily offset because there are even more moderately high votes. |
Just look at the top 5 (maybe more) images of the challenges currently on the front page to see this demonstrated with real data. |
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02/21/2011 07:30:32 PM · #9 |
Originally posted by RayEthier:
Deviation or not... a 1 vote is an expression of what someone thinks this image is worth. The collective may not agree with this view, but that in itself does not make it invalid.
Ray |
All true of course except those who vote high tend to leave a positive comment. Those who vote 1's tend not to leave a comment so it's hard to understand why they've vote that way or why they seem out of step with the rest of the community.
bazz. |
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02/22/2011 04:00:27 AM · #10 |
All this talk of voting stats reminds me of a similar occurrence of people complaining of outcomes irrationally-
Your favorite basketball( my point is best proved with basketball, but it works for all sports) team gets down to the final seconds, and the superstar for the team has the ball and can win the game by making a 2 pt shot. The star misses, time runs out, and the fans and the media and everybody around says "Oh man they lost that game!"
Just as Del pointed out that glimpsing the average at any given point is a snapshot, so is this true of the game. That miss lost the game no more than the countless other misses (unless the team shot 100%). Just as a shoddy overall game will lose games, so too will a shoddy average lose challenges. The average is not a single value, it is a compilation, so the only thing you can blame a bad average on is a bad average. If your average is low, it's because a large portion of the voting body thinks it should be.
If you want to argue about the actual strength of purported troll votes, that's different, but still silly. Presuming there are really all these people lurking that want to hate on every image they can, the only way to counteract them is to then lower their vote weight, either by decreasing their numbers (the job of the scrubber) or by increasing their relative minority status by having a high number of voters (the job of the general populace of this online community). Somehow I don't think that trollhunts succeed on any count at this. |
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02/22/2011 09:06:22 AM · #11 |
Originally posted by sir_bazz:
Those who vote 1's tend not to leave a comment so it's hard to understand why they've vote that way or why they seem out of step with the rest of the community. |
THIS is the real issue with the low votes as far as I am concerned. We are left asking "why?", but generally it's not worth the voters time to leave such a comment.
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02/22/2011 09:32:31 AM · #12 |
Originally posted by sir_bazz:
Those who vote 1's tend not to leave a comment so it's hard to understand why they've vote that way or why they seem out of step with the rest of the community. |
Just about every 1 vote I get means that the voter didn't like the image. Safe place to start, and, in reality, you likely already know why they don't like it. If you don't know, then you don't understand your own entry. |
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02/22/2011 09:59:06 AM · #13 |
Originally posted by bspurgeon:
Originally posted by sir_bazz:
Those who vote 1's tend not to leave a comment so it's hard to understand why they've vote that way or why they seem out of step with the rest of the community. |
Just about every 1 vote I get means that the voter didn't like the image. Safe place to start, and, in reality, you likely already know why they don't like it. If you don't know, then you don't understand your own entry. |
Difference is, if I dont like an entry I give a 3. I've never given a 1 nor do I understand anyone giving a 1. |
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02/22/2011 10:08:06 AM · #14 |
Originally posted by gcoulson:
Originally posted by bspurgeon:
Originally posted by sir_bazz:
Those who vote 1's tend not to leave a comment so it's hard to understand why they've vote that way or why they seem out of step with the rest of the community. |
Just about every 1 vote I get means that the voter didn't like the image. Safe place to start, and, in reality, you likely already know why they don't like it. If you don't know, then you don't understand your own entry. |
Difference is, if I dont like an entry I give a 3. I've never given a 1 nor do I understand anyone giving a 1. |
I never give 3s, why do you use the 3? This argument doesn't make sense. A vote is a vote as the stats support. |
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02/22/2011 10:26:01 AM · #15 |
Originally posted by bspurgeon:
If you don't know, then you don't understand your own entry. |
I posses a distinct lack of understanding. I don't understand the high scoring ones either.
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02/22/2011 10:56:51 AM · #16 |
The fix is so obvious, I don't know why anyone hasn't pointed it out already.
Have the scale go from 1-10 then add a 12, but nobody vote the 12 unless someone sends an email because they are upset about a low vote. Then we will go vote a 12 so they feel better.
We could also add a -1 vote to offset accidental 12s, but then we'd need a 16 to offset accidental -1s.
This will all be OK as long as we *pinky swear* not to use them unless we get the email.
Oh, we probably need to go ahead and disable 1 and 2 and only have those votes count "if they really think it and are not just being mean," which we could also do with an extra email template.
Easy. |
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02/22/2011 10:59:52 AM · #17 |
| When people demand an explanation for a low vote it's been my experience that they don't really want to understand, they simply want to argue. |
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02/22/2011 11:12:18 AM · #18 |
Duplicate post.
Message edited by author 2011-02-22 11:17:28. |
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02/22/2011 11:17:00 AM · #19 |
Originally posted by gcoulson:
Originally posted by bspurgeon:
I never give 3s [...] |
Curious why not? Does a photo automatically get a 1 or 2 if you don't like it even if it is a good photo technically? |
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02/22/2011 11:17:48 AM · #20 |
is this a statistics or photography forum?
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02/22/2011 11:32:16 AM · #21 |
Originally posted by ubique:
When people demand an explanation for a low vote it's been my experience that they don't really want to understand, they simply want to argue. |
Perhaps that has been your experience, but such is not always the case.
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02/22/2011 11:45:11 AM · #22 |
Originally posted by gcoulson:
Curious why not? Does a photo automatically get a 1 or 2 if you don't like it even if it is a good photo technically? |
I rarely give a 1. Usually only to charliebaker's colored squares, because I know that's what he wants. I did give a very rare 1 to a pretty decent photo in a current challenge. I also left an explanatory comment. I won't discuss it further until the challenge has ended.
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02/22/2011 11:52:37 AM · #23 |
| i like to give out 10's to any image with gratuitous nudity, just to try to counteract the negative votes they surely get. i also give 1's to wine glasses, for the same counter effect. |
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02/22/2011 11:56:12 AM · #24 |
I only give a 1 if I feel the photographer is trying to be a jerk with his entry AND the entry is poorly shot. Purposeful shoe-horns, poorly composed abstracts, etc. tend to be my only victims in this area. Even a crappy snap shot, I will give a 3 or a 4 to depending on composition, color, and purpose. . . Of course, I tend to vote higher than not, so maybe thaqt is the issue. I do have to agree with some earlier comments. These discussions only come about because you can see the results go down live via "update". If we just got a score at the end of the week, this thread wouldn't exist. I know I hate it when a photo doing good (FOR ME), suddenly takes a hard dive because someone 1 or 2 voted it, but maybe I shouldn't hit UPDATE and have a spreadsheet that calculates what that vote is then. LOL.
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02/22/2011 12:01:50 PM · #25 |
Originally posted by mike_311:
i like to give out 10's to any image with gratuitous nudity, just to try to counteract the negative votes they surely get. i also give 1's to wine glasses, for the same counter effect. |
Well that's really... pathetic isn't the right word. But it's along the right lines.
Vote on something based on whether you like or not... not because you feel it's your duty to 'fix' its score.
If you don't like a wine glasse shot give it a 1 then. Not because there're wine glasses in the shot.
If you like a nude shot give it a 10. Not because it has nudes.
Not every subject can attain a 7+ score with a full set of votes (broad appeal, as Steve says). That's because a different subjects appeal to different people in different ways and different amounts. It's how it should be. Just because your feelings towards something are one way inclined doesn't allow you the pleasure of playing vigilante around the challenges.
Just because someone's showing some ass doesn't make it a good shot.
Just because there's a wine glass doesn't make it a bad shot.
Don't vote like that. It's dishonest, and doesn't judge the images based on what it should be judged on.
Message edited by author 2011-02-22 12:02:43.
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