## uDG08 Voting Results and Methods

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Post: #61
tcIgnatius Wrote:This is when you would use the mean of all the categories to determine the winners. I mean it's a tie-breaker, a mean only would make sense. (and would be the average of the medians, which were not nerfed)

Whoops, I missed that last part about needing to use the average of the *medians*. I just recalculated using the medians, and quite to my surprise, the results are identical. In fact, the averages of the medians are *very* similar to the averages of the raw scores. I'd bet there's a statistics thesis hidden in there somewhere.
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Post: #62
Quote:
Quote:He already explained it (it was my original post). Read the posts again. They've been edited.

If another 10 is added, or another 1 is added, the score changes by 5. It's absurd.

How can you not see how arbitrary that is?

And again, the scores are *not* nerfed. One wacky number is potentially biased. 10 of them is likely not.
The score does not change by 5 if another 10 or 1 is added. You're still not considering the special case I have already stated. Also when will half the voters vote 1 and the other half 10? That's incredibly unrealistic. That's why I'm saying it's outrageous.
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Post: #63
tcIgnatius Wrote:The score does not change by 5 if another 10 or 1 is added. You're still not considering the special case I have already stated.

Dude, you still have described no "special case." As best we can tell, you're describing the definition of median and you're not even following it. The median of 1 1 10 is 1, not 5.5. I don't know where you're getting that from.

Apparently you're on some higher plane of thought because no one reading this thread has any idea of what "special case" you're talking about.

Quote:Also when will half the voters vote 1 and the other half 10? That's incredibly unrealistic. That's why I'm saying it's outrageous.

If you're going to propose a change to the voting system, you had better think of all possibilities. It *is* possible to have a polarizing game as I already even gave an example of, which apparently you either ignored or didn't see.

You look mighty silly chiding other people for "not using logical arguments" when you won't even consider all cases affected by your proposed "fairer" system.
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Post: #64
Quote:Dude, you still have described no "special case." As best we can tell, you're describing the definition of median and you're not even following it. The median of 1 1 10 is 1, not 5.5. I don't know where you're getting that from.
I did, the special case is when the range of the closest medians is greater than two, then you take the mean of the median range.

ex:
11444444888888810
the difference between 4 and 8 is greater than two
the range is less than two away from each other (4(6) + 8(7)) now divide by two.
edit: the 6 and 8 example basically re-illustrates what I just said, pretty pointless.

I'm basically saying use the mean in that special case because that is the only case that it's fair.
Why use something that is not fair most of the time for ALL cases.

Quote:Apparently you're on some higher plane of thought because no one reading this thread has any idea of what "special case" you're talking about.
Nope, still with you in this dimension. (i hope)

Quote:If you're going to propose a change to the voting system, you had better think of all possibilities. It *is* possible to have a polarizing game as I already even gave an example of, which apparently you either ignored or didn't see.
For such polarization you'll see that my method is fair.

I should also mention (again) interquartile mean would be the most fair, because it's basically the method I just described without needing special cases. 25% off the top and bottom, then the mean of what would be the remaining medians.
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Post: #65
tcIgnatius Wrote:ex:
11444444888888810
the difference between 4 and 8 is greater than two
the range is less than two away from each other (4(6) + 8(7)) now divide by two.
edit: the 6 and 8 example basically re-illustrates what I just said, pretty pointless.

I'm basically saying use the mean in that special case because that is the only case that it's fair.

I totally don't understand. I assume you mean:
1,1,4,4,4,4,4,4<-median here->8,8,8,8,8,8,8,10

There are 8 numbers on each side, 16 in total. There is no number in the middle, referred to as "the median". This is the even case when calculating a median. The odd case simply selects the central number. Here we have to manufacture a central number by averaging the closest two numbers to it.

By definition, the median in this case is calculated by adding 4 and 8 together and then dividing by 2 (the average of the two closest numbers to what would be the center):

(4 + 8)/2 = 6

So 6 is the median in this example.

This is *not* to be considered a special case; it is how a median is calculated when there are an even number of samples. This is text book.
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Post: #66
Quote:I totally don't understand. I assume you mean:
1,1,4,4,4,4,4,4<-median here->8,8,8,8,8,8,8,10

There are 8 numbers on each side, 16 in total. There is no number in the middle, referred to as "the median". This is the even case when calculating a median. The odd case simply selects the central number. Here we have to manufacture a central number by averaging the closest two numbers to it.

By definition, the median in this case is calculated by adding 4 and 8 together and then dividing by 2 (the average of the two closest numbers to what would be the center):

(4 + 8)/2 = 6

So 6 is the median in this example.

This is *not* to be considered a special case; it is how a median is calculated when there are an even number of samples. This is text book.
ugh, good grief, did I accidentally put an even number of integers? Pretend it is odd, now understand the special case is not really the median, but the mean of two medians.

I would like to know how you understood the median concept, yet completely missed out on what I was trying to say... because you assumed I was wrong? Charity people, that's all I'm asking for here.

I should also restate that the interquartile mean would be the most fair as it pretty much says what I am trying to say in a more elegant way.
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Post: #67
Quote:Charity people, that's all I'm asking for here.

Apparently so.
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Post: #68
Hehe... Yes, tcIgnatius, this is a very long discussion, but it's a good one IMHO.

I am not assuming your wrong; I honestly do not understand what your special case is. I just haven't seen a post that I could wrap my mind around and understand (other than using median for voting, which I am still opposed to in theory, but I'm still willing to hear the arguments). If you take the time and clearly explain things one more time, perhaps we'll get this straightened out. Admittedly, math is not my forte (by any stretch), so you really do have to communicate things in simple terms.

I just picked up on the idea that you're trying to describe your "special case" as the mean of two medians, not just two samples. Sounds like you need to rewind at least back to the part where we've derived two medians to work with in the first place, and not just two samples, because I don't know where those two medians came from.

What I'm envisioning by your using the interquartile mean is to take the raw votes for a game in a given category, then throw out the top and bottom 25%, and then calculate the median based upon that center 50%.

Maybe a step by step description would be helpful.

Looks like I'll have to pick up on this in the morning...
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Post: #69
tcIgnatius Wrote:Pretend it is odd, now understand the special case is not really the median, but the mean of two medians.

If it was odd, the median would be the one in the middle!

What determines whether you use this special case or not? Them being far apart? How far apart? Seriously... you need to be more thorough in explaining this because so far this is still going nowhere, and there's absolutely zero chance of any one else going along with this

And either way, this still doesn't address the fact that most games would be tied, requiring an arbitrary tie breaker based on other merits.

Quote:I should also restate that the interquartile mean would be the most fair as it pretty much says what I am trying to say in a more elegant way.

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Post: #70
Anyway since no ones willing to try understand (or decode, which possibly might be a better way to put it) what I'm saying, a simple example might help explain why the mean is just plain unfair for scoring. (and why they don't use this in any professional scoring events where competitors score each other)

Game A gets a score 1 5 5 5 5 5 5 5 5 5 = 4.6
The one 1 vote just outweighed the other nine 5's. Why should this person score below a 5, if nine people gave it a 5?

Game B gets a score 5 5 5 5 5 5 5 5 5 10 = 5.5
The one 10 vote just outweighed the other nine 5's. Why should this person score above a 5, if nine people gave it a 5?

Interquartile mean works fairly in most cases.
25% of the top scores removed
25% of the bottom scores removed
Do the mean of whatever is left. (which will be more or less a mean of medians)

The median with the addition of Special cases:
Do the median except for the cases when:
1a. The two largest sub-medians difference in occurrence is < 2
Do the mean of the two values in each sub-median.
1b. The two largest sub-medians difference in value is > 2
Do the mean of the entire set of the largest two sub-medians.

Highly Polarized/Nerfed examples:

ex g1: 3 3 5 5 5 5 7 7 7 7 9 9 10 = (5+7)/2 = 6
g2: 3 3 5 5 5 5 8 8 8 9 9 10 10 = (4(5) + 3(8) )/7 = 6.28 [edit in my sleep deprived state i forgot to put the divisor as the sum of the differences in occurrence)

ex:g2 should have won, and did.(even in a worst case scenario)

Now g1 gets un-nerfed:4 4 5 5 5 5 7 7 7 7 9 9 10 mean= 6.4 and sp. median= 6
and g2 gets more nerfed:2 2 3 5 5 5 5 8 8 8 9 9 10 mean= 6.0 and sp. median= 6.28
I feel like g2 should win, but doesn't under the mean vote.

[Edit for clarity]
Anyway, I'm tired as hell. Time for sleep.
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Post: #71
Eek! I only intended to provoke a little debate by posting the full results.

Never seen a thread go to 5 pages in 24 hours before!

- Iain
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Post: #72
Still incomprehensible.

-

However the special cases work, a non-special case clearly shows that a median is wrong:

Story:
G1: 7 8 8 8 8 = 8 med, 7.75 mean
G2: 8 8 8 8 8 = 8 med, 8 mean
G3: 7 7 7 8 8 9 9 = 8 med, 7.85 mean

Everything else:
G1: 8.3
G2: 6.5
G3: 7.2

The median forces a tie, which is broken by scores irrelevant to the story category. G2 should clearly win the category and yet it loses mightily to G1, which has the lowest score in the Story category and yet still wins because it has better Graphics, Audio, Polish, etc.

A mean is indisputably the most accurate method for ranking here, and this example should clearly be enough to throw this out the window.

And if somehow those scores fall into a "special case" where they have to be recomputed in some other way, then I'm sorry, but that's just too complex for my tastes. Scoring should be simple and understandable by everyone. Throw out "obviously" biased values, and take the average of everything that's left. There's simply no need for anything more complex.
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Post: #73
FreakSoftware Wrote:Throw out "obviously" biased values, and take the average of everything that's left.

Dunno how you define "obviously". Genuine outliers are to be expected, so you need to drop a fixed percentage of high/low scores. Doing so effectively reduces the standard deviation, which makes things seem more consistent.

Otherwise I agree, using the median is pointless, the mean is the only metric that makes sense. And the cropped mean *is* used in sporting events.
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Post: #74
The average method is fine. If five people love it and one person HATES it, then that person is allowed to give that game a 1! We do not need to arbitrarily throw out his vote!

USA example: Would you throw out a Republican vote in a strongly Democratic district just because it was an "outlier"? Come on now!

Ideally, we would have voters submit their own sets of results, specifying 1st through 3rd place for each category. This is a tried and true method of determining winners in situations like this. However, it requires a lot more thought and testing, and so we would have fewer voters. There is always a tradeoff, and making some crazy convoluted system will not magically solve your problems!

My web site - Games, music, Python stuff
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Post: #75
Honestly, I am sick of arguing about this, but no one seems to want things to be fair. (are the people who are arguing against me nerfing votes???)

Quote:Story:
G1: 7 8 8 8 8 = 8 med, 7.75 mean
G2: 8 8 8 8 8 = 8 med, 8 mean
G3: 7 7 7 8 8 9 9 = 8 med, 7.85 mean

G3. Is WRONG there are three 7's and two 8's and two 9's that means under the special case (the diff in occurrence of the sub-medians < 2) you would say (8+9)/2 = k
(3(7) + 4(k))/7 = 7.85
G2 is RIGHT, and it should be.
G1 is correct, and why did only five people vote for such a high scoring game? Once again, why should one vote outweigh the others? the majority felt it deserved an 8, one person felt it deserved less then 8, so it gets less then 8?

Quote:A mean is indisputably the most accurate method for ranking here, and this example should clearly be enough to throw this out the window.
Exactly how did you argue the weight of a single score? oh wait, you didn't...

Quote:The median forces a tie, which is broken by scores irrelevant to the story category. G2 should clearly win the category and yet it loses mightily to G1, which has the lowest score in the Story category and yet still wins because it has better Graphics, Audio, Polish, etc.
G1,G2,G3 would have all won in the graphics category. Sure G2 would have been second, but it still would have won.

Quote:USA example: Would you throw out a Republican vote in a strongly Democratic district just because it was an "outlier"? Come on now!
This is a horrible analogy for you, because this is pretty much what the electoral system does. A state with a majority of votes for a party, receives ALL the electoral votes from that state.

Quote:There is always a tradeoff, and making some crazy convoluted system will not magically solve your problems!
Actually the special case median (which is not entirely a median, but a combination of median, mean, and mode) does "magically" solve any nerfing issues. I can't see why you are against this.