Quote:
Originally Posted by Infinity2718
I find both of these interesting, so I would like to expand on them:
1 vs 10 = 26 to 12 = 2.16:1 ratio
1-2 vs 9-10 = 37 to 16 = 2.31 ratio
1-3 vs 8-10 = 48 to 23 = 2.09 ratio
1-4 vs 7-10 = 55 to 29 = 1.90 ratio
1-5 vs 6-10 = 67 to 33 = 2.03 ratio
No matter how you slice the deck, for every one person approving the championsplit, there are two people opposing it.
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This method isn't exactly fair either. In your first comparison, you are comparing the ratio of 25% of negative responses to 20% of positive. In your second it is 50% to 40%, and so on. In your last comparison, you count 5 (neutral) as negative.
What if we rescaled to a scale from 0 to 10? We can map the negative responses linearly to get the new responses. We replace 1 with 0, 2 with 1.25, 3 with 2.5, and 4 with 3.75. After performing the average based on this data, we get:
.26*0+.11*1.25+.11*2.5+.07*3.75+.12*5+.04*6+.06*7+ .07*8+.04*9+.12*10 = 4.06
This weights everything symmetrically. It keeps positive values positive, and negative values negative. However, I think it is still likely to be flawed, as someone who is approximately neutral might be more likely to lean towards the favorable side than negative simply because the positive side is larger. Someone who votes roughly neutrally based on the "center" of the scale may be unfairly counted as voting positively.
A better method might be to map the entire scale from 1-10 to 0-10. We replace 1 with 0, 2 with 1.111, 3 with 2.222, 4 with 3.333, 5 with 4.444, 6 with 5.555, 7 with 6.666, 8 with 7.777, and 9 with 8.888 (10 remains 10).
We now get:
.26*0+.11*1.111+.11*2.222+.07*3.333+.12*4.444+.04* 5.555+.06*6.666+.07*7.777+.04*8.888+.12*10 = 3.86
This scale is likely to be slightly biased towards negative, because it treats "neutral" according to the instructions as very slightly negative.
I think the true average, if the scale had been 0-10 instead of 1-10, would lie somewhere between these two numbers. In any case, they are closer to each other than they are to FIRST's number for the average (4.47).
There also are quite possibly some psychological effects that I have not accounted for. Do the numbers on the scale themselves affect how we vote? If given a poll, 1-5, and the average is 4, does this imply that if the same poll was conducted on a scale from 1-9, the average would be 7? This would be expected if people simply scaled their votes linearly (or at least, linearly on average) but that may not be the case.
If we remap the entire scale