So you seem to be hung up on the math of it. Let's start with a simple and clear point: The "math" you're talking about doesn't matter. The decision has been made and it is not going to change. Sorry to tell you, it's just the way it is. Trust me, today is my 3rd anniversary here on Arqade, I've been around a little while, and we are happier because of this decision.
That said, let's talk about your math. You're assuming a standard deviation of a random sampling and calculating it (incorrectly, I might add) by talking the square root of the value. First, if that were the case, you would need to start with the total value, not the value of each vote, to get the standard deviation. That would be 34 + 27, which comes out to 61. A simple square root gives us a margin of error ~7.8, but taking into account the proper way to calculate margin of error for a population given a random sampling, it is actually ~12. The vote would have need to pass by a margin of 12 by those number to actually work correctly into your formula.
But here's the problem: Those calculations of margin of error are based on a random sampling, which a vote is not! It just isn't. If you consider it a study you have self-selection bias, involvement issues, duration and knowledge constraints, and, oh yeah, you're not actually taking a sampling. That last one is actually the most important, so it is going to take up a whole paragraph, but first we're going to ignore it and focus on the other issues. Users who visit meta are not representative of the entire population because they choose of their own free will to participate. We limit that participation in meta based on how active they are on the main site (reputation privilege), and we further cut that down by taking into account the fact that those who have knowledge of the system and how it works are the ones being most vocal, which would skew the results.
But even without that, we are not taking a sampling. Statistics and margins of error don't apply because we are not trying to measure something statistically. We are voting. And votes can be decided by a margin of 1. There is no margin of error. None. It doesn't even makes sense to apply a margin of error because anyone (in our case, with enough rep) can vote. Everyone had the power to participate, and we had 61 people who did. That's pretty high around here for meta participation. But that's not meant to be a statistical representation of a bigger number. If people wanted representation in the numbers, they had the power to be included. That is the number. Not a stat, a number.
A vote does not come down to a margin of error. The active users of the site, especially those who have experience with the system, took a vote. After a long long discussion we decided majority rules and counted heads. And we came to the conclusion that ITG was off-topic. We decided it because we felt it was best for the health of the site. And I honestly don't know a single person who has been here for a while who would want to revisit that discussion, no matter how they voted. That decision has been good for the site, and it is not changing. Sorry if you disagree, but it honestly doesn't matter in the end. We've tried it and it failed, miserably, even if you weren't around when it was going on.
As stated in numerous other places, it's not that we hate or have a vendetta against those questions. This is just not the place to ask them. We are not that kind of site. Just like we are not a forum for speculation or discussion. There are other places to ask that question and get good answers. And we are happy to point you in that direction.
Sqrt
.Sqrt[34] = 6
andSqrt[27] = 5
. The votings intersect by error. This is false decision.100 vs 80
it would be honest. It still would be simple majority, but it would be honest simple majority. But when you have34 vs 27
it is not simple majority, it is just random outcome. This is because the most members didn't vote and you don't know how many are them of. These34
do not reperesent ones who are againstITG
correctly