In the end, 14 respondents cooperated and 6 defected, exactly as would be expected from extrapolating the first 7 responses\. If we imagine that it was entirely fair to extrapolate the results this precisely, then the average respondent among the first 7 would need to imagine roughly 2 of the next 13 respondents being correlated with them\. Your move being correlated with 2 others would not, in this particular setup, be enough to swing the balance toward Cooperating instead of Defecting\. Even moving in unison with 4 others wouldn't be enough to swing the result\. ?
I'm not sure I understand this part. Did you get "roughly 2" just by dividing 13 by 7?
Why should the first 7 respondents think of themselves as being part of the first 7 (rather than the first 4, etc)?