That is, a decision on the basis of particular assumptions would be the same if those assumptions were wrong.
For example, if evidence is ruled admissible on the basis that there was no impropriety in the way it was obtained, a judge may say that even if the alleged impropriety had existed the evidence would still have been excluded.
I criticised that sort of reasoning a while ago: "Shaheed balancing: three propositions"  New Zealand Law Journal 475. So did the Chief Justice last month, when with Blanchard, Tipping and McGrath JJ she delivered the reasons for granting leave to appeal in Hamed v R  NZSC 27 (24 March 2011) at :
"After considering all of these matters, we have not been persuaded that the outcome of the trial would necessarily have been the same if Mr Condon had been legally represented. In our view there was therefore unfairness in the trial and accordingly a substantial miscarriage of justice has occurred."
On this point the Court had reasoned better in Sungsuwan v R  NZSC 57, which was noted here in August 2005, and I observed that the majority of the Privy Council in Howse v R (New Zealand)  UKPC 31 had fallaciously asked what course the trial would have taken if the relevant errors had not occurred. The way to avoid this artificial exercise is to ask, given that the errors occurred, what was their effect on the fairness of the trial.
In Sungsuwan the effect of the error on the verdict was a sufficient, but not a necessary, condition for a finding that the trial was unfair. It is one of the ways in which unfairness may be manifest. Another is where partiality existed although the verdict was inevitable. The sufficient condition should not be treated as if it was a necessary condition, as occurred in Matenga v R  NZSC 18 at  footnote 39 where the Court defined a substantial miscarriage of justice as one which affects the result of the trial.