Barristers, being fair-minded observers of the judiciary, are constantly amazed at how fair-minded judges are. (I smirk, but then I often smirk – it doesn't mean anything.) No doubt judges have acquired this fair-mindedness in the course of their practice at the bar before they were appointed – elevated can hardly be the right word – to the bench. No doubt barristers acquire their own fair-mindedness by learning from the example of judges. Aside from the chicken and egg question that comes to mind, we are justified in rejoicing at this perpetual cycle of fair-mindedness.
Occasionally the complaints of clients make it necessary for counsel to submit, reluctantly but courageously, that a judge has been biased, and so an examination of the concept of fair-mindedness is required. The House of Lords, back from their surprisingly long summer break, have addressed this in Helow v Secretary of State for the Home Department  UKHL 62 (22 October 2008).
They don't say so, but in describing the qualities of fair-mindedness the Law Lords are portraying themselves. There is, as modesty demands, a gentle tone of mockery in Lord Hope's opening remarks:
"The fair-minded and informed observer is a relative newcomer among the select group of personalities who inhabit our legal village and are available to be called upon when a problem arises that needs to be solved objectively. Like the reasonable man whose attributes have been explored so often in the context of the law of negligence, the fair-minded observer is a creature of fiction. Gender-neutral (as this is a case where the complainer and the person complained about are both women, I shall avoid using the word "he"), she has attributes which many of us might struggle to attain to."
Too modest, and a signal we are in for some sarcasm on the sexual-politics front. So,
"2. The observer who is fair-minded is the sort of person who always reserves judgment on every point until she has seen and fully understood both sides of the argument. She is not unduly sensitive or suspicious, as Kirby J observed in Johnson v Johnson (2000) 201 CLR 488, 509, para 53 [I interpose here to note that Kirby J in that passage is absurdly conscientious in avoiding use of the male pronoun]. Her approach must not be confused with that of the person who has brought the complaint. The "real possibility" test ensures that there is this measure of detachment. The assumptions that the complainer makes are not to be attributed to the observer unless they can be justified objectively. But she is not complacent either. She knows that fairness requires that a judge must be, and must be seen to be, unbiased. She knows that judges, like anybody else, have their weaknesses. She will not shrink from the conclusion, if it can be justified objectively, that things that they have said or done or associations that they have formed may make it difficult for them to judge the case before them impartially."
A further quality of this creature of fiction is that he is "informed":
"3. Then there is the attribute that the observer is "informed". It makes the point that, before she takes a balanced approach to any information she is given, she will take the trouble to inform herself on all matters that are relevant. She is the sort of person who takes the trouble to read the text of an article as well as the headlines. She is able to put whatever she has read or seen into its overall social, political or geographical context. She is fair-minded, so she will appreciate that the context forms an important part of the material which she must consider before passing judgment."
Some caution is needed when a judge has been associated with a political cause, as Lord Walker said (26), adding that the judicial oath is not a panacea (27). Lord Cullen noted that some faith could be placed in the judge's training and experience (30) – just as I thought. Lord Mance referred briefly to a principle of automatic disqualification (40) that could arise in circumstances that didn't apply here. He also observed that cogent evidence is needed to show judicial bias (57) but he also described the judicial oath as a symbol, not a guarantee, of impartiality. As to whether a judge's failure to disclose an interest is necessarily an indication of lack of fair-mindedness, things get a bit circular when Lord Mance points out (58) that failure to disclose might indicate real fair-mindedness because the judge was so fair minded that it wouldn't have occurred to him that he might not be fair-minded.
Well it's all marvellous stuff, and very reassuring.