A conviction can only be "according to law", but an acquittal need not be.
We don't often mention the jury's power to return a perverse verdict acquitting a defendant. It is probably best not to mention it at all. Sometimes it is put in a way that is obviously wrong, as when a self-represented defendant submitted on appeal that it is the jury's
Mckee v R  NZSC 122 (14 November 2013) at . Naturally the Court rejected this submission.
A problem with this sort of broadside submission is that it will provoke a sweeping reaction. The Court said :
More accurately, a jury's duty is to ensure that if a verdict is guilty it results from applying the law in accordance with the judge's instructions.
If the jury has applied the law in accordance with the judge's instructions, the defendant cannot appeal saying that the jury shouldn't have done that. Perversity of verdict is a matter entirely for the jury and cannot be taken up as ammunition for the defendant on appeal.
Nor can a prosecutor appeal against an acquittal on the grounds that it was perverse.
Obviously, I must point to some authority in support of my criticism that the Supreme Court was not accurate at . In R v Shipley (1784), 4 Dougl. 73, 99 E.R. 774, at p. 824 Lord Mansfield said:
"It is the duty of the Judge, in all cases of general justice, to tell the jury how to do right, though they have it in their power to do wrong, which is a matter entirely between God and their own consciences."
This was cited with approval by the Supreme Court of Canada in R v Krieger  SCC 47, discussed here on 27 October 2006 where I also referred to the views of Lord Devlin and Geoffrey Robertson QC.
To those dicta I add Lord Judge's speech "Jury Trials" Judicial Studies Board lecture, Belfast, 16 November 2010, available at http://www.judiciary.gov.uk/Resources/JCO/Documents/Speeches/speech-lcj-jury-trials-jsb-lecture-belfast.pdf. Lord Judge alluded there (p 2) to the power of the jury to return a perverse verdict:
So yes, subtlety is everything on this point. But whether a sweeping statement like that at  of McKee can really abolish the power of a jury to perversely acquit may be doubted. Can the perversity of a jury's acquittal ever be eliminated? The prosecutor would need a right to appeal on the grounds that an acquittal was unreasonable, and obtaining that would be a rather ambitious law reform project, at least in a robust democracy.