The phrase sentence first (and) verdict afterwards is used to denounce arbitrariness.

The allusion is to a demand by the Queen of Hearts during the trial of the Knave of Hearts in Chapter XII. Alice’s Evidence, the last chapter of Alice’s Adventures in Wonderland (1865), by the English author Lewis Carroll (Charles Lutwidge Dodgson – 1832-98):

[New York: D. Appleton and Co., 1866:]
“Let the jury consider their verdict,” the King said, for about the twentieth time that day.
“No, no!” said the Queen. “Sentence first—verdict afterwards.”
“Stuff and nonsense!” said Alice loudly. “The idea of having the sentence first!”

The frontispiece to the 1866 edition by D. Appleton and Co. of Alice’s Adventures in Wonderland is a depiction of the trial, by the English illustrator and cartoonist John Tenniel (1820-1914):

 

The earliest instance that I have found of the phrase sentence first (and) verdict afterwards is from The Pall mall Gazette (London, England) of Friday 5^th February 1869:

YESTERDAY’S EXPERIMENTS AT SHOEBURYNESS.

The experiments which took place yesterday at Shoeburyness in the presence of the Secretary of State for War and of the Commander-in-Chief contrasted favourably in more ways than one with several of their predecessors. The contrast appears especially marked when one recalls those hot days of last summer, days inflamed by the fire of controversy which blazed about them, as well as by the more material heat of a glaring sun. For, in the first place, the number of visitors was not too great, which, on a “show day” at Shoeburyness, is a point of some importance. There are few persons so keenly interested in the science of attack and defence as to be altogether insensible to the cravings for luncheon after a long morning at the targets; and days have been known at Shoeburyness when these cravings were not easily to be appeased. But, whatever your feelings about luncheon, it is reasonable to assume, if you have travelled down to Shoeburyness to see a target fired at, that you will be desirous of personally examining the effects of the shot. This, again, is a matter not always to be accomplished without much jostling and a considerable exercise of personal exertion. Then, there is always the chance that by a sweep of the magic wand which rules the War Office the whole programme of experiments may be overturned and a new system of experimental investigation precipitately established on no scientific basis whatever. That, too, was a noticeable objection of the experiments last summer. “Sentence first and verdict afterwards” is a condition of things not very far from representing the method which prevailed at the first crowded day of the Plymouth fort experiments last June, when all the results of the prolonged deliberations of various scientific bodies were rudely upset. Yesterday all this was changed. There was no crowd; there was enough luncheon for everybody; there was every opportunity of manning the targets; there was no change in the programme worth naming. But this is not all. There was for once a remarkable and most agreeable absence of that bitterness and personal feeling, of those eager, often disappointed, and angry faces, which have made Shoeburyness at times anything but a peaceful arena of scientific contest, A more philosophical temper prevailed; and the philosophers were rewarded this time with a thoroughly decisive result.

The second-earliest occurrence of the phrase that I have found is from a letter about the new rowing boats designed by Jack Clasper, of Oxford, published in The Morning Advertiser (London, England) of Monday 29^th January 1872:

The London Rowing Club has, without distressing its crews, and rowing a slower stroke than its opponents, approved of the boats; yet at Oxford they are regarded with suspicion, and thrust aside as an unnatural product of the Tyne which the Isis refuses to acknowledge. The maxim “experto crede”* is despised, and the judicial process in “Alice in Wonderland” of sentence first and verdict afterwards is universally adopted.

[* The Latin phrase experto crede means believe one who has had experience. It is from experto credite, used by Roman poet Virgil (Publius Vergilius Maro – 70–19 BC) in the Aeneid (Book XI, line 283) – crede is the second person singular, credite the second person plural, of the imperative of the verb crēdĕre, to believe, to trust.]

Another early instance of the phrase occurs in a letter published in The Derby Mercury (Derby, Derbyshire, England) of Wednesday 9^th January 1878:

SCHOOL BOARD EXTRAVAGANCE.
TO THE EDITOR OF THE DERBY MERCURY.

Sir—Six thousand yards of land will suffice for the erection of schools for more than 3,000 children. Yet the Derby School Board considers this a reasonable provision for a third of the wants of Litchurch and the adjacent districts. 3,000 children cannot be raised from a less population than 13,000. 3,000 children at one set of schools means an intolerable nuisance to the neighbourhood. The cost of such a block of buildings would involve a first outlay of [illegible sum].
It will no doubt be replied that the Board does not contemplate the erection of schools for so large a number of children, in which case ratepayers will feel that the Board has acted most rashly in purchasing so large a plot of land in one place. “Sentence first, and verdict afterwards” is hardly a safe way of doing business.
Ratepayers have no objection to pay for educational necessaries, but extravagant outlay does not suit people who have to look at both sides of a sixpence before spending it.
Are the other blocks of schools to be equally immense?
Yours obediently,
Derby, Jan. 7^th 1878.                                                                             Alfred Whymper.

Published in the Daily Herald (London, England) of Wednesday 30^th March 1927, the following drawing, titled Alice in Bumbleland, illustrated an article about a debate in the House of Commons on the elected Guardians of Chester-le-Street, a town in County Durham, England. The Conservative Minister of Health, Neville Chamberlain (1869-1940), who accused those Guardians of having given illegal relief to striking mineworkers during a coal dispute, had just replaced them with appointed Guardians. (Boards of Guardians administered assistance to the poor, and were often—as in Chester-le-Street—controlled by the Labour Party.) During the debate, the Labour Party denounced the fact that the elected Guardians of Chester-le-Street were denied the opportunity of rebutting that accusation before an impartial tribunal. A parody of the illustration by John Tenniel, this drawing depicts Neville Chamberlain as the Queen of Hearts, “Neville’s Commissioner” as the King of Hearts, Chester-le-Street as the Knave of Hearts, a “Tory die-hard” as the Hatter, and the Labour Party as Alice; Bumbleland denotes petty bureaucracy, with reference to Mr. Bumble, a beadle characterised by his officious and self-important attitude in Oliver Twist; or, the Parish Boy’s Progress (1837-38), by the English novelist Charles Dickens (1812-70):

ALICE IN BUMBLELAND

“Now,” said the King, “I will read my verdict.”
“No, no!” cried the Queen; “sentence first, verdict afterwards.”
“Hear, hear!” interrupted the Mad Hatter; “that’s the stuff to give ’em.”
“Well,” said Alice, “this certainly gets curiouser and curiouser.”