A remarkably complex question, actually. To judge whom of the three showed Shylock the most mercy, one needs to look at what each demands and how that will affect Shylock. Obviously, the one whose demands bear the slightest adjustment to Shylock's circumstances, should be deemed the most merciful.
Let us peruse the three separately, starting with Portia:
The law hath yet another hold on you.
It is enacted in the laws of Venice,
If it be proved against an alien
That by direct or indirect attempts
He seek the life of any citizen,
The party 'gainst the which he doth contrive
Shall seize one half his goods; the other half
Comes to the privy coffer of the state;
And the offender's life lies in the mercy
Of the duke only, 'gainst all other voice.
In which predicament, I say, thou stand'st;
For it appears, by manifest proceeding,
That indirectly and directly too
Thou hast contrived against the very life
Of the defendant; and thou hast incurr'd
The danger formerly by me rehearsed.
Down therefore and beg mercy of the duke.
It is clear from what she says that Portia has no compassion at all for Shylock. She (in the role of lawyer) had given him numerous opportunities to renege on his demand for a pound of Antonio's flesh, but he stubbornly refused and here she is exercising the prescripts of the law. She is almost brutal in her judgment and wishes to punish Shylock for his stubbornness, lack of sympathy, and the alacrity he displayed to cut a piece of Antonio's flesh when told that he would be acting within his rights.
What Portia states above is that Shylock has committed a capital crime. In wishing to cut a pound of Antonio's flesh, he was being vengeful and spiteful, for such an act would surely have caused Antonio either grievous injury or death. This was against Venetian law and thus, not only would Shylock forfeit his entire estate, which would be divided equally between the state and Antonio, but also his life. She has proven Shylock's guilt and now leaves him at the mercy of the duke, whom Shylock should plead with for his life.
Portia has only been indirectly affected by Shylock's actions. The only reason she chose to present herself at court, in disguise, was to save the life of her beloved's closest friend and confidante. She wanted to spare him the pain and suffering of having lost a dear friend. Her compassion is therefore directed towards Bassanio and Antonio. Clearly, Portia shows Shylock no mercy.
The duke now has to dispense justice and says the following:
That thou shalt see the difference of our spirits,
I pardon thee thy life before thou ask it:
For half thy wealth, it is Antonio's;
The other half comes to the general state,
Which humbleness may drive unto a fine.
He points out a clear contrast between what Shylock wanted (Antonio's life) and what he is about to do. He pardons Shylock his life and commands that he surrender half his wealth to Antonio and the other to the state, as compensation for his vindictive desire to harm Antonio. Truly, the duke has been most merciful, for if he had decided to issue a death sentence, well, Shylock would have been no more.
Antonio later beseeches the duke and the court to do the following:
... quit the fine for one half of his goods,
I am content; so he will let me have
The other half in use, to render it,
Upon his death, unto the gentleman
That lately stole his daughter:
Two things provided more, that, for this favour,
He presently become a Christian;
The other, that he do record a gift,
Here in the court, of all he dies possess'd,
Unto his son Lorenzo and his daughter.
Antonio requests that the duke cancel the fine for half of Shylock's wealth and states that he does not want the other half. He asks that he should be made trustee of that half to be kept until Shylock's demise when it would then be transferred to Lorenzo, Shylock's newly-acquired son-in-law. He furthermore makes two requests: that Shylock become a Christian and secondly, that he wills all his possessions to Lorenzo and Jessica who will then inherit such upon his death.
Antonio's request seems truly compassionate and merciful, however, there is some malice in his appeal. Asking Shylock, a deeply devout Jew, to become a Christian is quite vindictive. It is a lifelong punishment which Shylock, most probably, would not be able to bear. He would have to adopt Christian values which means that he would be unable to continue his trade - moneylending at interest. This would surely mean his end. One may ask whether Antonio, shrewd man that he is, expects that Shylock may very well take his own life for having suffered this most devastating humiliation.
If one weighs the three against each other, the duke has surely been the most merciful for his judgement has been without malice, unlike that of the other two.
