Joseph Kaifa is the high priest of the Jews and chairman of the Sanhedrin. This court has sentenced Yeshua Ha-Nozri to death, and the court order has to be ratified by Pontius Pilate. Which happens, so that four scoundrels have to be executed that day: Dysmas, Gestas, Bar-Rabban and this Yeshua. In honour of the feast of Passover which begins that day, one of them had to be released according to the law and custom. The first two "would not be talked about here". They had ventured to incite the people to rebel against Caesar. So the procurator wished to know which of the two criminals the Sanhedrin intended to set free: Bar-Rabban or Ha-Nozri. The Sanhedrin asks that Bar-Rabban be released. Pilate tries to save Ha-Nozri, but Kaifa shows his skills in manipulating negotiations. Bar-Rabban gets away with it.
The Sanhedrin was the Jewish judicial council under Roman rule. The council also functioned as supreme court. The Sanhedrin followed jewish legislation under Roiman supervision. It had no direct authority to sentence to death except in case of desecration of the temple. That's why their death penalty for Jesus of Nazareth had to be ratified by Pilate. The Sanhedrin was presided by the high priest. The historical Joseph Caiaphas was appointed to that function by Pilate's predecessor, Valerius Gratus, in the year 18.
In the Bible it's not Pilate nor the Sanhedrin deciding on whom had to be set free, but the people of Judea, inspired to this by the high priests an the elders. Matthew 27:20 - "The chief priests and the elders persuaded the crowds to ask for Barabbas but to destroy Jesus".
In the novel Bulgakov let Kaifa make the decision, and he does it in his own style. But he's careful: he makes sure not to speak in the first person as far as Yeshua's destiny is concerned, he always uses the third person. Bulgakov however doesn't blame the whole of the Jewish people, but the leaders who manipulated the people to keep their privileges. But Pilate warns Kaifa: "Know, then, that from now on, High Priest, you will have no peace! Neither you nor your people".
In the gospel he says this to the entire people: Matthew 27:23 - But he said, "Why? What evil has he done?" They only shouted the louder, "Let him be crucified!" 27:24 - When Pilate saw that he was not succeeding at all, but that a riot was breaking out instead, he took water and washed his hands in the sight of the crowd, saying, "I am innocent of this man's blood. Look to it yourselves." 27:25 - And the whole people said in reply, "His blood be upon us and upon our children."