Caesar seems especially prone to basing decisions upon flattery. One of the first examples in the play of this flaw is his refusal of the crown three times--he is flattered that the people want him as king, but continues to refuse the crown so that he can enjoy more begging and offers of the crown. Additionally, just as Calpurnia has almost convinced Caesar to stay home and not go the the Capitol, Decius Brutus flatters Caesar into going. He tells him that the Senate is going to offer Caesar the crown and that if he refuses to go, people will not respect him as they currently do.
Brutus, while not as susceptible to flattery, does enjoy Cassius's beseeching him to join the conspiracy and relishes the many praises of his wisdom and leadership skills that the conspirators bestow upon him during the course of the play. Cassius makes it seem as if the conspiracy cannot succeed without someone of Brutus's level being involved. He suggests that Brutus would make a better leader than Caesar. Similarly, all of the conspirators easily give in to Brutus's suggestions and nay-saying when they plot the assassination. Their attitude toward Brutus make it seem as if they think he is infallible--one of the highest forms of flattery.
In Shakespeare's Julius Caesar, in Act I, Cassius tells Brutus that when Caesar returned to Rome after defeating Pompey, he is given a crown to wear, but he refuses it. Nonetheless, Marc Antony replaces it upon his head for Caesar to refuse it again to the laudatory shouts of the crowd. Again, Antony attempts to place the laurel on Caesar's head, and again Caesar dramatically refuses it. His actions here indicate that he makes a show of his refusal and loves the adulation that accompanies his demonstration of humility. Later, in Act II when Calpurnia tells her husband of her dream and begs him to not "go forth today" to the Senate, he concedes, saying,
Marc Antony shall say I am not well,
And, for thy humor, I will stay at home. (II,ii,58-59)
However, after one of the conspirators, Decius arrives, he tells Caesar that the Senate has decided to give him a crown; however, if he decides to not go today, they may change their minds, Decius cautions Caesar. Also, Decius suggests, they they think Caesar is weak and listens to his wife's directions and is afraid. Then, he adds,
Pardon me, Caesar, for my dear dear love
To your proceeding bids me tell you this,
And reason to my love is liable. (II,ii,106-109)
Thus, Decius flatters and cajoles Caesar into attending the Senate.
That Brutus is also swayed by flattery is evidenced in the famous "seduction scene" of Act I in which Cassius convinces Brutus to join with the conspirators in the assassination plot of Caesar. For instance, when Brutus tell Cassius that he loves "the name of honor more than [he] fear[s] death (95), Cassius flatters Brutus:
I know that virtue to be in you, Brutus,
As well as I do know your outward favor.
Well, honor is the subject of my story...(I,ii,96-98)
And, when the crowd shouts for Caesar, Cassius tells Brutus that his name is as important as Caesar's, his name is just as good, and that there was a Brutus once who would have fought the devil to keep his status in Rome as easily as he would find a king:
O, you and I have heard our father say
There was a Brutus once that would have brook'd
The eternal devil to keep his state in Rome
As easily as a king (I,ii,164-167)
With this statement coming after the remark of Cassius that the fault of their destinies is not in the stars, but in themselves, the suggestion that Brutus is as worthy of leading Rome as is Caesar is apparent. When Brutus replies that he will tell Cassius later what he thinks about the assassination plan, Cassius continues his flattery:
I am glad that my weak words
Have struck but thus much show of fire from Brutus. (II,i,182-183)
In still another instance, Marc Antony flatters Brutus in Act III when he asks Brutus, who he acknowledges as a "master spirit of this age," to kill him beside Caesar:
No place will please me so, no mean of death,
As here by Caesar, and by you cut off,
The choice and master spirits of this age. (III, i, 175-178)
In fact, after Brutus tells him that he will provide the reason why Caesar has been assassinated, Marc Antony flatters Brutus--"I doubt not of your wisdom"--as well as all the conspirators as he asks to shake their bloody hands. He even tells the conspirators,
...you must conceit me,
Either a coward or a flatterer. (III,ii,208)
It is because of this flattery from Marc Antony that Brutus makes the fateful error of allowing Antony to give his funeral oration.