Whom does the judge believe?
The judge believes the more credible witness.
Weight of witness testimony is all about credibility. "There is no law on judging credibility. Judges and jurors receive guidelines and elementary observations in the form of stock instructions but are essentially free to decide for themselves." (Judging Credibility, by John Kane)
Here is a jury instruction from CT:
Police will be testifying in this case. You must determine the
credibility of police officials in the same way and by the same
standards as you would evaluate the testimony of any other witness.
The testimony of a police official is entitled to no special or
exclusive weight merely because it comes from a police official. You
should recall (his/her) demeanor on the stand and manner of
testifying, and weigh and balance it just as carefully as you would
the testimony of any other witness. You should neither believe nor
disbelieve the testimony of a police official just because (he/she) is
a police official.
And a jury instruction about weight of testimony (page 11):
In evaluating the testimonial evidence, remember that you are not
required to believe something to be a fact simply because a witness
has stated it to be a fact and no one has contradicted what that
witness said. If, in the light of all of the evidence, you believe
that the witness is mistaken or has testified falsely or that he or
she is proposing something that is inherently impossible or unworthy
of belief, you may disregard that witness' testimony even in the
absence of any contradictory evidence....
...just because one witness testifies on one side of an issue and one
witness testifies on the other side does not necessarily mean that you
must consider the evidence evenly balanced. If you feel that one of
the witnesses was more credible than the other, for whatever reason,
you may find that the weight of the evidence lies on the side of that
In criminal cases juries do not decide consent:
...the question of the competency of the evidence... by reason of the
legality or otherwise of its seizure was a question of fact and law
for the court and not for the jury.
Steele v. United States, 267 U.S. 505, 45 S.Ct. 417, 69 L.Ed. 761 (1925)
see also Gila Valley, Globe Northern Railway Company v. John Hall, 232 U.S. 94, 34 S.Ct. 229, 58 L.Ed. 521 (1914)
Questions of the admissibility of evidence are for the determination
of the court; and this is so whether its admission depend upon matter
of law or upon matter of fact.
Judges make determinations on motions to suppress during pretrial motions (Fed. R. Crim. P. 12(b)(3)(C)) This "is designed to eliminate from the trial disputes over police conduct not immediately relevant to the question of guilt." Jones v. United States, 362 U.S. 257, 80 S.Ct. 725, 4 L.Ed.2d 697, 78 A.L.R.2d 233 (1960) overruled on other grounds by United States v. Salvucci, 448 U.S. 83, 85, 100 S.Ct. 2547, 65 L.Ed.2d 619 (1980)
There is a great old article arguing that juries should decide questions of consent based on the power of jury nullification. (A Case For Jury Determination Of Search And Seizure Law by Ronald J. Baciga) The argument goes something like this - a crime was committed in a bedroom, and during the course of the trial on the merits the jury found out that the reason the police knew about the crime was because a cop was peeping through the curtains. If the jury was so offended by the police activity they could acquit, thus nullifying the judges determination that a search was lawful. On the other hand, what usually happens is that the cop goes and gets a warrant, and all the jury hears about during the trial is the warrant because the judge decided before the trial on the merits that the chain of events leading to the warrant was lawful. (Incidentally, this is not a question of credibility but could easily be extended there.)
There is no indication of whether this question regards criminal or civil cases. Based on the order the facts are presented (cop goes first), I assumed criminal. But the facts could also apply to a civil case for deprivation of constitutional rights. In a § 1983 civil action the jury decides the issue of consent, and it's the plaintiff who must prove that the search was not voluntary or, said differently, that an asserted exception to the warrant requirement did not apply. Larez v. Holcomb, 16 F.3d 1513, 1517–18 (9th Cir.1994) The standard of proof is preponderance of the evidence. (according to the Model Civil Jury Instruction for the 9th Circuit - Washington State uses a similar instruction for fourth amendment cases) The model instruction also provides some factors for the jury to consider:
whether the consenting person was in custody;
whether officers’ guns were drawn;
whether the consenting person was told he or she had the right to
refuse a request to search;
whether the consenting person was told he or she was free to leave;
whether Miranda warnings were given;
whether the consenting person was told a search warrant could be
any other circumstances applicable to the particular case.