I will defend the following 4 contentions. I do not claim that they follow from natural law or mathematical proof--they are merely designed to represent actual human behavior:
- All else equal, multiple witnesses reporting one event each is more compelling than one witness reporting multiple events
- Multiple independent witnesses are more compelling than the same number of dependent witnesses
- Increasing the number of events/witnesses will eventually experience diminishing returns
- In the real world, "all else" is not equal, and one credible witness is more compelling than multiple less-credible witnesses
1. One witness or many: Whistleblowers
The OP cited whistleblowers, which are an effective example to defend contention one. It is common practice in a corporate environment for there to be a small subset of employees who are angry, loud, and dissatisfied. Corporate surveys tend to discount these voices if they are numerically overwhelmed by different perspectives.
In this case, one disgruntled employee who voices numerous concerns is going to be taken much less seriously than multiple employees voicing similar concerns.
Evidence of this can be found in examples such as:
- Organizational Health Indices, which aggregate large data sets and use averages to compare company performance with peers. In the mathematical summaries of these surveys, one very angry, long response with many examples will be weighted no differently than one very short, satisfied response. One dissatisfied voice will do little to drag down the company's score. Multiple dissatisfied voices--especially if they are dissatisfied for similar reasons--will make a bigger splash.
- Voting: most political organizations with democratic norms acknowledge that a better result is achieved if each person votes once than if some people vote more than once. So strongly do most nations believe this, that in most jurisdictions, voting more than once is a crime that comes with hefty penalties. Lots of people voting once rather than one person voting many times is an example of placing trust in multiple attestation.
As a result, lone whistleblowers often take significant blowback, even if they are reporting serious violations in good faith--this is why whistleblower protection laws exist.
2. How multiple attestation works for historians
Most events in human history are not preserved in any extant records. And most events that are preserved survive in only one source. For this reason, especially in the study of ancient history, having two sources for an event is a very high, very important standard, which historians refer to as the criterion of multiple attestation.
However, if we have two sources and source 2 is quoting source 1, this does not count as multiple attestation. We could just as well write another work today quoting source 1 and claim we now have triple attestation. Source 2 is only effective in corroborating source 1 if there's reason to believe source 2 isn't simply regurgitating what source 1 said.
The most prominent usage of the criterion of multiple attestation is seen in New Testament studies, and particularly in relation to the Synoptic Problem (disclaimer, the linked source is my own work on the Synoptic Problem). If one Gospel appears to be quoting another, this is single attestation. If two Gospels have the same event recorded independently, this is multiple attestation (what fits in which category depends very much on how one solves the Synoptic Problem).
To give one, concrete example from Roman history: Dio Cassius, Orosius, and the Acts of the Apostles all tell us that Emperor Claudius made a decree expelling the Jews from Rome (circa AD 49). Each provides distinct details that could not have been obtained from the other two. From the standpoint of a historian of ancient history, this is the gold standard (we'll call finding an inscription the "platinum standard" =)) - this is a very solid piece of history and the likelihood is much, much greater that the decree happened than that it didn't.
3. Diminishing returns: We've heard this story before
Alien abduction is a good example here. There have been so many stories of alien abductions told that many are numb to it. Hearing one more alien abduction story is very unlikely to persuade someone who has already heard 100 of them and didn't believe any of them.
Additionally, as pointed out in other answers, because so many alien abduction stories have been told, people can be influenced by each other's stories, diluting the value of an incremental alien abduction story.
An illustrative example is the JFK assassination (arguably the grand-daddy of all conspiracy theories). For those who believe the lone gunman theory, hearing yet another alleged eyewitness account that proves a conspiracy, or another complex cover-up scheme described, can be exasperating--it's not going to move the epistemological needle. Ironically, even if many of the witnesses & theorists are wrong, it does not necessarily mean all of them are wrong. In this sense, having too many witnesses can be damaging: if 10 people claim they saw a man on the grassy knoll shoot JFK, and 9 of them were mistaken...JFK was still shot by a man on the grassy knoll--but the erroneous witnesses make it the claim less credible, not more.
4. Credible Witnesses
In both the ancient history and the JFK examples, the credibility of a witness can overpower (positively or negatively) the quantity of witnesses.
If most of recorded history is preserved by a single source, do we discard most of what we think we know about history? No. We evaluate the credibility of the historian by comparison to other sources of information. If the historian gets it right when we can fact check the claim, we have a greater level of confidence that the historian is correct when we cannot fact check the claim.
In practice, one highly credible witness can provide a compelling basis to believe something even if it is opposed by numerous, less-credible witnesses. Because people tend to consider themselves to be credible witnesses, we have sayings such as "I saw it with my own eyes", where despite receiving criticism for doing so, people believe something others disbelieve, because it is consistent with their own experience (since all evidence arises from experiential evidence, this practice is not wholly irrational).
I'll offer one specific example here as well: what was the last song played by the band of the Titanic? (spoiler alert, we're not going to solve that vexed question here).
This question is interesting and relevant, because most Titanic survivors who spoke on the matter said the band played Nearer My God to Thee, and for many years this was uncritically accepted as correct. However, more recent historians have challenged this claim, largely on the basis of a single witness: Harold Bride.
Bride was the junior wireless operator on board, his profession was one which required attention to detail and a sharp memory, and he was closer to the Titanic in its final moments than most other survivors were (he survived aboard the overturned collapsible B lifeboat (ibid)).
Bride said nothing about the band playing hymns, but spoke of their playing lively tunes.
The Titanic musical debate rages on with no end in sight, but it is a useful example of my 4th contention. Many are prepared to take the word of one, particularly strong witness over and against the majority of witnesses who said something different.
Eyewitness testimony cannot be ruled out entirely, as it is the ultimate basis for all data that we have to work with. We look for aggregation and repeatability in order to establish credibility.
On a matter as subjective as judging the accuracy of an eyewitness, we should not expect to find a formula for weighing one claim against another. But in actual practice, all else equal people tend to take more seriously something they hear from multiple sources versus than something they hear repeatedly from one source, but credibility of sources can readily outweigh quantity of sources.
I submit that the most secure epistemological claims are those that come not from quantity but quality of sources.
Which sources are high quality? This requires epistemological evaluation as well...