Yet another class of objections may argue for 1e8 being too large, on the basis of people being intentionally deceptive rather than being mistaken. It may go like this:
"1e8 is a ridiculously large Bayes' factor for people's testimonies. People lie all the time. Do you really think that only 1 out of 1e8 things that people say are lies? There are conspiracies, con artists, and fame seekers everywhere, at all times. What makes you think that the disciples reporting on the resurrection were not just one of these people?"
The objection here, and its answer, is much the same as before. Yes, people lie, or are otherwise unreliable, in some circumstances. These circumstances rightly require us to adjust the Bayes' factor downwards. But the comparison of such circumstances with with what the disciples actually faced will only reveal their vast differences. If you think that people are likely to lie under certain circumstances, you must then therefore think that the disciples were highly likely to be truthful about the resurrection, due to the absence of these circumstances.
So, taking lottery winners again as an example: if someone claims to have won the lottery, their claim should be given about a 1e8 Bayes' factor. But what if they then go on to say that they've left their winning ticket with a Nigerian prince, and that they would share their winnings with you if you would only give them $5000 to cover their travel expenses to retrieve the ticket? Well, now the Bayes' factor drops precipitously, down towards zero.
However, what if the supposed lottery winner instead gives lavish gifts to their friends and family, buys a new house, then hires a financial adviser to discuss the tax implications of their sudden windfall? Then the Bayes' factor would dramatically increase, towards values like 1e120.
So then, what are the circumstances under which people are likely to lie? And in contrast, what are the circumstances that the disciples faced?
Well, people often lie for material gain, as in the above example of a con artist. The disciples, however, did not accrue wealth by claiming that Jesus had risen from the dead; in fact the very nature of their claim made this outcome highly unlikely, with the emphasis on serving the poor and a general disdain for worldly gain. If money was their goal, this was certainly the wrong way to go about it.
People may also lie under social, psychological, or physical pressure, as in the cases of false confessions obtained under harsh interrogation or torture. The disciples, however, resisted such pressure, and held on to their testimony under immense opposition of all kinds. The imminent possibility of persecution is a constant theme throughout the entire New Testament. In fact, many of the early Christian leaders underwent torture and martyrdom, including all three of the named witnesses I used in my calculation (James, Peter, Paul). We know how effective such treatment can be in eliciting false confessions even from their modern victims. We must therefore consider anyone who resisted the far harsher ancient versions of these treatments to be exceptionally trustworthy.
One may argue that at least the negative social pressure from society at large may be made up for by the approval from the close-knit Christian community. But this simply does not apply. Again, among the three named witnesses I used in my calculation, only one (Peter) was originally one of Jesus's disciples. James and the rest of Jesus's family are considered to have been in a somewhat disharmonious relationship with Jesus before the resurrection, and Paul was a complete outsider - an early persecutor of the church, whose personal and social identity was very much set in opposition to Christianity. So in a majority of these cases, the social pressure would have gone the other way: they would have ample reasons to reject the resurrection. Their testimonies in spite of this, therefore, must be counted as being much more reliable than the average.
Incidentally, if you thought that I forgot to adjust my calculations for the fact that the testimonies are not independent, this is why - the three named witnesses in my argument ARE largely independent; they come from very different backgrounds and met the risen Christ under different circumstances. Especially in Paul's case, if anything you'd expect his testimony to be anti-correlated with Peter's. For the other witnesses where dependency is expected, I explicitly called it out and severely discounted the Bayes' factor values in the calculation.
Now, back to the subject of lying: people may also lie for fame - they claim to have achieved something remarkable or to be someone special. But as we have just seen, the fame that came with proclaiming the resurrection would have been exactly the wrong kind of fame; the witnesses would have been shunned both by the Roman and Jewish society at large, and in many cases by their immediate social circle. Furthermore, it is the nature of fame to be fleeting; few would continue to lie for fame, in the face of intense opposition, for decades at a time, long after the shock of the initial claim wore off, to the point of death. Indeed, if the witnesses were fame-seekers of this type they would have done quite well by recanting the resurrection at the last minute and becoming a kind of whistle-blower for this deception that Christians pulled over the world. And yet, the witnesses did no such thing; they all died as martyrs.
People also sometimes lie for a cause. If they believe that some agenda is good and important, that may cause them to be deceptive "for the greater good", to advance that agenda. But this is impossible given the theology of the early church. Jesus was the greatest good; his resurrection was the most important event in the whole world. There was nothing greater which would be worth lying about the resurrection.
In all this, the actions of the witnesses were in perfect accord with their genuine belief in the resurrection. They had no reason to lie and every reason to tell the truth. We, also, have no reason to believe they were liars and every reason to believe that they were truthful.
So, it is true that men often lie. But this is a shallow observation. Upon considering the actual, specific circumstances surrounding the resurrection testimonies, we find that they are diametrically opposed to the circumstances conducive to lying. Therefore, the observation that "men often lie" only serves to enhance the trustworthiness of the witnesses to the resurrection, by pointing out how different these witnesses are from typical liars.
We ought to have reduced the Bayes' factor for the resurrection testimonies down from 1e8 had we found the surrounding circumstances conducive to lying. But since the opposite has happened, we must therefore increase the Bayes' factor. 1e8 is a drastic underestimate of its true value.
We will continue with more possible objections next week.