Mitchell Porter: There is a nonzero probability of death per unit time, and so the probability of literal immortality is infinitesimal, being a product of infinitely many quantities less than 1.

This is mathematically incorrect. If the quantities tend to 1 fast enough, their product will converge to a positive number. For example, if you have a 1/2 chance of living another 50 years, then if you do, a 3/4 chance of another 50, then a 7/8 chance of another 50, and so on, the probability that you will never die is about 0.29.

So the trick is to always be getting better fast enough at not dying.

In terms of individual rationality, I hope I would notice my own severe confusion and then assign >50% probability to the majority vote.

Noticing your own severe confusion should lead to investigating the reasons for the disagreement, not to immediately going along with the majority. Honest Bayesians cannot agree to agree either. They must go through the process of sharing their information, not just their conclusions.