How so you select who is saved?

Faced with an existential crisis and a chance to save some few humans: How do you select the population that will survive?
Will war (humanities historic driver of survival of the fittest) be the selection mechanism? Will the elite be automatically selected? Could we use a lottery process? Will the process be fair or directed? Will we use science to select the best candidates.
The first step on deciding who to save is to determine why you are saving them. A short answers is: You save those that can carry on the species. This means you save a healthy breeding population of humans.
It would seem unlikely that an open lottery system would work. A lottery would mean that the existential threat to the Earth needs to be revealed to the general population. The odds of being picked in a lottery would be low. Something like 500,000 in 10,000,000.000 I doubt the general population would trust a lottery or would ever believe they had a chance. A lottery would not be sufficient incentive for the general population to cooperate and devote their wealth and last opportunity to survive toward a plan to save a small group of others. People would cease to participate in civilization and anarchy would reign.
A lottery has added problems. It doesn’t take into account people of undesirable genetic qualities. It would have to exclude older people; those outside the breeding years. It would most likely exclude criminals and other social characteristics considered undesirable. Who would make these decisions and what do you tell those people considered undesirable? Further a lottery system does not guarantee that the lottery winners have the right genetics or mix or skills to settle a new world and survive. Individuals might not wish to leave loved ones behind. Many other problems with a lottery system remain.
Would you save the elite? This class of people might have the power and money and control of resources needed to mount a project to save the human species. But that does not make them the right people to save. Simply because you have money or political power does not mean you have the age, genes or skills to settle a new world. I would imagine the elite would work very hard and do anything to save themselves. If a mission to save the species is to be successful the elite would somehow need to be kept in check. I think the best way to do this is to promise the few who control both wealth and weapons a place in the survival group.
This small group of elites would then assist you to confiscate most of the wealth of the others. This would not be an easy task. Every measure including threats of militant action would be needed to bring them in line. But eventually you would have the control of the Earth’s resources you needed to build a mission to save the human race.
There is still one class of people who would need to be in complete agreement with your mission plan. The world clergy. Not every single preacher or elder needs to be involved, just the very high up. Once again you might have to promise some of these people a place in the survival group.
Oddly however some of them possess a quality not found in the general population. A quality not found even in the congregations that fill the temples, churches synagogues and mosques. They posses a true belief in a supreme being and in a heaven. These very few have the mentality to sacrifice their own life for something greater that will secure them a place in heaven. Besides, they are not being asked to die horribly or prematurely. They could live out their lives guaranteed wealth, status, and obedient flocks.
The question remains. How do you get them all to agree to a selection plan where science, not doctrine will choose those to be saved. Many religions believe in divine retribution and would easily war with other religions for the chance to be saved. Many others would be willing to see the entire species die out believing it to be the will of God.
At the end of the day I think the only solution is to unify all religions under one theology. This sounds like an impossible task. But I believe that faced with a choice of death of the human species or cooperation to save something of humanity, they would cooperate.
Once you have the cooperation and resources you need to mount a mission to save the humans species, you must select those to save. Possibly the best selection mechanism is science. Science can select the genes and skills that will give the human species the best chance for survival.
If you use science as the mechanism you would have to keep your analysis hidden from the general population or suffer the same problems as the lottery. Science has all the tools necessary to decide on the best genetic mix to continue the species. Routine medical testing of the general population could target appropriate genetic candidates or their relatives as candidates to be saved. These people could be monitored for cultural and behavior patterns and skill sets that would be needed.
The final question is. How to you extract the people picked by science from society? Unfortunately you would have to virtually shanghai them. Simply offering them an opportunity to be saved, risks them refusing and revealing the plan.
Finally your selection process would look for candidates with limited ties to others. If you intend to shanghai them its best to select people with small extended families or friends that would come looking for them.