The Thanos scenario: why it doesn't work

     If anyone out there has missed all of the Avengers' movie cycle -- in particular the "Infinity War" then I apologize for what may be a spoiler and warn you to not continue -- though this pertains only to a little bit of the movies.
     Thanos, the antagonist (villain/lunatic/self-described savior/your label here), has a mission -- to improve the lives of sapients in the galaxy by reducing overpopulation. Most people would probably agree that overpopulation can be very stressful to a society and its available resources. However, eliminating half of the human population would be, at best, a very short term solution. As seen from the following graph on human population, doubling population -- while variable -- is typically not an infinite process (though it could be):

As seen above, the human (it would likely be different for other sapients) population doubling rate has varied throughout history -- with the most rapid doubling taking place around 1987. Expected doubling time slows down to 95 years in 2088 -- about 2 2/3 times as long as in 1987.
     Population increase rate is a correlation between birth rates, death rates, and life expectancy. If as many people die within a year as are born, the growth rate is 0 (zero). If more people die than are born, there is a negative growth rate. It people never die (the goal of universal immortality is achieved) then you would need a zero birth rate to achieve stability. All of these scenarios have been examined in literature (and speculated upon in "non-fiction").  Many of the variants, as considered, have their own challenges and advantages.

Some factors which affect birth rates, death rates, and lifespan:

• Medical care -- the ability to prevent, or fix, "natural" causes of death
• Peace/war  -- how many people's lives are preserved or eliminated by direct action.
• Procreative drive -- the desire for more, or fewer, children
• Fertility -- the ability to create more, or fewer, children
• Resource access -- having enough food, environmental support, etc.
• Environmental health -- local and global contaminants and poisons
• Societal policies -- agreed upon rules that decrease, or increase, birth rates, death rates, and lifespan
• More -- ???

     Most of the above factors are self-explanatory. Of course, the above factors sometimes interact -- in surprising ways, at times. Increases in resource access tends to reduce the procreative drive (desire for more children). It appears (unproven) that environmental contaminants are decreasing fertility -- especially in the more resource accessible areas of the world. Thanos' wars, or use of the Infinity Stones, falls into the "peace/war" category while Dan Brown's "Inferno" works by doing an "end around" for medical care by creating a pandemic -- or perhaps it is a decrease in environmental health? Certainly, the conditions that foster cholera, or accelerated the bubonic plague, could be directly attributed to environmental health. The book, and movie, "Logan's Run" had all adults over 30 killed -- a definite societal policy. Categorization can be a problem -- is access to birth control a "resource access" problem or a "societal policies" problem?
     However it is categorized, we can easily see that a single event will not make a long-term result. If we look at general human history, wars and pandemics made only a very temporary dip in population. Long-term problems require long-term analysis, agreement, and planning.