Well this is a foray into ethics, not politics.
First, the population needs to be stable.
A reduction of 10% year on year over a decade or two will result in the situation where recreational hunters lose interest, it is more and more expensive to maintain or reduce numbers and we don’t know if that would be enough to meet goals for preserving natural native plant communities. A consensus goal would be preventing colonisation of new territory by designating “exclusion zones” for affordable intensive control. So much for the low end.
An increase of 10% year on year will eventually result in large numbers, ecological damage and expanding range. Eventually there has to be a limit and it should not be by tahr eating all the food and starving, not by disease. it sounds as if we are now in a “high population” situation. While we all feel it undesirable to kill more than we can eat, this is not an absolute ethical imperative. We accept weeding vegetable gardens, swatting flies (don’t like doing it myself), poisoning mice, and trapping stoats. I’d better not go on. So, almost every person accepts that some form of population control is ethically OK.
What is the valid goal and what is the best way to do it ? The size of the population is most effectively controlled by limiting the number of breeding females. Males eat their share of food of course but don’t contribute much to pressure increasing population size. Just a few are enough. Meanwhile hunters prefer to shoot older more prestigious males ( same for deer pigs and goats). Hunters are also an resource which contributes to the consumer economy rather than a drain on tax, so are economically preferable to government culling. Commercial recovery would be similar and arguably efficient in some terrains.
Finally, it is no justification to say “If I don’t someone else will.”
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