You account for the time hassle in one case but not the other. You need to account for it in both, with the population using the average value of time for that population.
The end result is that it is likely worth it for some people whose time is worth more than for others.
The only problem is the worth of time. Is a CEO making $200/hr missing their kid's baseball game really losing more than the $10/hr admin staff missing their kid's baseball game?
>This is like the antibiotics trade-off. We don't want the population to overuse antibiotics to avoid building resistance in the population. But if I'm sick, and there's only a 10% chance that the antibiotic is useful (and 90% chance that my illness is viral and therefore the antibiotic is useless but otherwise harmless), then it's still in my individual interest to take it.
I'm not sure this is all that related. For antibiotics, the problem is that someone else taking an antibiotic has a cost to you (in bacteria becoming more resistant). Thus, you taking it gets you a gain of 1000 at a cost of 1 but someone else taking it gets you a gain of 0 at a cost of 1. This is an example of everyone using a strategy that helps them at the cost of others, which is a strategy that does not scale well when trying to maximize the gain of the whole group. In the security example, if it is beneficial for the average person to use the 'increased security' strategy, then the strategy is a net benefit when scaled (if done so evenly across the population, which may be a faulty assumption).
In short, security scales the benefit (or cost) evenly. k gain for 1 person, kn gain for n people. k Cost for 1 person, kn cost for n people. Antibiotics does not. (k - j) gain/cost for 1 person, n(k - nj) gain/cost for n people.
Edit:
To specify, the n(k - nj) is based on a person getting k benefit at j costs from using an antibiotic, while everyone else gets only j cost. So one use of an antibiotic is 1 person get k benefit while n people get j cost, or (k - nj). This is then multiplied by those n people each taking an antibiotic.
The end result is that it is likely worth it for some people whose time is worth more than for others.
The only problem is the worth of time. Is a CEO making $200/hr missing their kid's baseball game really losing more than the $10/hr admin staff missing their kid's baseball game?
>This is like the antibiotics trade-off. We don't want the population to overuse antibiotics to avoid building resistance in the population. But if I'm sick, and there's only a 10% chance that the antibiotic is useful (and 90% chance that my illness is viral and therefore the antibiotic is useless but otherwise harmless), then it's still in my individual interest to take it.
I'm not sure this is all that related. For antibiotics, the problem is that someone else taking an antibiotic has a cost to you (in bacteria becoming more resistant). Thus, you taking it gets you a gain of 1000 at a cost of 1 but someone else taking it gets you a gain of 0 at a cost of 1. This is an example of everyone using a strategy that helps them at the cost of others, which is a strategy that does not scale well when trying to maximize the gain of the whole group. In the security example, if it is beneficial for the average person to use the 'increased security' strategy, then the strategy is a net benefit when scaled (if done so evenly across the population, which may be a faulty assumption).
In short, security scales the benefit (or cost) evenly. k gain for 1 person, kn gain for n people. k Cost for 1 person, kn cost for n people. Antibiotics does not. (k - j) gain/cost for 1 person, n(k - nj) gain/cost for n people.
Edit:
To specify, the n(k - nj) is based on a person getting k benefit at j costs from using an antibiotic, while everyone else gets only j cost. So one use of an antibiotic is 1 person get k benefit while n people get j cost, or (k - nj). This is then multiplied by those n people each taking an antibiotic.