If a false positive results in someone staying home and getting paid, one can easily work out the economic cost of that. Then it becomes a simple economics problem - how much should the government spend on improving the test to regain a bit of productivity.
A false negative (someone going about their day despite being infectious) is just the status quo, and has served us well for centuries.
I would expect a gaming system to emerge (to force positive test results when people wanted time off without suffering any consequences). Done well, that might be the most valuable purely wasteful invention ever created.
Where I live, it's common for people to just call in and stay home for the day when they are sick. They don't need to game a device or convince a doctor. There is some trust. Maybe this could be tried elswhere?
When the money comes from the employer, there is incentive to root out and eliminate significant fraud. When the money comes from the sky/government, there is much less.
We have a nice wooden fence that was (properly) built around/over the roots of a city-owner tree. The city later removed the tree and the fence now looked dumb where it had been trimmed around the roots. A neighbor stopped by and advised me that I should call the city and have them pay to replace that section of fence. Said it shouldn’t be my responsibility to pay for it. I asked her if she thought it was her responsibility to pay for it. “Of course not; that’s ridiculous!” “Well, that’s why I’m not asking the city to pay for it...”
> I asked her if she thought it was her responsibility to pay for it. “Of course not; that’s ridiculous!” “Well, that’s why I’m not asking the city to pay for it...”
That's a really dumb argument. I can list a thousand things where I shouldn't pay (all) of it, but I should pay (1/10000) of it as part of having the city pay for it.
You're playing a cheap rhetorical trick, not winning a real debate.
The money actually comes from the employer. Employers are obliged to keep paying until the sickness is over. (The details are complicated, but this guarantee generally lasts two years from onset.) Employers have insurance against longer episodes but short-term they usually eat the cost directly. It's in the budget.
When employers suspect employees of fraud they will investigate. They can ask for a sick note but most do so only after a few days. Three days is customary. When a case is handed over to insurance, the insurance company will tend to involve its own doctors to assess the claim.
A false negative (someone going about their day despite being infectious) is just the status quo, and has served us well for centuries.