[gwnn]

Suppose two guys share a flat.

It would be normal that whenever the garbage bin is full and one of them notices, he takes it out. This way they will do this approximately equally frequently. But this gets a little more complicated.

In my experience people have differing opinions on when a garbage bag is full. Suppose one guy considers a garbage bag full when it's at 60% of its total physical capacity and the other guy has the threshold at 80%.

Now unless the garbage accumulates at a high rate or the first guy isn't at home for a long time, it will be almost always the first guy who takes it out. So there is a tricky question here. How can this chore be divided fairly?

If you just do nothing, guy 1 will do it almost always, which sounds unfair for just 20% of difference.
If they do it strictly alternatively (for example accepting a 70% limit), guy 1 could be bothered by the sight of the 'over-full' bin - also, it seems logical for the first guy to do it more often than the second guy.

Luckily enough I have not had this problem with my roommates (or I was guy 2 lol), but I think this resembles some math problem I read about a while ago, with possible applications in useful fields.

[Winstonm]

gwnn, on Apr 25 2009, 11:50 AM, said:

Suppose two guys share a flat.

It would be normal that whenever the garbage bin is full and one of them notices, he takes it out. This way they will do this approximately equally frequently. But this gets a little more complicated.

In my experience people have differing opinions on when a garbage bag is full. Suppose one guy considers a garbage bag full when it's at 60% of its total physical capacity and the other guy has the threshold at 80%.

Now unless the garbage accumulates at a high rate or the first guy isn't at home for a long time, it will be almost always the first guy who takes it out. So there is a tricky question here. How can this chore be divided fairly?

If you just do nothing, guy 1 will do it almost always, which sounds unfair for just 20% of difference.
If they do it strictly alternatively (for example accepting a 70% limit), guy 1 could be bothered by the sight of the 'over-full' bin - also, it seems logical for the first guy to do it more often than the second guy.

Luckily enough I have not had this problem with my roommates (or I was guy 2 lol), but I think this resembles some math problem I read about a while ago, with possible applications in useful fields.

The simple answer is whenever the garbage gets half full, move.

[kenberg]

They could treat the emptying of the trash as a service that they agree to hire themselves to do. Since Fussbudget wants the service performed more frequently than Slob feels is necessary, it is reasonable for FB to pay more than SL in order to get the more frequent service. So: If SL empties the trash when it is 60% full, FB gives him a Euro. If FB empties the trash when it is 60% full, SL gives him half a Euro. Either will now happily empty the trash when it is 60% full. The trash gets emptied when it is 60% full, FB is happy with his cleanliness, SL is happy with his cash.

[hrothgar]

Get a second garbage can...

[jdonn]

How about guy 1 takes out the garbage, guy 2 sweeps the freaking floor.

[hanp]

Differentiate.

[Echognome]

If you are actually interested in equations and theory and whatnot, then there are plenty of similar situations discussed under the topic "Externalities", which can be found in economic theory.

[y66]

I think kenberg's solution is rather elegant. In my house, both those guys could make some change.

[matmat]

what if the garbage is compressable?

[mikeh]

matmat, on Apr 27 2009, 01:41 PM, said:

what if the garbage is compressable?

or edible?

[G_R__E_G]

Doesn't "full" inherently mean 100% full? I mean - when I go to the gas station and ask for them to "fill 'er up" I don't expect the attendant to fill my tank to the 3/4 mark.

If I had a roommate that felt the garbage was full when it was 60% (or 80% for that matter) full I'd quite cheerfully tell them "Great - go ahead and empty it". If they felt this was not fair I'd have to ask them who they felt was to blame - me for having the insane idea that full actually means full, or them who seems to think that full means that it is somewhere in the area of approaching full.

[jdonn]

G_R__E_G, on Apr 27 2009, 02:28 PM, said:

Doesn't "full" inherently mean 100% full? I mean - when I go to the gas station and ask for them to "fill 'er up" I don't expect the attendant to fill my tank to the 3/4 mark.

If I had a roommate that felt the garbage was full when it was 60% (or 80% for that matter) full I'd quite cheerfully tell them "Great - go ahead and empty it". If they felt this was not fair I'd have to ask them who they felt was to blame - me for having the insane idea that full actually means full, or them who seems to think that full means that it is somewhere in the area of approaching full.

Why would someone be at fault for believing a garbage can should be emptied at some particular point before it gets technically full? I think you should interpret "full" in this problem as "full to the point at which it should be emptied" not "100% full".

If you were my roommate and tried that on me I would probably dump the trash on your bed.

[gwnn]

I specified "total physical capacity" to suggest a theoretical limit, i.e. the state where no additional items can be added, however well planned the other items' position.

[G_R__E_G]

gwnn, on Apr 27 2009, 02:54 PM, said:

I specified "total physical capacity" to suggest a theoretical limit, i.e. the state where no additional items can be added, however well planned the other items' position.

Okay - if we're going to get into "well planned" positioning of stuff then nevermind - I'm just going to take out the trash. (or possbily dump it on Josh's bed if he happens to have pissed me off that day)

[Winstonm]

Is the garbage can half-empty of half-full?

[blackshoe]

George Carlin said:

The optimist says the glass is half full. The pessimist says the glass is half empty. I say the glass is too damn big!