On Tue, 13 Aug 2013 17:06:29 +0100, The Natural Philosopher put finger to
keyboard and typed:
>On 13/08/13 13:45,
ng...@aol.com wrote:
>> On Tuesday, 13 August 2013 13:42:42 UTC+1, Gropius Riftwynde wrote:
>>> I have not been on cam.misc for a very long time, and it seems to have changed mainly into a lost & found & wanted group. Am I mistaken? I hope so. There always used to be mathematicians and others around who could answer questions such as "Is it more sociable to leave a loo seat up or down?"
>> Down is definitely warmer, though to be fair you might be able to get more people on if you leave it up.
>The answer is obviously to leave it as you used it last.
>
>To change it after use implies that you have at least added one extra
>loo seats movement, and if the following person is of the same
>persuasion,two.
That doesn't answer the question as asked. The question is not "which
option minimises the number of seat movements?", it's "which option is more
sociable?". The number of seat movements made by the departing user is,
therefore, irrelevent. What matters is the likelihood that the incoming
user will need to move it.
The correct answer, therefore, is the option which is most likely to be
favoured by the next user. And that in turn depends on the number of people
likely to be using it, and the proportion of different sexes.
Taking the most simple scenario, of a single toilet in a house shared by
two people of the opposite sex, then, assuming approximately equal
bladder/bowel capacity in both, usage will generally alternate. So each
user should, therefore, leave the seat in the position most likely to be
desired by the other.
If, though, there are more people using the toilet - a student house-share,
for example, then things change. If there are two male and three female
occupants there is a 75% probability that the next user after a male user
(again, assuning approximately equal waste capacity) will be female, so the
obvious answer is that the men should leave the seat down. Following a
female user, there is an equal probability of male or female. However, men
sometimes use the seat down while women always do. So, in this case, all
the users - male and female - should leave the seat down.
If we reverse the numbers, so there are three male and two female
occupants, then things change a bit. If the user is male, then there is an
equal probability that the next user will be either male or female. Women
always use the seat down, and men use it down sometimes, so the likelihood
that the next user will need the seat down is greater than the likeihood of
needing it up. So male users, in this scenario, should leave the seat down.
But if a woman uses it, then there is a 75% probability that the next user
will be male. This is where it gets complicated, because to answer the
question we now also need to know the approximate ratio of poo to wee[1] in
the average adult male. I had to Google this (sad, but true), and
apparently the average person poos once a day and pees 7 times a day. That
means that, in this scenario, there is a 75% probability of the next user
being someone who has an 87.5% probability of wanting the seat up. That's a
65.625% probability that the next user will want the seat up. So, up it
gets left.
You can do the calculations for various different combinations, but what it
comes down to is that any user should leave the seat up if more than 57% of
the other users (disregarding the departing user) are male, and down if
fewer than 57% are male. That, of course, assumes an average poo/wee
frequency on the part of all users.
It gets more complicated, though, because time matters as well. In
particular, the averaqge person is more likely to poo fairly early in the
morning, shortly after getting up, and less likely to as the day goes on.
That creates a bias towards leaving the seat down in the morning, and up in
the evening.
So, it isn't simple at all.
[1] I'm ignoring other possible deposits, for now.
Mark
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