The complaint you always hear is that men leave the toilet seat up, while women would prefer it be left down. Well, let’s crunch a few numbers to determine the total effort required by each party in the two cases. I’m going to ignore the lid in the following calculations:

With the seat up, men need to:

  1. Nothing.
  2. Lower it before, raise it after.

Women need to:

  1. Lower it before, raise it after.
  2. Lower it before, raise it after.

So the seat up yields a number of operations of 2 for men and 4 for women.

With the seat down, men need to:

  1. Raise it before, lower it after.
  2. Nothing.

Women need to:

  1. Nothing.
  2. Nothing.

So the seat down yields a number of operations of 2 for men and 0 for women.

The conclusion here is that, to men, it makes absolutely no difference whether the seat is left up or down, while women do less work with it down. The interpretation goes both ways: It could be viewed as selfish of women to want to do less work, or it could be viewed as selfish of men, as it makes no difference to them.

A second level of analysis makes the situation clearer. Considering that everyone (unless I’m strange) finds themselves in situation… uh… 1 more often than 2, if my meaning is carried, we find that men do more work with the seat down. Let’s go with a conservatively average estimate of three 1’s and a 2 each day. We find:

  • Seat up: Men have 2 operations each day, women have 8.
  • Seat down: Men have 6 operations each day, women have 0.

We now see the emergence of the complaint. Men do much less work with the seat up, Women do none with it down. As a unit, a couple does less work with the seat down. But the true conclusion here is that couples argue about this because people are greedy.

If the couple does indeed prefer the lid down, I’ll give the totals. The assumption I’ll make is that lifting both the lid and the seat together counts as one operation. A fair assumption.

  • Seat and lid up: Men have 2 operations each day, women have 8.
  • Seat down, lid up: Men have 6 operations each day, women have 0.
  • Seat and lid down: Men have 8 operations each day, women have 8.

The only conclusion we can definitively draw is that the toilet lid belongs up.

We could continue with an expected value calculation (assigning negative values to sitting on a closed lid, peeing on the seat or even the lid, or the infamous “falling in”), but we won’t. I’ll end this with a synopsis: The toilet lid should be up (at some point, even absent), and beyond that, I might say the seat should be left down for the greater good, but the argument exists for a reason.

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