> Even the simple act of two people wanting to go through the same door at the same time is an impossible conundrum.

Tangential, but I hit this issue very often with couple of friends during university years; two of us wanted to go through a door, and get stuck in a "you go", "no, you go", "I insist" loop. At some point I said, "you know what, let's do rock-paper-scissors, if you lose you go first". It immediately caught on with my friends, and ever since that, when attempting to go through a door at the same time, we'd just exchange looks, and immediately play a wordless round of rock-paper-scissor to resolve the conflict, while the rest of the class looked at us and asked "WTF just happened?!".

> Even the simple act of two people wanting to go through the same door at the same time is an impossible conundrum.

I believe that the optimal solution to this problem is to offer, and then if there is a counter-offer, take it. If the other person is offended then they have followed the letter of the social law but do not understand it in their hearts. In addition, it is often polite to take what is offered to you.

  La extrema urbanidad y cortesía
  agota y cansa la paciencia mía.
  Figúrate lector, y es un ejemplo,
  que entrar queremos en sala, alcoba o gabiente
  y que somos por juntos seis o siete.

  ¿No es un feroz y bárbaro tormento el
  "pase Usted primero" y "faltaría mas, caballero"?
  Y han así de pasar horas galanes y señoras[1],
  estando todos ellos convencidos 
  de lo inútiles que son tales cumplidos.

  Voy a dar aquí un mínimo consejo[1],
  y mírese quien quiera en este espejo:
  cuando te digan que pases adelantes, 
  no te hagas rogar, pasa al instante.

                      Figueroa

[1] Paraphrased, I don't remember this verse right now.

it's not just polite to accept offers. It allows the other person to feel good for the act of giving.

That's absolutely true. But I think it's worth noting just how often polite acts are specifically for making others feel good. The two things are meant to be fundamentally linked.

So you took a negative result (deadlock) and solved it in a mutually beneficial way (break deadlock + in-group reinforcement). That's awesome.

This is known as a "Canadian Standoff".

Disregarding the amusement from the game you might get, why waste time when attempting to go through a door. The rest of the class might be annoyed at waiting while you decide who goes through the door first...

When we started to do rock-paper-scissors, the process became really quick - about two seconds to notice the situation, exchange the looks, shake our fists three times and show rock/paper/scissor. Sometimes it took a bit longer if there was a tie in the first round - but never long enough for anyone else to be bothered.

Haha, that reminds me of whenever one of my friends and I used to come across a door. We'd both hold it open and say "you first, I insist" and stand there. One time, I believe it went on for a solid 20 minutes.

(Other... "unusual" behaviors include standing in the pouring rain for an entire hour till the other gives up, passing the party leadership onto each other for a solid 10 minutes until one of us starts the game queue...)

At some point I decided there's generosity in knowing how to gracefully accept a gift. From then on I didn't get caught in these kinds of paradoxes. When the offering party's sincerity is established, I shift into thankfulness and everyone wins.

Rock, paper, scissors might work too. Haven't tried that.

I think the main danger is when truth and improvement is compromised in favor of niceness. Sometimes you are wrong, and that's definitely not a comfortable position to be in. It's not going to feel good to have it pointed out. And yet it's imperative that it is communicated. Wise individuals should not attribute the discomfort to the person pointing things out, but to mistakes themselves of course.

There are cases where marking errors is done to belittle, offend, portray incompetence, etc.; however it shouldn't be too hard to avoid those perils -- it's just a matter of showing how mistakes are (mostly, and to a measure) inevitable, not disqualify the person for the mistake (i.e. recognize it's something that is not inherent and can be fixed). Avoid broadcasting mishaps (communicate one-to-one), be supportive when pointing things out, and the environment is going to be better for everyone.

Superficial niceness might be worse than sincere harshness indeed. But the best is bold sincerity and support, which ultimately creates trust and robust, enduring relations.