A two person agreement protocol

The problem is this: You have two people, many options. Each of them have preferences amongst those options. How do you decide which is the best one?

I mean sure you could talk to each other. But that’s way too straight forward. Also it introduces some weird biases (e.g. the person who is better at persuasion is more likely to get their way). Wouldn’t it be nice if there was a simple system which let you come to a mutually acceptable agreement?

One option for this is yootling, but it would be nice if we could do this with democracy instead of economics. But how do you democracy with only two people?

I should say, I didn’t come up with this idea. It was a question posed to me by James Aylett while we were on /dev/fort, and he also suggested the solution. The idea stuck with me, I decided to think through the implications, and I realised that this was actually a very nice way of doing things.

The solution is to apply a standard voting system called Majority Judgement, which turns out to reduce to a pleasantly simple form in the two person case. It works as follows:

  1. For each of the options, each person writes down a grade. In classic majority judgement there are six grades (Reject, Poor, Acceptable, Good, Very Good, Excellent). Personally I like to drop the “Very good” option down to 5 grades. It doesn’t matter excessively though. You can even cut it down to three if you like (Bad, OK, Good).
  2. Score each option with the smallest grade either of you assigned. So if I rated something good and you rated it bad, it’s bad. Drop everything that has a strictly worse score than some other option (so if we have two options which got scored as good, drop everything that didn’t score good).
  3. If we only have one option left, that one wins. We’ve picked the most mutually acceptable option.
  4. If we have more than one option left, repeat the same thing amongst the remaining options only this time use the highest score either of assigned.
  5. If we still have more than one option, there’s nothing to choose amongst them. Either fall back to that talking thing or pick at random.

I think this sounds more complicated than it really is. Lets do a worked example. We want to go for a drink. Our options are:

  • Land o’ beer
  • Gin gin gin
  • Ye Olde Hipster
  • Whisky for you

We each score these:

Watering hole Me You
Land o’ Beer Reject Excellent
Gin Gin Gin Excellent Bad
Ye Olde Hipster Acceptable Good
Whisky For You Excellent Acceptable

This gives us the following scores:

Watering hole Round 1 Round 2
Land o’ Beer Reject Excellent
Gin Gin Gin Bad Excellent
Ye Olde Hipster Acceptable Good
Whisky For You Acceptable Excellent

So in the first round Land o’ beer drops out (because I hate it) and Gin gin gin drops out (because you hate it). This leaves “Ye Olde hipster” and “Whisky for you” remaining because we both find it at least acceptable. In the second round, we are choosing only between these two options. I rated Whisky For You excellent, whileas you consider Ye Olde Hipster merely Good, so we go for Whisky For You. Yay, Whisky.

I’ve not actually tried this in practice, but I suspect it might work quite well. And this of course generalises naturally to more people given that it’s actually a voting system designed for more people (one caveat: When generalising to > 2 people you don’t take the smallest score: You take the middlemost, rounding to the left. So e.g. if there were three of us and we rated something as Bad, Good and Excellent respectively, the rounds would go Good, Bad, Excellent)

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